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Artificial neural networks for predicting ultimate strength of steel plates with a single circular opening under axial compression
Abstract
In the current paper, using finite element models (FEM), an extensive numerical study is performed on the behaviour of the steel plates with a circular hole in their centre subjected to compressive axial loading. For this purpose, 270 perforated steel plates were modelled and analysed using ABAQUS software. The effects of four main variables including plate length, hole diameter, plate thickness, and yield stress were discussed. Then, using the database provided by FEM, the artificial neural network (ANN) method was used to develop a predictive model to estimate the ultimate strength of steel plates with a circular hole in the centre. Finally, an ANN-based formula was proposed to predict the ultimate strength of perforated steel plates and its accuracy was compared with the formulations presented in previous studies. Based on the results, the proposed formula provided high accuracy and can be used as a reliable formula in practice.
... In recent times, the progress in computing has led to a substantial rise in the utilization of artificial intelligence (AI) across various sectors. Machine learning (ML) and soft computing (SC) techniques have found extensive application in civil engineering, tackling diverse issues such as design optimization, stochastic simulations, reliability analysis, and the performance evaluation of intricate structural systems [34][35][36][37][38][39][40][41][42]. ...
Despite the existence of numerous code requirements and heuristic equations concerning the shear capacity of slender beams reinforced with steel fiber without stirrup, engineers specializing in structural retrofitting and analysis frequently encounter difficulties in identifying a suitable equation. This paper presents a soft computing study designed to predict the shear capacity of slender steel fiber-reinforced concrete (SFRC) beams without stirrup. It introduces a novel equation based on the multivariable adaptive regression splines (MARS) method, supported by an extensive dataset comprising 488 experimental observations sourced from existing literature. Besides a series of existing equations proposed by researchers was introduced to assess the accuracy and capability of the MARS equation against other existing ones. The study rigorously compares the accuracy and capability of the proposed MARS equation with pre-existing equations, demonstrating its superiority and effectiveness in estimating the shear capacity of slender SFRC beams without stirrup, thus contributing significantly to the field of civil engineering.
... Fu and Feng [32] developed time-depended soft computing method of the gradient boosting regression tree (GBRT) in order to estimate the shear strength of the corroded reinforced concrete beams. Hosseinpour et al. [33] conducted FEM-ANN approach to predict the ultimate compression strength of steel plates with a circular hole. Recently, Kumar et al. [34] investigated the ability of four different machine learning methods of ANN, decision tree (DT), extreme gradient boosting (XGBoost), and adaptive-neuro fuzzy inference systems (ANFIS) for estimating the shear strength of corroded reinforced concrete beams. ...
The principal purpose of the present investigation is to examine the ultimate shear strength (USS) of one-side corroded plates with cracks using the nonlinear finite element method (FEM). To this accomplishment, different geometrical parameters of crack position (CP), crack length (CL), pit depth (PD), pit diameter (PDM), pit position (PP), number of pits (NoP), and angle of crack (AoC), are investigated. Then, according to the provided numerical dataset, the USS of crack-pitted plates is estimated by designed artificial neural network (ANN). The numerical results indicate the highest significance of AoC (with a relative significance percentage of 21.44%) on the USS, while PDM (with a comparative significance percentage of 8.11%) has the lowest impression on the USS to shear yield strength ratio of considered plates. Moreover, the maximum mean square error (MSE) and the minimum correlation coefficient (R) of designed ANNs obtained 0.0077, and 0.8564, respectively. Also, an equation suggested estimating the USS of crack-pitted plates according to the weight and bias of designed ANNs.
... It is more effective than Cutout and DropBlock functions in high-dimensional data processing. It does not need manual selection and can obtain data features intelligently after training (Hosseinpour et al. 2022). In addition, radial basis functions (RBF) are used in SVM and GPR learning models because RBF has fewer hidden layers and optimised local approximation calculation methods. ...
Due to the strong nonlinear interaction between the flow field and blades, the prediction of turbine energy acquisition capacity is still quite complex, the traditional methods take too long time to evaluate. In this article, the digital twin model + CFD simulation + monitor data are used for turbine energy efficiency assessment. A self-designed vertical wave flow turbine (VWFT) is taken as the research object, the prediction takes into account the coupling of the VWFT for motion and blade rotation, which is in good agreement with the monitor data at sea. The simulations show that the torque, thrust force and lateral force flow rate data can be loaded from the database into the digital model. If those data are not in the database, the interpolation method is used along with deep learning of recurrent neural network to obtain the energy harvesting parameters, all the error is no more than 10%.
... For this purpose, they developed neural networks with different number of hidden neurons, and proposed an ANN-based equation with an average error of 13.2%. Hosseinpour et al. (2022b) investigated the ultimate strength of perforated steel plates using ANN method. The results showed the high accuracy of the developed method compared to other formulations presented by researchers. ...
In recent years, the use of artificial intelligence-based methods in engineering problems has been expanded. In the current study, the method of artificial neural networks (ANN) has been employed to predict the ultimate strength of bolted shear connectors in cold-formed steel (CFS) composite beams. For this purpose, multilayer perceptron (MLP) networks with a hidden layer were used. Three parameters affecting the performance of these networks, including the training algorithm, the activation function in the hidden layer, and the number of neurons in the hidden layer, were examined and the most accurate network was selected. The input and target data for training the network were provided by conducting an extensive numerical study on the behavior of bolted shear connectors in CFS composite beams. Consequently, using ABAQUS software, finite element (FE) models validated with experimental results were first developed. Then, 216 models with different characteristics were analyzed and a reliable database was provided for the development of neural networks. Moreover, in order to prove the high accuracy of the ANN method, the stepwise regression (SR) method was also developed as one of the powerful regression-based methods, and the performances of these two methods were compared. Finally, the most important purpose of this study is to propose an accurate ANN-based formulation in order to predict the ultimate strength of bolted shear connectors in CFS composite beams. Due to the fact that so far no relationship has been proposed to predict the resistance of shear connectors in CFS composite beams, the formula presented in this paper can be helpful in the design process of this type of beams.
