Project

Stability Analysis in Elastic States of Very Slender Columns

Goal: All Dear Colleagues – Collaborators and Their Laboratories are invited to attach to this project Their old, new, and future works or messages about "Stability analysis in elastic states of very slender columns" ...

... if any RSGate Member wants to be added to the project as the Collaborator (at least a co/authorship of one work about the "Stability Analysis in Elastic States of Very Slender Columns" and following of 30 Members of the Project would be required), He needs to be a follower of a member ... , sorry ... , but in another way, the system of the project doesn't recognize Him, and He can't be added ... ,

... if any Dear Colleague–Collaborator of the Project wants to add other Colleagues, which work on the stability (at least the co/authorship of one work about the stability and following of 30 Members of the Project would be required) ... - don't hesitate to invite them ...

The main rules of our Project are as follows:
1. every Colleague–Collaborator of our Project should attach at least 1 work about "Stability Analysis in Elastic States of Very Slender Columns" or a message about it,
2. every Colleague–Collaborator of our Project should follow each other (at least 30 Members of the Project),
3. every Colleague–Collaborator of our Project should read and recommend, if only would be so possibility regarding a scientific level of researches, all works with each other,
4. every Colleague–Collaborator of our Project should comment works to each other if only would be a reason to do that - comments naturally may be critical but with respect to authors,
5. every Colleague–Collaborator of our Project should cite each other - if only would be so possibility regarding research works of each one, i.e. in every new work attached to our Project should be cited a big number, e.g. 100 works of Collaborators of our Project,
6. every Colleague–Collaborator of our Project should collaborate and write common (with the Collaborators as co-authors) papers, books, ... and other kinds of works, if only would be so possibility,
7. if any Colleague–Collaborator of our Project has a possibility to help to publish works (e.g. as a member of a scientific journal or publishing house editorial board) should give a message about it in the "goal of the project" or in "updates" in our Project,
8. if any Colleague–Collaborator knows about a conference with "Stability Analysis in Elastic States of Very Slender Columns" as a panel or topic - He should inform us in the "goal of the project" or in "updates" in our Project ...

I hope that the above rules of our Project would help us to get success in our scientific work ... , every one of us would like that His work would be noted, read, recommended, commented, discussed, and cited ... , but somebody should do that ...


All Dear Colleagues – Collaborators are invited to be added to the Stability of Structures’s Lab regarding the rules of the Lab:

https://www.researchgate.net/lab/Stability-of-Structuress-Lab-Krzysztof-Murawski

Faithfully Yours
Krzysztof Murawski

Date: 25 June 2017

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Project log

Charles Chinwuba Ike
added 2 research items
ARTICLES IN MY RESEARCH GATE PROFILE CITED BY ARTICLES PUBLISHED IN THOMSON REUTERS IMPACT FACTOR JOURNALS, SCOPUS, SCIMAGO, AND CLARIVATE ANALYTICS JOURNALS.
Fatih Karpat
added an update
Blending Engineering & Science for Societal Complex Problem Solutions
Transdisciplinary Journal of Engineering & Science (TJES) (ISSN 1949-0569) is an international peer-reviewed open-access journal published once a year online by The ATLAS Publishing. The Academy of Transdisciplinary Learning & Advanced Studies (ATLAS) is affiliated with TJES. All papers published by the ATLAS in the Transdisciplinary Journal of Engineering & Science have undergone peer review and upon acceptance are immediately and permanently free for everyone to read and download. Read More
OPEN ACCESS -- free for readers and with no article processing charges (APC) paid by authors or their institutions. The cost of the publications is subsidized by the ATLAS George Kozmetsky Endowment (GKE).
 
Charles Chinwuba Ike
added 2 research items
This paper presents the generalized integral transform method for solving the bending and elastic buckling problems of rectangular thin plates clamped along the edges /2 yb = and simply supported along the other edges (x = 0, x = a). The considered plate is homogeneous, isotropic and subjected to uniformly distributed transverse load for the case of bending. In the elastic buckling problem studied, the plate is subject to (i) biaxial (ii) uniaxial uniform compressive load. The method uses the eigenfunctions of vibrating thin beams of equivalent span and support conditions in constructing the basis functions for the plate deflection and the integral kernel function. The transform is applied to the governing domain equation, converting the problem to integral equations for both cases of bending and elastic buckling. The integral equation reduces to algebraic problems for the bending problem, and algebraic eigenvalue problem for the elastic buckling problem. The deflections are obtained as double infinite series with rapidly convergent properties. Bending moments are double series of infinite terms with rapidly convergent properties. Maximum deflections and bending moments occur at the plate centre in agreement the symmetry. Solution of the resulting eigenvalue problem gave the closed form expression for the buckling loads. Buckling loads are computed for the cases of biaxial and uniaxial uniform compression of square thin plates using one term approximations. The buckling load obtained for one term approximation of the eigenfunction gave results that are 12.23% greater than the exact solution.
Panumas Saingam
added a research item
Given the excessive demolition of structures each year, the issues related to the generated structural waste are striking. Bricks being a major constituent in the construction industry, also hold a significant proportion of the construction waste generated annually. The reuse of this brick waste in new constructions is an optimal solution considering cost-effectiveness and sustainability. However, the problems related to the substandard peak stress and ultimate strain of concrete constructed with recycled brick aggregates (CRAs) limit its use in non-structural applications. The present study intends to improve the unsatisfactory mechanical characteristics of CRAs by utilizing low-cost glass fiber chopped strand mat (FCSM) sheets. The efficacy of FCSM sheets was assessed by wrapping them around CRA specimens constructed with different concrete strengths. A remarkable increase in the peak compressive stress and the ultimate strain of the CRA specimens were observed. For low, medium, and high strength CRAs, the ultimate strain improved by up to 320%, 308%, and 294%, respectively, as compared to the respective control specimens. Several existing analytical models were utilized to predict the peak compressive stress and ultimate strain of the CRAs strengthened using FCSM sheets. None of the considered models reproduced experimental results accurately. Therefore, equations were formulated using regression predicting the peak stress and ultimate strain of the CRAs confined with FCSM sheets. The predicted values were found to correlate well with the experimental values.
Panumas Saingam
added 3 research items
Seismically retrofitting reinforced concrete (RC) building with a combination of buckling-restrained braces (BRBs) and elastic steel frames offers a practical solution that provides additional lateral stiffness and energy dissipation capacity. However, the available methods to vertically distribute the BRB sizes based on equivalent linearization do not consider the additional stiffness due to the composite behavior between the RC frame and the elastic steel frame, which may lead to an overly conservative estimate of the BRB stiffness demands. This study proposes a retrofit design method incorporating the composite behavior. Numerical models considering the detailed composite behavior are developed and calibrated against quasi-static cyclic loading tests, and a simplified evaluation method is proposed. A four-story RC school building is used as a benchmark model, and the proposed retrofit design method is validated using nonlinear response history analysis. The analysis results suggest that taking the composite behavior into account by using the proposed retrofit design method more accurately estimates the lateral stiffness of the retrofitted structure and leads to a more economic retrofit.