... The suggested model's results were compared to those produced using FEM and found to be in excellent agreement. Using FEM, Hosseinpour et al. [39] investigated the behavior of steel plates with a central circular cut-out when exposed to compressive axial force. As a consequence, an ANN-based formula for determining perforated steel plate's ultimate strength was developed, and its reliability was contrasted to that of previous research formulas. ...
Steel plates are used in the construction of various structures in civil engineering, aerospace , and shipbuilding. One of the main failure modes of plate members is buckling. Openings are provided in plates to accommodate various additional facilities and make the structure more serviceable. The present study examined the critical buckling load of rectangular steel plates with centrally placed circular openings and different support conditions. Various datasets were compiled from the literature and integrated into artificial intelligence techniques like Gene Expression Programming (GEP), Artificial Neural Network (ANN) and Evolutionary Polynomial Regression (EPR) to predict the critical buckling loads of the steel plates. The comparison of the developed models was conducted by determining various statistical parameters. The assessment revealed that the ANN model, with an R 2 of 98.6% with an average error of 10.4%, outperformed the other two models showing its superiority in terms of better precision and less error. Thus, artificial intelligence techniques can be adopted as a successful technique for the prediction of the buckling load, and it is a sustainable method that can be used to solve practical problems encountered in the field of civil engineering, especially in steel structures.
... The artificial neural networks (ANNs) method, as a powerful and high-precision technique, is able to map the input signal to the output signal by learning the relationship between input and output variables. So far, this method has been used successfully in many fields of civil engineering (Hosseinpour, Sharifi, and Sharifi 2018;Wong and Kim 2018;Sharifi et al. 2019aSharifi et al. , 2019bSharifi and Hosseinpour 2019;Sharifi and Hosainpoor 2020;Hosseinpour, Sharifi, and Sharifi 2020;Hosseinpour, Hosseinpour, and Sharifi 2022). In this paper, a three-layer feed forward-back propagation network with Levenberg-Marquardt training algorithm and three neurons in the hidden layer were adopted to evaluate the ultimate capacity of the U-shaped shear connectors in CFS composite beams. ...
Due to the low thickness of cold-formed steel (CFS) sections, welding of traditional studs on them is not recommended; and there is a need to use shear connectors suitable for this type of sections. In this paper, the behavior of U-shaped shear connectors as connectors compatible with CFS composite beams has been investigated, to offer practical relationships for predicting the ultimate strength of this type of connectors. Accordingly, after the development of finite element (FE) models with the ability to predict the ultimate strength of U-shaped connectors, their performance against experimental results was validated. Then, an extensive parametric study, consisting of 216 numerical samples, was accomplished to provide a reliable database. As the main and most important of this study, two methods of artificial neural networks and stepwise regression were developed, and practical formulations were proposed to predict the ultimate strength of U-shaped shear connectors in CFS composite beams. Finally, in addition to evaluating the accuracy of the proposed formulas, a comparison was made between them and the relationships proposed by AISI, AS/NZS and EC3 codes for CFS screw connections. The relationships presented in this paper can be used by practical engineers in the design process of CFS composite beams.
... The importance of data processing technique and its application to ships and offshore structural design is highlighted in many studies by Kim et al. (2020aKim et al. ( , 2020bKim et al. ( , 2020c2019b). In addition, deep learning, i.e., neural network techniques, application is highlighted (Hosseinpour et al., 2020(Hosseinpour et al., , 2022Wong and Kim, 2018). In this section, the procedure to propose an empirical formulation in predicting the ultimate strength of initially deflected plate subject longitudinal compression is addressed. ...
This study proposes a simplified empirical formulation to predict the ultimate strength of the initially deflected plate subjected to longitudinal compression. The empirical formulation's applicability and accuracy were verified by comparing the nonlinear finite element method (NLFEM). In total, 700 cases of initially deflected plate scenarios by assuming the buckling mode shape were adopted as the input data. For the simplification of the plate design process, a general shape of the empirical formula is proposed based on input data. A reliable technical solution is obtained with good agreements (R² = 0.98 to 0.99) compared to NLFEM. The advantage of the proposed outcome is documented by comparing the previous study. The obtained result could be beneficial for the structural design of the initially deflected plate in predicting its ultimate strength performance under longitudinal compression.
Proper design and accurate mechanical assessment of composite C‐beam after opening are of great importance in structure engineering. This paper aims to experimentally and analytically investigate the postbuckling response of large‐size C‐beam with web opening under bending‐shear coupling load. New specimen with four different open shapes were designed and tested. Strain gauges and displacement measurements were applied to monitor its buckling behavior, strain field distribution and critical failure load. Four specimens with various openings were loaded until catastrophic failure occurred. Additionally, an analytical model was introduced to predict the residual strength of circular opening. The results indicate that while the presence of an opening significantly decreases the load carrying capacity, it has minimal effect on the bending stiffness. Compared with intact specimen, the initial delamination, buckling and ultimate strength of the circular opening decreases less than those of the rectangular opening. By altering the position of the rectangular opening, improvements can be made in terms of initial delamination resistance and buckling load; however, ultimate strength remains largely unaffected. Reinforcing the edge of an opening further reduces resistance to initial delamination but other two indicators are improved. Overall, from buckling to failure stages, post‐buckling bearing capacity after opening decreases by 40%. Moreover, the shear failure mode is observed during catastrophic failures. And the analysis method employed is relatively conservative.
Highlights
Ten large size composite C beams are conducted under coupling loads.
Deformation, strain distribution and failure mode are presented.
Influence of openings on postbuckling behavior of beam is analyzed.
An analysis method is employed to predict the residual strength of beam.
It could provide valuable insights for assisting in designing beam openings.