In recent years, seismic design and detailing requirements for buildings have considerably improved worldwide. For example, in Thailand, a new seismic design code was published in 2021, but many existing buildings do not satisfy the new code and require retrofit. The seismic retrofit is required to improve the seismic performance of the existing building. However, the response control method to control the target story drift ratio of the retrofitted RC buildings using the viscous damper is lack introduction. This study proposes a response control retrofit strategy using viscous dampers, designed using an equivalent linearization approach. A constant stiffness method is introduced to efficiently distribute the dampers along with the building height. The stiffness of the damper is equally distributed for all stories. A design example is introduced of a low-rise reinforced concrete school building in Thailand, which was damaged in the 2014 Mae Lao earthquake. Nonlinear response history analysis is used to validate the introduced method. The results indicate that the average peak story drifts ratios can be controlled within the target story drift ratio of 0.67% rad.KeywordsResponse controlSeismic retrofitLow-rise RC buildingViscous dampers
Previous earthquakes have caused extensive damage to reinforced concrete (RC) structures with insufficient lateral force resistance or energy dissipation capacity. There is a need to retrofit vulnerable existing RC buildings, particularly those not originally designed for seismic effects or designed to an outdated seismic specification. This study investigates the use of friction dampers as displacement-dependent energy dissipation devices to retrofit RC moment frame structures. First, an experimental program was conducted to characterize the dynamic behavior of friction brace dampers with several different materials, finding that a sintered metal compound provided a stable friction coefficient of 0.4. A strength-based equivalent linearization design procedure was then developed based on the required friction slip force and considering the cracked state of the existing RC structure. A four-story RC school building was then designed using the proposed retrofit design method, validated using nonlinear response history analysis and compared to a previous retrofit scheme that employed buckling-restrained braces (BRBs) and a stiffness-based equivalent linearization design method. The analysis results suggest that the proposed retrofit design method and friction brace dampers are effective in reducing the maximum story drift.
Amer Alomarah
added a research item
The present paper reports on the post-yield behaviors of an auxetic structure, honeycomb with representative re-entrant topology. Specimens were made of stainless steel and polymer, respectively. Quasi-static uniaxial tensile tests were conducted in the two principal directions, followed by simulations using the commercial code – ABAQUS 6.11-2. The deformation, tensile stress-strain curves and Poisson’s ratio were of interest. A good agreement was observed between the numerical simulations and the experimental results. Subsequently, the effect of cell wall thickness and initial cell angle was studied by means of finite element analysis. An analytical equation was also given for the yield stress of such materials under tension.
Amer Alomarah
added a research item
This paper reports a structural modification of an auxetic metamaterial with a combination of representative re-entrant and chiral topologies, namely, a re-entrant chiral auxetic (RCA). The main driving force for the structural modification was to overcome the undesirable properties of the RCA metamaterial such as anisotropic mechanical response under uniaxial compression. Additively manufactured polyamide 12 specimens via Multi Jet Fusion (MJF) were quasi-statically compressed along the two in-plane directions. The experimental results confirmed that the modified structure was less sensitive to the loading direction and the deformation was more uniform. Moreover, similar energy absorptions were obtained when the modified metamaterial was crushed along the two in-plane directions. The energy absorptions were improved from 390 to 950 kJ/m³ and from 500 to 1000 kJ/m³ compared with the RCA when they were crushed along the X and Y directions, respectively. The absorbed energy per unit mass (SEA) also improved from 1.4 to 2.9 J/g and from 1.78 to 3.1 J/g compared with that of the RCA under the axial compression along the X and Y directions. Furthermore, parametric studies were performed and the effects of geometric parameters of the modified metamaterial were numerically investigated. Tuneable auxetic feature was obtained. The energy absorption and Poisson’s ratio of the modified metamaterial offer it a good alternative for a wide range of potential applications in the areas such as aerospace, automotive, and human protective equipment.
Amer Alomarah
added 3 research items
A new auxetic structure, re-entrant chiral auxetic (RCA) structure, is proposed for the first time in this paper. The RCA structure combines the topological features of hexagonal re-entrant and anti-tetrachiral honeycombs. Additive manufacturing technique, stereolithography (SLA), and traditional waterjet machining (WJM) were employed to fabricate six samples made from photopolymer (VisiJet SL Flex) and aluminum alloy (6061), respectively. Quasi-static uniaxial tensile tests were conducted in the X and Y directions, respectively. Numerical models were developed using ANSYS/LS-DYNA and verified by experimental data. Deformation modes, stress–strain curves, and Poisson’s ratios were considered to examine the effects of loading directions and material types. A comparative study was conducted experimentally and numerically between the well known hexagonal reentrant honeycomb, and this newly developed RCA structure. The proposed RCA structure presented here was found to display lower density compared with re-entrant honeycomb. Moreover, it shows higher tensile properties and auxetic effect compared with re-entrant honeycomb when loaded in the X direction. The validated FEA models were employed to investigate the effect of friction on the deformation pattern and mechanical properties of the RCA structure when it is loaded in both directions.
The compressive properties of a novel 3D tetrachiral auxetic structure have been investigated in this study. The 3D unit cell has been developed with solid cubes and struts. Two types of this structure with different struts lengths have been proposed. A 3D printing process, Multi Jet Fusion (MJF) has been employed to print six samples from polyamide 12 (PA 12). Quasi-static compressive tests have been performed in the X, Y, and Z directions to investigate the mechanical response and auxetic feature. Finite element (FE) models have been developed using ANSYS/LS-DYNA. The experimental microscopic measurements reveal high accuracy of MJF process and consistent deposition of the material powder. The proposed structure type S2 (short struts) displays auxetic feature while the auxetic feature of type S1 (long struts) is not evident. The energy absorption capability of the proposed structure varied corresponding to the load direction. The FEA results show that the energy absorption of the proposed structure type S2 outperforms that of type S1.
Chrysanthos Maraveas
added a research item
The design and construction of tall and slender steel structures is always challenging. This paper presents design aspects (structural information, analysis methods, applied loads and cost optimisation) and a case study regarding the design and construction of 10-m-tall windbreak panels for a Greek electricity producer to reduce wind turbulence and improve the performance of its air-cooled condenser. In this case, the longitudinal direction was that of the main wind load, with friction inducing only a small amount of wind load in the transverse direction. The steel columns were constructed from 10-m-tall hot-rolled IPE 360 (S235) cross sections and were supported by cables in the longitudinal direction and bracing systems in the transverse direction. Concrete anchorages for the cables and concrete footings for the steel columns were used. System optimisation in terms of the steel weight, cable length and overall cost is discussed, and practical issues are explained regarding technical decisions. Furthermore, the construction details, construction methods and cost estimation are discussed.