Due to their advantageous mechanical and physical characteristics, fiber-reinforced polymer (FRP) bars have been used extensively in various structural elements in recent years. Numerous researchers examined the structural behaviour of such elements reinforced with FRP bars to forecast their capacity. Despite a large number of existing code provisions and proposed procedures based on the heuristic methods, a practical yet accurate equation for utilisation by the engineers who are dealing with structural retrofitting and analyzing is not available. Here, a gene expression programming (GEP) based simple algorithm is used in conjunction with an extensive database containing 481 stirrup-free experimental samples that were gathered from tests conducted in the lab. Next, using data from an additional programme, the GEP output is examined in order to produce a workable formula for determining the shear capacity of these members. Lastly, a comparison is done using the current equations. The outcomes show that, in comparison to the current ones, the suggested GEP equation along with the CSA S806-12 code provision yields more accurate values.
The popularity of fiber-reinforced polymer (FRP) bars as a structural element has soared due to their advantageous mechanical and physical properties. Despite an abundance of code requirements and heuristic equations, engineers specializing in structural retrofitting and analysis often struggle to utilize a suitable yet precise equation. This study introduces a novel approach by presenting a firefly optimization algorithm (FOA) combined with an artificial neural network (ANN)—termed as FOA-ANN—as an advanced hybrid machine learning model. The primary objective is to predict the shear capacity of slender FRP reinforced concrete (FRP-RC) beams without stirrup. An extensive experimental database of slender FRP-RC beams without stirrup was compiled. Leveraging this database and the proposed hybrid method, a simple yet accurate closed-form equation for determining the shear capacity of slender FRP-RC beams without stirrup was formulated. Additionally, a selection of pre-existing equations was provided for comparison of accuracy. Results indicate that the suggested FOA-ANN equation offers a more accurate alternative, outperforming equations derived from CSA S806-12 and AASHTO LRFD. The FOA-ANN hybrid technique proves to be highly effective in predicting the shear capacity of slender FRP-RC beams without stirrup.
Although engineers working on structural retrofitting and analysis have access to numerous code provision equations for calculating shear strength in steel fiber-reinforced concrete (SFRC) beams, pinpointing an accurate and practical equation remains a challenge. This paper introduces a novel hybrid machine learning model, PSO-ANN, which combines the characteristics of artificial neural network (ANN) with the particle swarm optimizer (PSO). A comprehensive experimental database of SFRC beams was assembled for this research. SFRC beam shear capacity was evaluated using this database and the proposed hybrid technique, resulting in an accurate closed-form formula. To assess the accuracy of existing equations, a set of them was also provided. The PSO-ANN equation emerged as a more straightforward but equally accurate alternative than other previously used formulas. The hybrid technique, known as PSO-ANN, demonstrates significant success in estimating the shear capacity of SFRC beams during the design and planning phases of civil engineering projects
Lateral torsional buckling (LTB) is a common mode of failure in steel structures due to instability. However, current standard recommendations have limitations in accurately determining the ultimate capacity of members subjected to LTB. To address this issue, this paper presents an in-depth parametric study that uses the finite element method (FEM) to conduct an investigation into the effect of major parameters, including various types of loading, on the strength of steel beams. Additionally, an artificial neural network (ANN) technique is employed to find a reliable procedure for assessing the LTB strength of steel I-beams using a generated database. To demonstrate the efficacy of the developed formulation, it is compared against existing equations. Our study concludes that the presented formula demonstrates strong accuracy, making it an effective tool for engineers designing I-beams to resist LTB. This research makes significant contributions to the structural engineering field and has important implications to create and evaluate steel structures.
Structural capability evaluation of ship hull plate subjected to multiple cracks damage is of profound importance for the inspection and maintenance programs of aged ships. In the current paper, ultimate strength of the ship plate with multiple cracks under axial compression is investigated by using nonlinear finite element method (FEM) and artificial neural network (ANN). Influences of orientation angles, lengths, longitudinal positions and transverse positions of the multiple cracks as well as the plate slenderness ratio on the strength characteristics are elaborated based on series of parametric analyses. According to the numerical results, the intricate behaviors of ultimate strength reduction are caused by the coupling effect of these influential factors. As the characteristics demonstrate high nonlinearity against the calculated parameters, ANN is applied to develop the empirical formulation for predicting the residual strength of ship plate with multiple cracks on the basis of 11850 numerical results. Additional independent database is used to validate the accuracy and applicability of the suggested approach.
Lateral torsional buckling (LTB) of steel I-beams is characterized by simultaneous lateral deflection and twist. LTB is an instability failure mode that has been intensively investigated. However, existing standard procedures and formulations still have limitations in determining the LTB ultimate moment, especially when considering the use of perforated beams. Consequently, in the current paper, by conducting an extensive parametric study, it was tried to investigate the effect of all main parameters as well as the effect of different loading conditions on the ultimate LTB resistance of steel I-beams with sinusoidal web openings. Then, based on the provided database, the artificial neural network (ANN) method was employed, and based on it, a high-precision formulation was proposed to predict the ultimate LTB strength of steel I-beams. In addition to the ANN method, a regression-based formula was also developed as a classical method to examine the differences between the two methods. Finally, the proposed formulas were compared with other existing formulas for estimating the LTB strength. The results showed that the proposed formula based on ANN not only present a reasonable accuracy compared to the existing formulations but also can be used by engineers as practical equations in the design of I-beams with sinusoidal web openings.
Artificial neural network (ANN) models were applied for simulating and predicting the ultimate capacities of cellular steel beams. To do this, at the first, different neural networks by various learning algorithms and number of neurons in the hidden layer were simulated. The required data for networks in training, validating, and testing state were obtained from a reliable database. Next, the best network according to its predictive performance was chosen, and a new formula was derived to predict the failure loads of cellular steel beams subjected to LTB. The attempt was done to evaluate the most exact practical formula using different algorithm and method for LTB strength assessment of cellular beams. Next, a comparison was made between the ANN-based formula and a formula based on the stepwise regression (SR) to show the predictive power of the ANN model. The results provided some evidence that ANN model obtained more accurate predictions than SR model. At the end, a sensitivity analysis was developed using Garson’s algorithm to determine the importance of each input parameter which was used in the proposed ANN formulation.