Charles Chinwuba Ike
added 5 research items
This work presents the Galerkin-Vlasov method for solving the elastic buckling problem of Kirchhoff plate (length a and width b) under uniaxial uniform compressive load applied at the two opposite simply supported edges (x = 0 and x = a) with the edge y = 0 simply supported and the edge y = b free. Mathematically, the problem is a boundary value problem (BVP) represented by a partial differential equation (PDE) over the domain subject to boundary conditions at the plate edges. Upon suitable selection of basis functions the Galerkin-Vlasov method converts the domain equation to an integral equation, and ultimately to ordinary differential equations (ODE). The ODE is solved, and boundary conditions along y = 0, and y = b for the considered problem used to generate system of homogeneous equations in terms of the integration constants. The characteristic buckling equation is found as a transcendental equation from the condition for nontrivial solutions of the system of homogeneous equations. The roots of the transcendental equation obtained by computational software and iterative techniques are used to obtain the elastic buckling loads for the first two buckling modes, for various aspect ratios (a/b) and for Poisson ratio of  = 0.25. It is found that the critical elastic buckling load occurs at the first buckling mode, and the values of the critical elastic buckling loads computed are in close agreement with values obtained previously by Timoshenko.
Krzysztof Murawski
added a research item
In this study, a Finite Element Method (FEM) analysis is presented for the loss of stability in elastic states of very slender pinned without friction box-section thin-walled column axially compressed. From the FEM buckling linear stress analyses are determined the compressing critical forces for 36 cases, presented in tables and as the surface functions in dependence on the slenderness ratio and cross-section. Also are presented graphs obtained from the FEM post-buckling linear stress analysis for the elastic central line, slope, deflection and states of the stresses and strains of the box-section column 202812500 mm made of steel, by the assumption that a maximal deflection equals the half of a side dimension. The obtained from the FEM computing function and surface graphs are compared and then discussed with graphs corresponding to Euler's and Technical Stability Theory (TSTh) results. Finally are compared graphs of the stresses and strains of box-section thin-walled column 202812500 obtained from FEM and TSTh, but under compressing critical force determined according to TSTh.
Amer Alomarah
added a research item
Auxetic structural materials show distinctive properties by exhibiting a negative Poisson's ratio (NPR). When these structures are subjected to uniaxial loading, they expand in tension and contract in compression in both loading and lateral directions. In this paper, two AlSi12 re-entrant honeycomb samples were manufactured using direct metal printing (DMP). Quasi-static uniaxial tension was executed in both X and Y direction. A Digital VIC-2D Image Correlation System was used to record the deformation history. Force and displacement were measured by ZWICK machine. The results show that loading direction has a significant effect on the mechanical properties and auxeticity of the tested structure. Re-entrant honeycomb under X-loading withstand lower force and has smaller magnitude of Poisson's ratio compared with that under Y-loading.
Amer Alomarah
added 2 research items
A re-entrant chiral auxetic (RCA) structure is a new structure, which comprises three topologies: re-entrant, trichiral and anti-trichiral. The aim of this study is to numerically investigate the influences of geometrical parameters of a RCA unit cell on the in-plane tensile properties. Finite element (FE) models were developed using commercial software, ABAQUS 6.11–2, and verified by experimental results. Based on the verified FE models, a parametric study was performed to examine the effects of geometrical parameters on the stress–strain curve and Poisson’s ratio of a RCA structure. In order to reduce the variables studied, three dimensionless groups of geometrical parameters were proposed. Results showed that the RCA structure predominantly deformed by bending and stretching of walls as well as rotation of cylinders. The RCA structure displayed high stress, low strain and large negative Poisson’s ratio when it was loaded in the X direction. On the other hand, the RCA structure exhibited low stress, high strain and a transition from negative to positive Poisson’s ratio when it was loaded in the Y direction. The geometrical parameters of the RCA structure had significant effects on its stress–strain curves and Poisson’s ratios. The findings of this study provide an insight into the mechanical response of the RCA structure under uniaixal tensile loading.
A new auxetic structure, re-entrant chiral auxetic (RCA) structure, is proposed for the first time in this paper. The RCA structure combines the topological features of hexagonal re-entrant and anti-tetrachiral honeycombs. Additive manufacturing technique, stereolithography (SLA), and traditional waterjet machining (WJM) were employed to fabricate six samples made from photopolymer (VisiJet SL Flex) and aluminum alloy (6061), respectively. Quasi-static uniaxial tensile tests were conducted in the X and Y directions, respectively. Numerical models were developed using ANSYS/LS-DYNA and verified by experimental data. Deformation modes, stress–strain curves, and Poisson’s ratios were considered to examine the effects of loading directions and material types. A comparative study was conducted experimentally and numerically between the well-known hexagonal re-entrant honeycomb, and this newly developed RCA structure. The proposed RCA structure presented here was found to display lower density compared with re-entrant honeycomb. Moreover, it shows higher tensile properties and auxetic effect compared with re-entrant honeycomb when loaded in the X direction. The validated FEA models were employed to investigate the effect of friction on the deformation pattern and mechanical properties of the RCA structure when it is loaded in both directions.
Amer Alomarah
added a research item
Auxetic structures exhibit negative Poisson's ratio (NPR) and offer valuable enhancement of mechanical properties. This study presents a combined experimental and numerical investigation of the out-of-plane and in-plane performances of a recently proposed auxetic structure, re-entrant chiral auxetic (RCA), under quasi-static uniaxial compression. The popular hexagonal honeycomb and re-entrant honeycomb were also studied as benchmarks for comparison. Specimens were fabricated by fused deposition modelling (FDM) process. It was found that printing quality depends on the size and complexity of the printed structures. Deformation mode, stress-strain curves and energy absorption of the three types of structure were studied and compared. Specific energy absorption per unit volume, Wv, and per unit mass, SEA, were calculated up to the strain at the onset of densification. Results show that the out-of-plane energy absorption of the proposed structure outperformed that of the other two benchmarks. In contrast, when comparing the energy-absorbing efficiency, the hexagonal honeycomb revealed the highest energy absorption efficiency of 65%, compared with 44% and 52% for the re-entrant and the proposed RCA structure, respectively. For the in-plane compression, the proposed structure exhibited a negative Poisson's ratio and demonstrated anisotropic mechanical performance.
Krzysztof Murawski
added 53 research items
The behaviour of columns under fire conditions depends on three main features: the elongation of the column, which provokes an increase of the axial compression loads to which the column is submitted if it has restrained thermal elongation, the variation of the mechanical properties of steel due to heating and the end restraints stiffness coefficients, especially along the axial direction. These properties are taken into account in the modelling of a column under fire, and the analysis is based on a total potential energy formulation. Only Euler-Bernoulli columns are analysed and their kinematic description is performed in the context of the Generalized Beam Theory. The stability procedures are applied and an explicit formula for the buckling temperature is derived. The post-buckling behaviour is also analysed, and the paper ends with a set of conclusions.
Design of the slender members requires calculation of buckling loads in addition to stress and deflection demand/capacity ratios. The Rayleigh–Ritz Method, which allows one to present approximate closed-form solutions for certain cases, is one of the simplest methods for this purpose. This study evaluates the buckling analysis of the I-section prismatic beam–columns with the Rayleigh–Ritz Method in detail. First, algebraic, trigonometric, and exponential trial functions for various restraint configurations are derived carefully in finite series form. Then, an iterative procedure to calculate buckling loads and modes is described. Finally, a software is developed with Mathematica and the sensitivity of the results and performance to trial function type and the number of terms is investigated over 1000 computer-generated numerical examples, which include doubly and singly symmetric sections, simply supported and cantilever members, intermediate torsional and lateral restraints, transversal concentrated and distributed loads acting above/below the shear center, and axial loads.
Amer Alomarah
added 3 research items
In this study, the in-plane mechanical properties of auxetic structures subjected to dynamic compression have been investigated experimentally and numerically. The studied auxetic structures, which have negative Poisson’s ratios, include a recently developed auxetic structure named re-entrant chiral auxetic (RCA) structure, re-entrant honeycomb, tetrachiral honeycomb and anti-tetrachiral honeycomb. All structures studied were fabricated from polyamide12 (PA12) power using Multi Jet Fusion (MJF). Compressive tests were conducted at a constant crushing velocity of 5 m/s on an Instron VHS 8800 high speed testing machine. The experimental results showed that the RCA structure crushed in the Y direction offered better energy absorption capacity than the other three types of honeycombs. It was also found that loading direction had a significant influence on deformation modes and auxetic features of the RCA structure, while it had a moderate influence on the energy absorption capacity. Numerical models were developed using ABAQUS/Explicit and verified by experimental results. Parametric study was conducted to investigate the effects of crushing velocity and geometrical parameters on the dynamic performance of the RCA structure.
In this study, the in-plane mechanical properties of auxetic structures subjected to dynamic compression have been investigated experimentally and numerically. The studied auxetic structures, which have negative Poisson’s ratios, include a recently developed auxetic structure named re-entrant chiral auxetic (RCA) structure, re-entrant honeycomb, tetrachiral honeycomb and anti-tetrachiral honeycomb. All structures studied were fabricated from polyamide12 (PA12) power using Multi Jet Fusion (MJF). Compressive tests were conducted at a constant crushing velocity of 5 m/s on an Instron VHS 8800 high speed testing machine. The experimental results showed that the RCA structure crushed in the Y direction offered better energy absorption capacity than the other three types of honeycombs. It was also found that loading direction had a significant influence on deformation modes and auxetic features of the RCA structure, while it had a moderate influence on the energy absorption capacity. Numerical models were developed using ABAQUS/Explicit and verified by experimental results. Parametric study was conducted to investigate the effects of crushing velocity and geometrical parameters on the dynamic performance of the RCA structure.
Metamaterials that exhibit negative Poisson’s ratio (NPR) are known as auxetics. They laterally expand or contract when they are axially tensioned or compressed. A re–entrant chiral auxetic structure (RCA) is a recently developed structure, which combines the topological features of re–entrant and chiral honeycombs. Comparative study between the RCA structure and popular benchmarks subjected to uniaxial compression has been conducted experimentally and numerically. Specimens have been fabricated from polyamide12 (PA12) using Multi Jet Fusion (MJF). Numerical models have been developed using ABAQUS/Explicit and verified by the experiments. The experimental measurements manifest the high accuracy of the MJF process to produce robust components with precise details. It has been found that the RCA structure outperforms the other types of honeycombs in terms of strength and specific energy absorption when loaded in the Y direction, while only the tetrachiral honeycomb surpasses the RCA structure in terms of specific energy absorption when loaded in the X direction. The auxeticity (NPR) of the RCA structure compressed in the Y direction was larger than that of the other honeycombs. Numerical models have been employed to study the effects of friction and the number of cells on the mechanical response of the RCA structure.
Krzysztof Murawski
added 3 research items
EXPERIMENTAL DESIGNATION OF TANGENTIAL MODULUS FOR COMPRESSED SANDWICH TUBES Test results of the critical compressive stresses for hollow and sandwich tubes have been presented in the paper. Basing on the test results the tangent modulus in dependence on the slenderness ratio has been calculated. The obtained results have been compared to the tangent modulus according to the Engesser-Shanley’s theory. Calculations according to Engesser and Shanley give less critical compressive stress to 15 %.
The Engesser-Shanlay modified theory for thin-walled axially crushed cylindrical columns for the case when columns are made of plywood (patent application P.353556) is presented in the paper. The problems of critical loads in elastic-plastic states is considered. The squeeze ratio of critical transverse section is defined by an α-angle, which to slenderness ratio is related. The obtained theoretical curves σ H (λ) and σ cr (λ) for thin-walled plywood cylindrical shaped elements made of birch are presented with similar curves for steel R35 (standards PN-73/H-74240, PN-75/H-840I9) and aluminium alloy PA4N-tb (standards PN-85/H-74592, PN-79/H-88026).
Murawski (2011) presented the theory of the technical loss of stability of rods which was developed on the basis of experimental results. The study considered cases of slender rods axially compressed by force with ball-and-socket joints without friction or compressed by force at the free end of the rod, while the second end of the rod was fixed. The elastic-plastic and elastic states of rods were taken under consideration. According to this theory, the loss of stability of the slender rod in the elastic states occurred after the neutral layer left the critical cross-section of the rod, which developed in the result of the superimposition of bending and pure compression. The loss of stability of the slender rod in the elastic-plastic states took place when the neutral layer entered the plastic zone of the critical cross-section of the rod. As the simplification was assumed that the carrying capabilities were lost when a line of forces exited a transverse cross-section. The theory allowed determining the courses of the functions of elastic stresses and critical stresses of rods in elastic and elastic-plastic states. For cases in elastic states, the theory allowed determining the differential equation of the elastic line of the rod axis, its slope, the equation of the elastic line of the rod axis, the dependence of the deflection of the rod axis on the force - as the stability analysis as well the critical stress of rods as the surface function depending on the slenderness ratio and the cross-section area. The critical stress formulas of rods in elastic states, according to the author’s theory were different for rods with different transverse cross-sections – unlike Euler’s theory. The graphs of the stability analysis and the critical stress were presented in the thesis as the theoretical examples. The values of the critical stress: nine of cylindrical and nine of square shells, were compared with the results received from the Euler’s formula and from FEM. The author’s theory in relation to the elastic states also allowed determining the shell stresses and strains of rods losing their stability. The graphs of the values of shell stresses and strains as theoretical examples were also presented in the work. Two of the theoretical examples of the stability, stress and strain analysis: one for cylindrical and one for square shells, were compared with the results obtained from the simulation with the FEM with a model made of plate elements. The results showed the convergence to the author’s theory. Moreover, in the range of the critical stresses, they were compared with the results obtained from the simulation with the FEM with a model made of beam elements. The results showed here the convergence to Euler’s theory. The values of the critical stress according to the author’s theory in relation to elastic-plastic states: nine of cylindrical and nine of square shells, were compared with the results received from the Ylinen’s and Březina’s formulas and from FEM. The results of the comparison were also presented in the work. Two of the theoretical examples of the stability analysis in elastic-plastic states: one for cylindrical and one for square shells, executed with the FEM were presented in the work with the state of stress analysis in a few successive steps.