A new model based on Artificial Neural Network (ANN) was established as a trustworthy technique for predicting ultimate lateral torsional buckling (LTB) capacity of castellated steel beams. The required information for training, validating and testing of the developed model obtained from a reliable database. Consequently, a new formulation based on the ANN has been offered for predicting the failure load of castellated steel beams exposed to LTB. All parameters which may affect the LTB capacity of castellated beams were considered for presentation of this formula. Then, outcomes of the proposed formula were compared with predictions of Australian Standard (AS4100) for LTB capacity of castellated beams. This comparison indicated that proposed formula has a good performance for prediction of ultimate strength in castellated beams subjected to LTB. At the end, Garson’s algorithm has been established as a sensitivity analysis to determinate importance of each input in the proposed formula.
In this study (Part I), an advanced empirical formulation was proposed to predict the ultimate strength of initially deflected steel plate subjected to longitudinal compression. An advanced empirical formulation was proposed by adopting Initial Deflection Index (IDI) concept for plate element which is a function of plate slenderness ratio (β) and coefficient of initial deflection. In case of initial deflection, buckling mode shape, which is mostly assumed type in the ships and offshore industry, was adopted. For the numerical simulation by ANSYS nonlinear finite element method (NLFEM), with a total of seven hundred 700 plate scenarios, including the combination of one hundred (100) cases of plate slenderness ratios with seven (7) representative initial deflection coefficients, were selected based on obtained probability density distributions of plate element from collected commercial ships. The obtained empirical formulation showed good agreement (R² = 0.99) with numerical simulation results. The obtained outcome with proposed procedure will be very useful in predicting the ultimate strength performance of plate element subjected to longitudinal compression.
Marine riser is the critical component transporting hydrocarbon and fluid from well to the platform and vice versa. Riser experiences vortex-induced vibration (VIV) caused by current, leading to fatigue damage. Estimation of VIV fatigue damage is essential in designing feasible and operable riser. A simplified approach for predicting fatigue damage is required to reduce the computation time to analyse the fatigue damage. This study aims to propose a simplified approach to predict VIV fatigue damage of top tensioned riser (TTR) using artificial neural network (ANN). A total of 21,532 riser model was generated with different combination of six main input parameters: riser outer diameter, wall thickness, top tension, water depth, surface and bottom current velocity. The modal analysis was performed using OrcaFlex and VIV fatigue damage of the riser was computed using SHEAR7. The six input parameters and corresponding fatigue damage results made up the database for training a 2-layer neural network. Weight and bias values acquired from the training of ANN were used to develop the VIV fatigue damage prediction model of the riser. The hyperparameters of the ANN model were tuned to optimize performance of the model. The results showed the final ANN model predict fatigue damage well with shorter time compared to conventional semi-empirical method. Hence, the proposed approach is suitable to be used for prediction of VIV fatigue damage of TTR at early design stage of TTR.
A stepwise regression (SR) model is developed as a reliable modeling method for simulating and predicting the compressive strength of mortars containing metakaolin at the age of 3, 7, 28, 60, and 90 days. The required data in training and testing state obtained from a reliable data base. A new formulation based on the model have been proposed to predict the compressive strength of mortars containing metakaolin. Besides, to model verification a nonlinear least squares regression (NLSR) has been also developed. Then, a comparison has been made between the proposed SR formulae and NLSR to have an idea about the predictive power of the SR method.
There are several methods such as experimental, numerical, and analytical methods which are the mostly adopted in the verification of proposed design code or guidelines to calculate the ultimate strength performance of stiffened panel structures. This study proposes an advanced empirical formula shape, which is a function of plate slenderness ratio and column slenderness ratio with two (2) correction coefficients ( and ), used to predict the ultimate strength performance of stiffened panel structures in ships. In addition, the two aforementioned correction coefficients were decided and verified by obtaining the result of an ANSYS nonlinear finite element analysis. An average level of initial imperfection and 2 bay – 2 span (1/2 – 1 – 1/2) model were adopted in the proposed empirical formula. The effects of residual strength were not considered in this study. A total of 124 stiffened panels with four different plate slenderness ratios ( ) and changing column slenderness ratio (λ) were selected for the simulation scenarios. To confirm the accuracy of the obtained formula, a statistical analysis was also conducted on the ANSYS results and other existing formulas. The proposed method and its details were documented.
Steel bridges corrode due to environmental exposure. The consequence is a reduction in both the load-carrying capacity and safety of a bridge. Therefore, it is needed to evaluate procedures for an exact prediction of the load-carrying capacity and reliability of bridges, in order to make reasonable decisions about repair, rehabilitation and renewal. The aim of this study is to develop and demonstrate a procedure for the assessment of steel box girder bridge ultimate strength reliability that takes the degradation of plate members due to pit corrosion into account. The present paper treats the effect of pitting corrosion on the load-carrying capacity and reliability of steel box girder bridges and the results are compared with the uniform corrosion effect. The procedure and results of this study can be used for the better prediction of the service life of deteriorating steel box girder bridges and the development of optimal reliability-based maintenance strategies. © 2016, Hong Kong Institute of Steel Construction. All rights reserved.
Steel structural members are likely exposed to corrosive environments, and thus corrosion is one of the dominant life-limiting factors of steel structures. Extensive studies on the effects of pitting and uniform corrosion on the strength performance of steel structural members under a wide variety of loading conditions have been undertaken to assess the relationship between pitting corrosion intensity and residual strength. The aim of this study is to investigate the ultimate compressive strength characteristics of steel web plate elements with pit and uniform corrosion wastage. A series of ABAQUSnonlinear elastic-plastic large deformation finite element analyses are carried out on I-shapedsection steel girder models with varying pittingcorrosion intensities. Artificial pitting of different intensities is considered on the web plates and a uniform loading applied vertically on the upper flange section. The ultimate load-carrying capacity of deteriorated models with different levels of uniform thickness loss is also studied. The results are applied to assessing the ultimate compressive strength of web plates with different pitting corrosion intensities and a uniform loss thickness by developing design formula that represent the average loss thickness versus the ultimate load-carrying capacity.