L. Zhou
added a research item
This study, the coupled multi-physical cell-based smoothed finite element method (CS-FEM) was proposed to predict the temperature environment combining mechanical load effect on the dynamic characteristics of functionally grade magneto-electro-elastic (FG-MEE) thin-walled intelligent structures. Consider the coupling effects among elastic, electric, magnetic and thermal fields, and this method possesses higher accuracy, lower mesh restriction, much less computational cost and stronger handling ability when encountering strong mesh distortion and large deformation issues compared with standard FEM. The accuracy, convergence and efficiency of CS-FEM were validated via three numerical examples. Proposed CS-FEM integrating the modified Newmark scheme explored the thermal effect on generalized displacements (x- and z-direction displacement components, electric and magnetic potential) of FG-MEE based sensors. Further, parametric studies were carried out to analyze the index factor impact on thin-walled structure performances. This study presents an effective approach to investigate the coupled multi-physical problem, and the simulation results are definitely useful for the designation of intelligence thin-walled structures in service under complex load condition.
Mustafa Al-Kamal
added 6 research items
The conventional ACI rectangular stress block is developed on the basis of normal-strength concrete column tests and it is still being used for the design of high-strength concrete members. Many research papers found in the literature indicate that the nominal strength of high-strength concrete members appears to be over-predicted by the ACI rectangular stress block. This is especially true for HSC columns. The general shape of the stress-strain curve of high-strength concrete becomes more likely as a triangle. A triangular stress block is, therefore, introduced in this paper. The proposed stress block is verified using a database which consists of 52 tested singly reinforced high-strength concrete beams having concrete strength above 55 MPa (8,000 psi). In addition, the proposed model is compared with models of various design codes and proposals of researchers found in the literature. The nominal flexural strengths computed using the proposed stress block are in a good agreement with the tested data as well as with that obtained from design codes models and proposals of researchers.
The ACI building code is allowing for higher strength reinforcement and concrete compressive strengths. The nominal strength of high-strength concrete columns is over predicted by the current ACI 318 rectangular stress block and is increasingly unconservative as higher strength materials are used. Calibration of a rectangular stress block to address this condition leads to increased computational complexity. A triangular stress block, derived from the general shape of the stress-strain curve for high-strength concrete, provides a superior solution. The nominal flexural and axial strengths of 150 high-strength concrete columns tests are calculated using the proposed stress distribution and compared with the predicted strength using various design codes and proposals of other researchers. The proposed triangular stress model provides similar level of accuracy and conservativeness and is easily incorporated into current codes.
The purpose of this paper is to develop an analysis method to solve the free vibration response for a continuous system subjected to an initial velocity profile using an initial velocity approximation based on an equivalent impulse load. It has been shown that for a single degree of freedom system, the initial velocity can be applied as an impulsive loading with a very short duration. The proposed analysis method in this paper is done for a continuous system to show that this approximation works not only for a single degree of freedom system, but for a continuous system as well. The assumed initial velocity profile is from a case of interest to the authors. The available analytical solution for a continuous system such as a simply supported beam subjected to an initial velocity is compared with the finite element solution determined from SAP 2000 using the initial velocity approximation. The SAP2000 solution using the proposed approximation showed an excellent agreement to the analytical solution. Finally, this method can be used to find the dynamic response of complex frames subjected to an initial velocity profile, where the analytical solution for such cases is difficult to find.
L. Zhou
added 5 research items
The node-based smoothed radial point interpolation method for solving the transient responses of magneto-electro-elastic structures in thermal environment is proposed. Considering the coupling relations between the elasticity, magnetism, electricity and heat, the generalized displacement (displacement, electric potential and magnetic potential) is calculated using the modified Newmark method. G space theory and the weakened weak formulation are applied to derive the equations of node-based smoothed radial point interpolation method for the magneto-electro-thermo-elastic multi-physics coupling problems. We use triangular background meshes as they could be generated more easily for structures with complex geometry. In some cases, they could even be created automatically. Detailed numerical study has shown that node-based smoothed radial point interpolation method not only successfully overcomes the overly-stiff behavior in the FEM and provides more accurate results, but also works well with distorted meshes. Therefore, the node-based smoothed radial point interpolation method could be adopted to solve the magneto-electro-thermo-elastic multi-physics coupling problems in practical engineering.
It is well-known that the standard finite element method (FEM) has the disadvantage of ‘overly-stiff’ and could not offer reliable enough solutions. We proposed a novel stabilized node-based smoothed radial point interpolation method (SNS-RPIM) to analyze the free vibration and the behavior of functionally graded magneto-electro-elastic (FGMEE) devices under mechanical and thermal load, which cured the ‘overly-soft’ and temporally instability of traditional NS-RPIM. The gradient variance items associated with the field nodes are applied to construct the system stiffness matrix. The detailed numerical study has shown the superiority of the proposed method. SNS-RPIM performs well in solving static magneto-electro-thermo-elastic (METE) multi-physics coupling field problems, which validates the accuracy, convergence of the proposed method. Moreover, SNS-RPIM is less insensitive to mesh distortion than FEM and NS-RPIM. The advantages mentioned above make SNS-RPIM very helpful for the design of the actual intelligent devices.
The distinctive advantage of magneto-electro-elastic (MEE) materials is their capability to convert energy among elastic, electric and magnetic fields. The multi-physical coupling characteristic of MEE material is affected by the hygrothermal environment. The current research on the MEE structure proprieties remains the use of deterministic finite element (FE) simulations. However, the limitations of FEM such as poor accuracy when using linear triangular/tetrahedral elements, auto-generate elements difficulty when using quadrilateral/hexahedral elements are obstacles to their researches on multi-physical characteristic of precision intelligent structures. Here we proposed the multi-physical cell-based smoothed finite element method (MCS-FEM), a superior calculation in which the strain smoothing technique is utilized. The method is well applied to explore the multi-physical coupling problems. Numerical experiments explored the accuracy, convergence and efficiency of the MCS-FEM. The hygrothermal impacts on the MEE structures were demonstrated by presenting the variation of generalized displacements (x- and z-direction displacement components, electric and magnetic potential). The influences of temperature and moisture dependent elastic stiffness coefficients, boundary condition and structural configuration on MEE structure performance were analyzed. We expect that the methods and simulation results in this paper will benefit future research in investigating the coupled multi-physical problem, and contribute to the design of intelligence structures in service.
Emad Elhout
added a research item
Period equations provided by seismic codes are generally derived by calibration with recorded period data of buildings located in high seismicity regions. These period-equations do not account for either the design level of seismicity or the permissible limit of lateral drift. Buildings designed under high level of seismicity are expected to display higher stiffness and shorter periods than buildings designed under low-to-medium seismicity levels. In addition, buildings designed with high level of permissible lateral-drift are expected to display lower stiffness and longer periods than buildings designed with low level of permissible lateral-drift. In this study, the theoretical fundamental-periods of an ensemble of regular reinforced concrete (RC) and steel moment-resisting frame (MRF) buildings having 3-, 6-, 9- and 12-stories and designed with various levels of seismicity and permissible lateral-drift are evaluated. The obtained outcome indicates the sensitivity of the MRF theoretical-periods to the design seismicity and the permissible lateral-drift. The results also indicate the need for modifying the current period equations to realistically account for the variations in the design seismicity and allowable lateral-drift of MRF buildings.
Charles Chinwuba Ike
added a research item
We present the elastic buckling problem of moderately thick and thick beams as a boundary value problem of the classical mathematical theory of elasticity. The study considered homogeneous, isotropic, linear elastic beams. Small deformation assumptions were used together with kinematic, constitutive relations and the differential equations of equilibrium to obtain the governing field equations as a fourth order non-homogeneous ordinary differential equation (ODE) when both axial, compressive and transverse loads are considered, and a fourth order homogeneous ODE when only axial compressive force is considered. Using trial function method, the homogeneous ODE is solved in general for any end support conditions to obtain a general solution for the buckled beam in terms of four unknown constants of integration. The boundary conditions corresponding to the four cases of end support conditions considered were used to obtain the characteristic buckling equations, which were expanded to obtain transcendental equations with an infinite number of roots in each case, thus yielding an infinite number of buckling loads. The least root of the transcendental equations was used to obtain the critical buckling load, which was found to depend on the ratio h/l and the Poisson's ratio, . Critical buckling loads for each end support condition was calculated and tabulated. The results show that for each end support condition, as h/l < 0.02, the critical buckling load coefficient obtained was approximately equal to the critical buckling load coefficient of Euler-Bernoulli beam. As h/l > 0.02, which is the threshold for thin beams, the critical buckling load is found to be much smaller than the critical buckling load obtained from Euler-Bernoulli theory. It is thus concluded that the shear deformable theory is necessary for a more realistic analysis of the critical load buckling capacities of moderately thick, and thick beams for safety in their design.
Mustafa Al-Kamal
added a research item
This paper deals with the elastic stability of a column bolted at its mid-height to a simply supported square plate and subjected to a concentrated load, using energy method. A uniform homogeneous column is assumed to be pinned at both ends. From symmetry considerations, half of the column is modeled by making the plate acting as a torsion spring on the column at its mid-height. The column length and cross-section, plate dimensions and thickness, and the material properties for the column and the plate catch the interest of the author. The problem is solved by using energy method and ultimately, the elastic buckling load is found. The analytical elastic buckling load is compared with a numerical solution obtained from finite element method using SAP2000. The numerical results agree with the analytical solution. The finite element model is refined to catch the actual effect of the bolted plate on the elastic buckling load. It has been found that the elastic buckling load is increased due to the increase in the rotational stiffness provided from the plate.
Krzysztof Murawski
added a project goal
All Dear Colleagues – Collaborators and Their Laboratories are invited to attach to this project Their old, new, and future works or messages about "Stability analysis in elastic states of very slender columns" ...
... if any RSGate Member wants to be added to the project as the Collaborator (at least a co/authorship of one work about the "Stability Analysis in Elastic States of Very Slender Columns" and following of 30 Members of the Project would be required), He needs to be a follower of a member ... , sorry ... , but in another way, the system of the project doesn't recognize Him, and He can't be added ... ,
... if any Dear Colleague–Collaborator of the Project wants to add other Colleagues, which work on the stability (at least the co/authorship of one work about the stability and following of 30 Members of the Project would be required) ... - don't hesitate to invite them ...
The main rules of our Project are as follows:
1. every Colleague–Collaborator of our Project should attach at least 1 work about "Stability Analysis in Elastic States of Very Slender Columns" or a message about it,
2. every Colleague–Collaborator of our Project should follow each other (at least 30 Members of the Project),
3. every Colleague–Collaborator of our Project should read and recommend, if only would be so possibility regarding a scientific level of researches, all works with each other,
4. every Colleague–Collaborator of our Project should comment works to each other if only would be a reason to do that - comments naturally may be critical but with respect to authors,
5. every Colleague–Collaborator of our Project should cite each other - if only would be so possibility regarding research works of each one, i.e. in every new work attached to our Project should be cited a big number, e.g. 100 works of Collaborators of our Project,
6. every Colleague–Collaborator of our Project should collaborate and write common (with the Collaborators as co-authors) papers, books, ... and other kinds of works, if only would be so possibility,
7. if any Colleague–Collaborator of our Project has a possibility to help to publish works (e.g. as a member of a scientific journal or publishing house editorial board) should give a message about it in the "goal of the project" or in "updates" in our Project,
8. if any Colleague–Collaborator knows about a conference with "Stability Analysis in Elastic States of Very Slender Columns" as a panel or topic - He should inform us in the "goal of the project" or in "updates" in our Project ...
I hope that the above rules of our Project would help us to get success in our scientific work ... , every one of us would like that His work would be noted, read, recommended, commented, discussed, and cited ... , but somebody should do that ...
All Dear Colleagues – Collaborators are invited to be added to the Stability of Structures’s Lab regarding the rules of the Lab:
Faithfully Yours
Krzysztof Murawski
 
Charles Chinwuba Ike
added 2 research items
In this paper, quintic polynomial shape functions have used in a displacement finite element formulation to solve the elastic buckling problem of Euler-Bernoulli beam resting on Winkler foundation. A three node six displacement degree of freedom element was used. A weak formulation of the governing ordinary differential equation (ODE) converted the problem to an integral equation, which was solved to express the problem as an eigenvalue problem. Thus, the ODE was expressed in terms of the elastic, geometric and Winkler foundation matrices. Quintic polynomial shape functions were used to obtain the elastic stiffness, geometric stiffness and Winkler foundation stiffness matrices. A one element finite element solution of the problem was obtained for the case of Euler-Bernoulli beam clamped at the two ends. The reduced structure stiffness matrix was used to express the problem as an algebraic eigenvalue problem using the condition for nontrivial solutions. It was found that the critical elastic buckling load obtained using one finite element was 6.387% - 7.077% greater than the exact solution for the values of the Winkler parameter 2(0 < 2 <100) illustrating the accuracy of the method adopted in this study. Keywords: Quintic polynomial shape functions, critical elastic buckling load, Euler-Bernoulli beam on Winkler foundation, finite element method, algebraic eigenvalue problem.
Alexandre de Macêdo Wahrhaftig
added a research item
The ultimate limit state of stability by equilibrium bifurcation, the limit states for stress and strain resulting from this condition were evaluated for an extremely slender real structure of reinforced concrete, with geometry varying along its length. The aspects related to nonlinearities of the material were considered through the recommendations on NBR 6118:2014, from the Brazilian Association of Technical Standards (ABNT). In the analytical solution, developed for stability analysis, all elements of the structural dynamics present in the system were taken into account, including the column self-weight. The critical buckling load was then dynamically defined to different instants of time. Reductions of 70% for the modulus of elasticity and 59% for the critical buckling force were found in analyses performed from zero and five thousand days. It was also possible to obtain the induced stresses on the homogenized cross-sections and those transferred to reinforcement steel bars.