Half-through girders are not affected by conventional lateral-torsional buckling. I-section beams of simply supported half-through girders experience compression in their top flanges and tension in their bottom flanges. In this condition, the compression flange is restrained only by the stiffness of the web, and the buckling mode is generally restrained distortional. In this study, new and efficient model is derived to predict the Restrained Distortional Buckling (RDB) strength of half-through I-section bridge girders utilizing an Artificial Neural Network (ANN). The model is developed based on a reliable database obtained from the nonlinear finite element (FE) method. To verify the accuracy of the derived model, it is applied to estimate the RDB strength of parts of the FE analysis results that were not included in the modeling process. A sensitivity analysis has been also developed to determine the importance of each input parameters. ANN model is further compared to the some existing design codes. The results indicate that the proposed model is effectively capable of evaluating the RDB load of the half-through girders. The prediction performance of the ANN model is markedly better than prediction of the AISC/LRFD and the AS4100 specifications. The ANN-based design equation can reliably be employed for pre-design applications.
Deteriorated bridges are subjected to time-variant changes of resistance. Corrosion is one of the most important types of deterioration in steel bridges. The consequence is a reduction in safety of a bridge. Therefore, it is needed to evaluate procedures for an accurate prediction of the load-carrying capacity and reliability of corroded bridges, in order to make rational decisions about repair, renewal or rehabilitation. This paper presents a highway bridge reliability-based design formulation which accounts for pitting corrosion effects on steel box girder bridges. The study involves the idealization of pitting corrosion, development of resistance models for corroded steel box girders, development of load models, formulation of limit state function, development of reliability analysis method, and development of the time-dependent reliability for corroded steel girders. Numerical example illustrates the application of the proposed approach. The results of this study can be used for the better prediction of the service life of deteriorating steel box girder bridges and the development of optimal reliability-based maintenance strategies.
Unstiffened plates are integral part of all kinds of structures such as ship and offshore oil platforms. Openings are unavoidable and absolutely reduce the ultimate strength of structures. In this study, the finite element analysis package, ABAQUS, is used to analyze the behavior of unstiffened plate with rectangular opening. The rectangular opening form is divided into two cases. In case1, opening depth is constant, but opening width is varied. Meanwhile, in case2 opening width is fixed and opening depth is varied. Besides, for the two different form opening, the effect of plate slenderness parameter (β), opening area ratio (AR) and opening position ratio (PR) on the ultimate strength of plate with opening under axial compression are presented. It has been found that the ultimate strength of plate ofcase1is much more sensitive to the plate slenderness parameter (β) and opening area ratio (AR) than that of case2. However, for case1, opening position (PR) almost has no effect on the ultimate strength, whereas, regardingcase2, the influence of opening position (PR) depends on the plate slenderness parameter (β). Based on nonlinear regression analysis, three design formulae are not only developed butalso approved reasonably for the practical engineering design
The aims of this study are to investigate the effect of corrosion on the load-carrying capacity of stiffened steel box girder bridges and to formulate a repair schedule using reliability-based approaches for such bridges as they age. A credible scenario for a corroded steel box section is estimated. Corrosion rates and their probabilistic characterization are calculated based on the available data. A probabilistic model of ultimate box girder strength is established based on an analytical formula that considers corrosion-related time-dependent strength degradation. The results generated with this model may be useful in the development of an optimized and accurate maintenance and repair schedule for existing steel box girder bridges.
ABSTRACT:Corrosion is an unavoidable phenomenon in ship hull structures and thickness loss of the structural members due to corrosion is a great concern when the integrity of hull structures is considered. It is well known that pitting corrosion occurring on coated hold frames will surely result in a significant degradation of the ultimate strength of these members. Extensive study on the effect of pitting corrosion on structural strength under a wide variety of loading conditions is necessary to assess the relationship between pitting corrosion intensity and residual strength precisely. The aim of the present study is to investigate the ultimate strength characteristics of steel beams with pit and uniform corrosions wastage. Then pitted member will predict with a member that its thickness decreases uniformly in terms of ultimate strength. A series of ABAQUS nonlinear elastic-plastic analyses by Finite Element Method (FEM) has been carried out on I-shape section steel models, varying the degree of pit corrosion intensity. Load-carrying capacity of deteriorated steel beam models with different pit corrosion under patch loading has been estimated using Artificial Neural Network (ANN) method using FE results. The ultimate strength reduction factor due to web pitting corrosion of steel beams is empirically derived by ANNs of the computed results as a function of DOP. Hence, the results of this study can be used for better prediction of the failure of deteriorated steel beams by practice engineers.
This study develops an assessment procedure for the ultimate strength reliability of steel box girder bridges that takes into account the plate member degradation that results from uniform corrosion in different environmental condi-tions. This paper is a sequel to the authors' previous paper (Sharifi and Paik 2010), which deals with the effects of pit and general corrosion on the load-carrying capac-ity and reliability of these bridges. In contrast to that paper, the effects of different environmental conditions on such capacity and reliability are considered herein. Probabilistic corrosion rate parameters based on the available data are provided, and an analytical formula for predicting time-dependent ultimate strength is devel-oped. The results of this study can be used in accurately predicting the service life and earliest repair time of corroded steel box girder bridges constructed in different environmental conditions.
Marine-grade aluminium alloy is an established structural material for medium- to high-speed commercial craft and has also been used as the primary hull material for several naval vessels. The analysis of large high-speed craft operating in deep ocean environments requires rigorous methodologies to evaluate the ultimate strength of the hull girders. Representative plate load-shortening curves form part of simplified hull girder ultimate strength methodologies; for the case of a high-speed aluminium vessel, the curves need to account for the effects of parameters including alloy type, geometric imperfection, softening in the heat-affected zone, residual stresses, lateral pressure and biaxial load. This paper examines the strength of a series of unstiffened aluminium plates with material and geometric parameters typical of the midship scantlings of a high-speed vessel, using a non-linear finite element approach. The parametric studies show that these factors can have a significant influence on the strength behaviour of the plates both prior to and after the collapse point has been attained.
This paper examined the effects of web distortion on the buckling behavior of castellated steel beams. To this purpose, a series of nonlinear finite element (FE) models was constructed and well verified against an experimental work on the distortional buckling of castellated beams; both material nonlinearities and initial geometric imperfections were carefully applied to the models. Next, an extensive parametric study was performed using the finite element models to investigate the effects of beam length, steel grade and cross-section dimensions on the ultimate buckling load and buckling modes of castellated steel beams. The results showed that the use of low grade steel and thick flanges makes an economical design in the castellated steel beams. Moreover, it is concluded that lateral-distortional buckling (LDB) mode is more common in the castellated beams with intermediated overall slenderness, thick flanges and slender web. Finally, the ultimate loads obtained from finite element analysis (FEA) were compared with the results predicted by AS4100, EC3 and AISC codes. It was concluded that all three Specifications provide unsafe estimates for most specimens in this study.
Artificial Neural Network (ANN) model was developed as a reliable modeling method for simulating and predicting the ultimate moment capacities of castellated steel beams. The training and testing data for neural networks are obtained using Finite Element Analysis (FEA). For this purpose, a series of nonlinear finite element analyses have been carried out to simulate the distortional buckling behavior of castellated steel beams, and the effects of nine independent parameters on the lateral-distortional buckling mode, have been investigated. Moreover, unlike the existing design codes, the ANN model considers the effects of web distortion on the ultimate buckling strength of beams. Then, a new formula based on ANNs has been proposed to predict the ultimate moment capacities of castellated steel beams subjected to lateral-distortional buckling. The attempt was done to evaluate a practical formula considering all parameters which may affect the distortional capacity of castellated steel beams. Then, a sensitivity analysis using Garson’s algorithm has been developed to determine the importance of each input parameter. Finally, a comparison has been made between the proposed formula and the predictions obtained from AS4100, EC3, and AISC codes. It is shown that the proposed formula is more accurate than these design codes.
An artificial neural network model was developed as a reliable modeling method for simulating and predicting the ultimate force capacities of cellular steel beams. The required data in training, validating, and testing states were obtained from a reliable database. A new formula based on the artificial neural network was proposed to predict the failure loads of cellular steel beams subjected to lateral torsional buckling. The attempt was done to evaluate a practical formula considering all parameters which may affect the lateral torsional buckling strength. Then, a comparison was made between the proposed formula and the predictions obtained from Australian Standard (AS4100). The results provided some evidence that proposed formula obtained more accurate predictions than AS4100 design guides. Finally, a sensitivity analysis was developed using Garson’s algorithm to determine the importance of each input parameters.
To ensure the structural capacity of plates with multiple openings subjected compressive loads and to find a better design solution, the strength of different structural configurations is analysed here. A series of experimental buckling collapse tests have been carried out for steel plates with multiple openings, of three different degrees of openings. Each degree of opening is represented by two groups of openings, to investigate the effect of possible design solutions aiming for the maximum compressive strength. The effect of corrosion wastage is also studied, where the specimens are naturally corroded. The effect of manufacturing defects as the initial imperfection on both compressive capacity and the final deformed shapes is also studied. Several relationships as functions of the degree of openings and remaining volume of the corroded plates with multiple openings are developed, and recommendations regarding the early design stage are provided.
The objective of this work is to investigate experimentally and numerically the severe non-uniform corrosion degradation effect on the load carrying capacity of stiffened plates. Eight stiffened plates, which are initially corroded in real open sea conditions with different corrosion degradation levels, have been tested under compressive load. Different factors leading to a reduction of structural capacity have been investigated, including the material properties, degree of degradation, equivalent thickness and testing support conditions. The experimental results also showed to be very close to those estimated by the existing guideline procedure for a numerical evaluation of the ultimate strength, adjusted to be used for the severe corroded stiffened plates.
Unstiffened plates are integral part of ship structures, offshore oil platforms, lock gates and floating docks. Openings are provided in these plates for access and maintenance. Provision of opening influences the ultimate strength of plate elements. In this paper the effect of increase in the size of rectangular opening along the loading direction on the ultimate strength is determined using nonlinear finite element analysis. A general purpose finite element software ANSYS is used for carrying out the study. The software is validated for the ultimate strength of unstiffened plate under axial compression. A parametric study is done for different plate slenderness ratios and by varying the area ratio of opening to plate to determine the effect of ultimate strength on the size of rectangular opening. It is found that increase in area ratio along the loading direction decreases the ultimate strength. The variation in ultimate strength varies linearly for plate slenderness ratio less than 2.23 and varies nonlinearly for plate slenderness ratio beyond 2.23 for area ratio ranging between 0.02 – 0.18. Based on nonlinear regression analysis, a design equation is proposed for square plate with rectangular opening under axial compression.
The aim of the present paper is to investigate the ultimate strength characteristics of plate elements with pit corrosion wastage under axial compressive loads. Collapse tests on a box column type of steel-plated structures with different degrees of pit corrosion damage are undertaken. A series of ANSYS non-linear finite element analyses for steel plate elements under axial compressive loads are carried out, varying the degree of pit corrosion intensity and plate geometric properties. In this paper, a new parameter, i.e. the smallest cross-sectional area, is proposed to represent the ultimate strength reduction characteristics due to localized corrosion. It is proved that the proposed parameter-based approach is more useful than the traditional approach based on equivalent thickness in terms of the accuracy of ultimate strength predictions of pitted plates. Closed-form design formulae for the ultimate compressive strength of pitted plates, which are needed for the ultimate limit state-based risk or reliability assessment of corroded structures, are derived by regression analysis of the experimental and numerical results obtained from the present study. The insights developed will be very useful for the damage-tolerant design of plated structures with pit corrosion damage.