Naresh Kakur
added 2 research items
In the present work, two parameter Weibull distribution is used to measure the variability of the tensile strength of cross ply glass/epoxy, carbon/epoxy and hybrid (glass-carbon/epoxy) composites for different strain rates from 0.0083 to 542 s⁻¹. The Weibull parameters (shape and scale parameters) are obtained using linear curve fit method. The shape and scale parameters will be useful for composite product designers to quantify the component reliability. Using HitachiSEM instrument,the failure mechanisms observedinthe tested samplesof GFRP, CFRP and hybrid composites, are discussed.
Penetration resistance is an essential design requirement for fiber reinforced polymer (FRP) composites. Furthermore, the penetration energy of FRP composites is known to be sensitive to the indenter nose shape. This gives a challenge for understanding the composite failure mechanisms, as the target plate deformation and energy absorption capacity vary significantly from one indenter to another. The present work is intended to explore the indenter nose shape sensitivity of quasi-static punch shear behavior of glass/epoxy and different weight percentages (0%, 2%, 4%, 6% and 8%) of nanoclay/glass/epoxy composites. A series of punch-shear experiments with different indenter geometries (conical, elliptical, flat and hemispherical) and tensile tests are performed. The results show that the indentation time and energy absorption are more when the flat indenter passes through the laminates which lead to disc mode shape failure whereas conical indenter penetrates rapidly which is attributed to the lower contact surface as compared to the other indenters. The elliptical indenter generates more friction energy and causes the bulge shape damage. The optimum clay content is experimentally studied which improves the punch resistance. It is also examined that the tensile strength and stiffness increase and the percentage of failure strain decreases with the clay effect.
Alexandre de Macêdo Wahrhaftig
added a research item
In this study, an analytical procedure is developed to determine the critical buckling load based on the Rayleigh method. It should be noted that the fundamental strategy of the Rayleigh method is the adoption of a mathematical equation to represent the vibrational movement of the system, identified as a trial function. Therefore, the result obtained by this method is conditioned to the correct choice of this equation. Different equations that respect the boundary conditions of the problem can lead to different results. For comparative purposes, four mathematical expressions as trial function were used in the present study: a trigonometric, two polynomials and a potential equation. These functions respected the boundary conditions of the problem and were valid through the whole structure domain, being the integrals obtained by the Rayleigh method solved within the limits defined in its geometry. The structure analyzed was a 46-m-high reinforced concrete pole, including its foundation, which has geometry and reinforcement arrangement varying along its length. In the solution, three important items were considered: the geometric non-linearity, due to the slenderness of the system; the material non-linearity and the creep of the concrete. The last one aspect was introduced into the analytical procedure by means of the criteria provided by Eurocode 2. In the analysis, the ground was modeled as a set of springs distributed along the foundation, being the critical buckling load dynamically defined for different instants along the time.
Krzysztof Murawski
added a research item
Murawski (2019) presented the theory of loss of stability in elastic states of a very slender rectangular shell axially compressed by force through ball-and-socket joints. According to the theory, a loss of carrying capacity of a slender rod in elastic states occurred when a line of force left a critical transverse cross-section of a column. The critical transverse cross-section moved because of the superposition of bending and pure compression. The theory allowed determining the differential equations of curved central lines and their slopes, critical stresses of columns as the surface function in dependence on slenderness ratios and cross-sectional areas. The graphs of elastic deflected central line y(x), its slope dy/dx, dependence y (L/2, P), shell stresses and strains of the rectangular column made of steel with dimensions: a = 18 mm, b = 30 mm, t = 1 mm, L = 2500 mm compressed by ball-and-socket joints with-out friction as well as the surface graphs of critical stress were presented in the paper as the theoretical examples. The obtained surface graphs of critical stresses were compared to the surface function graphs of the Euler's formula.  Murawski K., 2019. Stability, shell stress and strain technical analysis in elastic states of very slender rectangular column compressed by ball-and-socket joints without friction. DOI: 10.13140/RG.2.2.28299.64808. https://www.researchgate.net/publication/338168898_Stability_shell_stress_and_strain_technical_analysis_in_elastic_states_of_very_slender_rectangular_column_compressed_by_ball-and-socket_joints_without_friction
Charles Chinwuba Ike
added a research item
The finite Fourier sine transform method was used in this work to solve the elastic buckling problem of thin-walled beams for the case of pinned ends, and uniform moments applied at the ends. The problem is a boundary value problem given by a fourth order ordinary differential equation and Dirichlet boundary conditions at the pinned ends. The Dirichlet boundary conditions at the pinned ends make the finite Fourier sine transform method ideally suited for the solution. The transformation of the governing domain equation converted the problem to an algebraic eigenvalue problem. The condition for nontrivial solution was used to obtain the characteristic buckling equation as a fourth degree polynomial. The eigenvalues of the characteristic buckling equation were used to obtain the n buckling moments. The critical buckling moment was found to correspond to the first buckling mode. The expressions obtained for the n buckling modes and the critical buckling moment were identical to those by other researchers who used other methods of analysis.
Pedro Dias Simão
added 2 research items
The paper presents a study on the buckling behavior of slender steel columns under fire conditions, which depends on two main factors: the thermal elongation of the column, which provokes an increase of the axial compression force if the column is axially restrained, and the degradation of the steel mechanical properties due to temperature’s rise. In order to model the restraining effect of the surrounding structure, the column’s model adopts an elastic axial spring at the top section, insensitive to fire, together with a constant axial force that represents the serviceability load of the column. The column’s mechanical behavior is based on a total potential energy formulation, considering an elasto-plastic law for steel, and the member’s kinematic description is performed in means of the Generalized Beam Theory. The Rayleigh-Ritz method is used to render the problem discrete, and the bifurcational stability procedures are applied, thus respecting the true bifurcational behavior of the system. The column’s behavior under fire conditions is appropriately described by plotting the restraining force at the top cross section against the column’s temperature, for several values of the restraining spring’s stiffness coefficients and the axial serviceability load. The influence of plasticity, which is triggered immediately after the buckling state, is assessed, and the critical temperature, defined by the temperature at which the restraining force returns to zero, is computed. A set of conclusions ends the paper.
Pedro Dias Simão
added 2 research items
The buckling of columns is the classic problem in structural stability. It has been studied by many researchers over a large number of years, and it is well known that the severity of the buckling response can be greatly amplified by initial geometric imperfections in the column shape. The current paper presents and discusses the effects of imperfection shape, orientation and magnitude on the buckling behavior of columns. Analyses are conducted for elastic columns with overall initial imperfections in the form of out-of-straightness and sway displacements, as well as local imperfections that, for instance, model constructional and material defects. Traditionally, the initial imperfections are modeled with the first buckling mode with a size selected according to fabrication tolerances. This approach will not necessarily provide a lower limit to the column pre-buckling stiffness and strength. These assertions are supported by numerical results for imperfection-sensitive columns. The influence of end restraint on column strength is also studied since columns in actual frameworks are connected to other structural members such that their ends are restrained.