The present paper is a sequel to the author's papers [Paik JK, Ultimate strength of perforated steel plates under edge shear loading. Thin-Walled Structures 2007; 45: 301–6, Paik JK Ultimate strength of perforated steel plates under axial compressive loading along short edges. Ships Offshore Struct, 2007; 2(3): (in press)]. In contrast to the previous papers with the focus on edge shear or uniaxial compressive loads, the aim of the present study is to investigate the ultimate strength characteristics of perforated steel plates under combined biaxial compression and edge shear loads, which is a typical action pattern of steel plates arising from cargo weight and water pressure together with hull girder motions in ships and ship-shaped offshore structures. The plates are considered to be simply supported along all (four) edges, keeping them straight. The cutout is circular and located at the center of the plate. A series of ANSYS nonlinear finite element analyses (FEA) are undertaken with varying the plate dimension (thickness). Based on the FEA results obtained, closed-form empirical formulae of the ultimate strength interaction relationships of perforated plates between combined loads, which can be useful for first-cut estimations of the ultimate strength in reliability analyses or code calibrations, are derived.
The Finite Element Method (FEM) has been employed to determine the elastic buckling load of uniaxially loaded rectangular perforated plates with length a and width b. Plates with simply supported edges in the out-of-plane direction and subjected to uniaxial end compression in their longitudinal direction are considered. Integer plate aspect ratios, a/b=1, 2, 3 and 4, have been chosen to assess the effect of aspect ratio on the plate buckling load. Two perforation shapes of different sizes are considered; circular, and rectangular with curved corners. The rectangular perforation is oriented such that either its long or its short side is parallel to the longitudinal direction of the plate. The center of perforation was chosen at different locations of the plate. The study shows that the buckling load of a rectangular perforated plate that could be divided into equal square panels is not the same as that of the square panel that contains the perforation when treated as a separate square plate. For rectangular plates, the study recommends not to have the center of a circular hole placed in a critical zone defined by the end half of the outer square panel, to try always to put the hole in an interior panel of the plate, and to have the distance between the edge of a circular hole and the nearest unloaded edge of the plate not less than 0.1b. The study concludes also that the use of a rectangular hole, with curved corners, with its short dimension positioned along the longitudinal direction of the plate is a better option than using a circular hole, from the plate stability point of view.
The elastic buckling behavior of rectangular perforated plates was studied by using the finite element method in this study. Circular cutout was chosen at different locations along the principal x-axis of plates subjected to linearly varying loading in order to evaluate the effect of cutout location on the buckling behavior of plates. The results show that the center of a circular hole should not be placed at the end half of the outer panel for all loading patterns. Furthermore, the presence of a circular hole always causes a decrease in the elastic buckling load of plates subjected to bending, even if the circular hole is not in the outer panel.
Openings can be seen on almost every main supporting member of all types of ships. These openings are mainly used for inspection and may be fitted for passing pipes or reducing steel weight. There has been a need for refined strength criteria with which scantlings of main supporting members in the way of and around openings can be more rationally determined. A plate with an opening behaves in a very complex manner when subjected to compressive or shear stress. The mechanisms that can possibly take place are yielding, buckling, stress concentration and cracking. To better understand the complex behaviour, a total of 954 linear and non-linear FEM (finite element method) analyses were performed. Both buckling strength (eigenvalues) and ultimate strength were calculated. Plate panels were analysed as the idealised structural model of main supporting members with openings. Parametric studies were conducted and the investigated variables were slenderness ratio and aspect ratio of panels, shape and dimensions of openings, longitudinal and transverse compressive stresses and shear stress. Simplified formulae were proposed based on the FEM results. Strength reduction factors were introduced to present the reduced buckling and ultimate strengths of plate panels with openings as ratios of those without openings. These simple mathematical functions can be incorporated in a design guidance and can help to estimate the strength of plates on main supporting members in the way of openings.
This paper is concerned with post-buckling behaviour and the ultimate load capacity of perforated plates with different boundary conditions and subjected to uniaxial or biaxial compression. Plates were analysed using the finite element method (FEM), and extensive studies were carried out covering parameters such as plate slenderness, opening size, boundary conditions and the nature of loading. A design formula to determine the ultimate load carrying capacity was established based on a best-fit regression analysis using the results from the finite element analyses. The accuracy of the proposed formula was established by comparison with experimental values of ultimate capacity and similar finite element values. Ultimate load values are also presented in the form of charts for various values of plate slenderness and opening size.
The ultimate compressive strength of unstiffened plates is very important from the design and safety viewpoint. However, the ultimate compressive strength of these panels will depend quite significantly on the initial welding distortions and residual stresses. Currently, most of the researches concerning the effect of welding distortions concentrate only on the maximum initial distortion amplitude. However, many evidences indicate that the welding distortion shape could also affect the ultimate compressive strength significantly. In this paper, we adopt a combination of the elastic large deflection theory and the rigid-plastic analysis, proposed by Paik and Pedersen and later was generalized by the present authors. Various factors including the initial deflection shape which affect the ultimate compressive strength of unstiffened plates are investigated.
The aim of the present study is to develop more advanced design formulations for the ultimate strength of ship plating than available at present. Plate ultimate strength subject to any combination of the following four load components-longitudinal compression/tension, transverse compression/tension, edge shear, and lateral pressure loads - is addressed. The developed formulations are designed to be more sophisticated than existing theoretically based simplified methods. The influence of post-weld initial imperfections in the form of initial deflections and residual stresses is taken into account. It has been previously recognized that a single ultimate strength interaction equation cannot successfully represent the ultimate limit state of long and/or wide plating under all possible combinations of load components involved. This is due to the fact that the collapse behavior of the long and/or wide plating depends primarily on the predominant load components, implying that more than one strength interaction formulations may be needed to more properly predict the plate ultimate limit state. In this regard, the present study derives three sets of ultimate strength formulations for the long and/or wide plating under the corresponding primary load by treating lateral pressure as a secondary dead load. The ultimate strength interaction formula under all of the load components involved is then derived by a relevant combination of the individual strength formulas. The validity of the proposed ultimate strength equations is studied by comparison with nonlinear finite-element analyses and other numerically based solutions.