Alexandre de Macêdo Wahrhaftig
added a research item
This study focused on improving the design of slender structures with reinforced concrete (RC) telecommunication towers as the main application. Analytical procedure based on Rayleigh’s method to compute the first natural vibration frequency and the critical buckling load was development. All the nonlinearities present in the system were considered, in addition to the soil-structure interaction and the variation of the geometric properties along the length of the structure. The geometric nonlinearity and imperfections of the tower structure were computed as functions of the axial load using a geometric stiffness matrix. Further, the material nonlinearity was accounted for by reducing the flexural stiffness. As concrete structures exhibit viscoelasticity, creep was calculated using the Eurocode 2 model. The soil-structure interaction was modeled as a set of distributed springs. To validate the proposed method, the first frequency and critical buckling load were compared with those yielded by FEM simulations. The frequency results were in good agreement with those of the FEM simulations, indicating that the proposed method is sufficiently accurate for use in engineering design applications and easy to implement. On the other hand, the buckling load results obtained using the proposed method and FEM differed significantly, motivating further investigation.
Krzysztof Murawski
added a research item
Murawski (2018) presented the theory of the technical loss of stability of columns, which was developed on the basis of the experimental results. The study considered cases of slender columns axially compressed by force with ball-and-socket joints or compressed by force at the free end of the column with the second end fixed. According to this theory, the loss of carrying capacity occurred when the line of the external forces left the critical cross-section. The theory allowed determining the courses of the functions of the differential equation of the elastic line and the critical stress of columns as the surface function depending on the slenderness ratio and the cross-section area – unlike in the Euler’s theory. The theory allowed determining the shell stresses and strains of columns losing their stability. The author had found that historical Euler’s theory already should not be used in engineering practice. The book is accessed in the e-book shop: http://www.lulu.com/shop/krzysztof-murawski/technical-stability-of-very-slender-thin-walled-orthotropic-columns/ebook/product-23856164.html
Krzysztof Murawski
added a research item
Murawski (2017) presented the theory of the technical loss of stability of slender columns under axially continuously load like columns loaded with self-weight in the elastic states. The differential equations of elastic lines of columns were determined. The formulas of the stability analysis and the critical parameters like critical specific gravity per Young’s modulus, critical weight, critical compressive stress, critical length of columns as the function depending on parameters like dimensions, slenderness ratio, cross section area and specific gravity per Young’s modulus were determined. The study considered cases of fixed columns at the bottom end as well as pinned columns, i.e. set between one fixed and one slide ball-and-socket joints without friction. In order to compare the book also presented the theory of the loss of stability of very slender columns according to Timoshenko and Gere. The theory explained the way of losing of carrying capacity and allowed optimizing by dimensions and material the very slender columns. The book is accessed in the e-book shop: http://www.lulu.com/shop/krzysztof-murawski/a-technical-stability-of-continuously-loaded-thin-walled-slender-columns/ebook/product-23408163.html
Krzysztof Murawski
added a research item
Murawski (2011) studied according to own technical theory cases of slender rods axially compressed by force with ball-and-socket joints without friction or compressed by force at the free end of the rod, while the second end of the rod was fixed. The elastic-plastic and elastic states of rods were taken under consideration. According to the technical theory, the loss of stability of the slender rod in the elastic states occurred after the neutral layer left the critical cross-section of the rod, which developed in the result of the superimposition of bending and pure compression. The loss of stability of the slender rod in the elastic-plastic states took place when the neutral layer entered the plastic zone of the critical cross-section of the rod. The theory allowed determining the courses of the functions of elastic stresses and critical stresses of rods in elastic-plastic states. For cases in elastic states, the theory allows determining the differential equation of the elastic line of the rod axis, its slope, the equation of the elastic line of the rod axis, the dependence of the deflection of the rod axis on the force - as the stability analysis as well the critical stress of rods as the surface function depending on the slenderness ratio and the cross-section area. The critical stress formulas of rods in elastic states, according to the author’s theory were different for rods with different transverse cross-sections – unlike in Euler’s theory. The graphs of the stability analysis and the critical compressive stresses were presented in the thesis as the theoretical examples. The values of the critical stress: nine of cylindrical and nine of square shells, were compared with the results received from Euler’s formula and from FEM. The author’s theory in relation to elastic states also allowed determining the shell stresses and strains of rods losing their stability. The graphs of the values of shell stresses and strains as theoretical examples were also presented in the work. Two of the theoretical examples of the stability, stress and strain analysis: one for cylindrical and one for square shells, were compared with the results obtained from the simulation with the FEM with a model made of plate elements. The results showed the convergence to the author’s theory. Moreover, in the range of the critical stresses, they were compared with the results obtained from the simulation with the FEM with a model made of beam elements. The results showed here the convergence to the Euler’s theory. The values of the critical stress, according to the author’s theory in relation to elastic-plastic states: nine of cylindrical and nine of square shells, were compared with the results received from the Ylinen’s and Březina’s formulas and from FEM. The results of the comparison were also presented in the work. Two of the theoretical examples of the stability analysis in elastic-plastic states: one for cylindrical and one for square shells, executed with the FEM were presented in the work with the state of stress analysis in a few successive steps.
Krzysztof Murawski
added 17 research items
Murawski K., 2004. Stability analysis in elastic states of very slender rods fixed by one end with stresses and strains analysis as exemplified by cylindrical shaped plywood made of birch, Acta Scientiarum Polonorum, Silvarum Colendarum Ratio et Industria Lignaria 3 (1)/2004, ISSN 1644-0722, 85-95 Abstract: The theory of the stability of an axially compressed cylindrical shaped plywood element is presented in the paper. The differential equation of the elastic line, its slope, the critical compressive stress, as well as the shell stresses and strains of very slender plywood tube in elastic states are considered in the paper under conditions of flat transverse cross-sections planes and little slopes of the elastic line. The obtained theoretical results of the critical compressive stresses are related to the slenderness ratio and the product of the radius and wall thickness of the tube. The shell stresses and strains are presented in the theoretical example of the plywood tube.
Finite Element Method Analysis of stability in elastic states of very slender cylindrical shaped plywood compressed by balls The stability analysis of axially compressed cylindrical shaped plywood made with computer program "ALGOR" based on Finite Element Method is presented in the paper. The critical stresses of very slender plywood tubes made of birch in elastic states are considered. The received results from computer of critical stresses are compared to the results of the theories.
Finite Element Method postbuckling analysis of stresses and strains in elastic states of very slender cylindrical shaped plywood compressed by balls. The stresses and strains analysis of axially compressed cylindrical shaped plywood element with computer program "ALGOR" ® based on Finite Element Method is presented in the paper. The postbuckling stresses and strains in very slender plywood tubes in elastic states are considered. The obtained results from the computer program are compared to the results from the author's theory.