It has been recognised that the current shipbuilding industry design practice for perforated plates is not relevant with relatively large opening size and/or with large plate thickness, and it is believed that this problem has caused structural damage accidents in actual ship structures with openings. The motive of the present study was to resolve this issue by introducing a new design formulation of the critical buckling strength for perforated plates, which is pertinent to the structural design application on the safety side. For this purpose, a series of experimental and numerical studies are undertaken on buckling and ultimate strength of plates and stiffened panels with an opening and subject to axial compressive actions. A total of 90 perforated plates and also a total of 9 stiffened panels with an opening are tested up to and beyond ultimate strength, where important parameters of influence such as plate aspect ratio, plate slenderness ratio, opening size and shape, and opening location are varied. Elastic-plastic large deflection finite element method analyses are performed on the test structures. Existing and newly derived design-formula solutions of buckling and ultimate strength of the test plate panels are compared with experimental results and non-linear finite element method computations, indicating that the critical buckling strength formulation developed in the present study as well as an existing ultimate strength formula is useful for design and strength assessment of steel plate panels with an opening. The experimental database on buckling collapse of steel plate panels with an opening will be very useful for future use. Details of experiments and numerical computations together with insights developed from the present study are documented.
The aim of the present study is to investigate the ultimate strength characteristics of steel plates with a single circular hole under axial compressive loading along short edges, which is a primary action type arising from vertical or horizontal hull girder bending moments of ships and ship-shaped offshore structures. The plates are considered to be simply supported along all (four) edges and kept straight. The circular hole is located at the center of the plate. A series of ANSYS nonlinear finite element analyses (FEA) are undertaken with varying the hole size (diameter) as well as plate dimensions (plate aspect ratio and thickness). By regression analysis of the FEA results obtained, a closed-form empirical formula for the ultimate longitudinal compressive strength of perforated plates, which can be useful for first-cut strength estimations and reliability analyses, is derived. The accuracy of the ultimate strength formula developed is verified by a comparison with more refined nonlinear FEA results.
The elasto-plastic buckling of perforated plates under uniaxial compression was investigated. The finite element method (FEM) was used to determine the buckling load in the plates. The inelastic behavior of rectangular perforated plates with aspect ratio of 2, was also studied. It was found that the critical buckling stress for perforated plates decreased as the plate slenderness ratio increased, and the decrease became steeper for large values of plate slenderness ratio. It was also observed that critical stress decreased as the hole size increased, and their value depend on the yield point of the steel used.
In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of
affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results
settle an open question about representability in the class of single hidden layer neural networks. In particular, we show
that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a
single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other
possible types of nonlinearities that might be implemented by artificial neural networks.
The aim of the present study is to investigate the ultimate strength characteristics of perforated steel plates under edge shear loading, which is a primary action type arising from cargo weight and water pressure in ships and ship-shaped offshore structures. The plates are considered to be simply supported along all (four) edges and kept straight. The cutout is circular and located at the center of the plate. A series of ANSYS nonlinear finite element analyses (FEA) are undertaken with varying the cutout size (diameter) as well as plate dimensions (plate aspect ratio and thickness). By the regression analysis of the FEA results obtained, a closed-form empirical formula for predicting the ultimate shear strength of perforated plates, which can be useful for first-cut strength estimations in reliability analyses or code calibrations, is derived. The accuracy of the ultimate strength formula developed is verified by a comparison with more refined nonlinear FEA results.
This paper is concerned with a finite element model to predict the behaviour and ultimate load of plate girders with web openings. The finite element package ABAQUS is used to model the plate girders with web openings. Accuracy of the model is assessed by applying it to plate girders tested earlier by other researchers. Comparison of analytical results with the available experimental results for yielding patterns, ultimate load values and load–deflection relationships show good agreement between the finite element and experimental results thus validating the accuracy of the proposed model. The proposed finite element method was extended to carry out a parametric study. The study covered parameters such as web slenderness and flange stiffness.
Closed-form expressions for approximating the influence of single or multiple holes on the critical elastic buckling stress of plates in bending or compression are developed, validated and summarized. The expressions are applicable to plates simply supported on 4 sides and plates simply supported on 3 sides, commonly called stiffened and unstiffened elements in design. The expressions serve as a convenient alternative to shell finite element eigen-buckling analysis, which requires commercial software not typically accessible to the engineering design community. The forms of the expressions are founded on classical plate stability approximations, and are developed and validated with parametric studies employing shell finite elements. The finite element parametric studies demonstrate that holes may create unique buckling modes, and can either decrease or increase a plate's critical elastic buckling stress depending on the hole geometry and spacing. The validated closed-form expressions and their associated limits are intended to be general enough to accommodate the range of hole shapes, locations, and spacings common in engineering practice, while at the same time also defining regimes where explicit use of shell finite element analyses is still needed for adequate accuracy.
The aim of the present paper is to investigate the ultimate strength characteristics of steel plate elements with pit corrosion wastage and under in-plane shear loads. A series of the ANSYS nonlinear finite element analyses for plate elements under in-plane shear loads are carried out, varying the degree of pit corrosion intensity and the plate geometric properties. Closed-form design formulae for the ultimate strength of pitted plates under edge shear, which are essentially needed for the ultimate limit state based risk or reliability assessment of corroded structures, are derived by the regression analysis of the computed results. The insights developed from the present study will be very useful for damage tolerant design of plated structures with pit corrosion wastage.
This paper is concerned with the ultimate load capacity of perforated cold-formed steel channel stub columns. A design equation has been developed to determine the ultimate load capacity of perforated channel short columns containing either single or multiple openings of square, circular and manufacturer's opening shape. The equation is based on extensive parametric studies carried out using finite element modelling on plain and lipped channel sections containing openings. A wide range of parameters such as plate slenderness, opening shapes and sizes have been considered in the study. Web plate slenderness and opening area ratio are the two main variables used to derive the design equations. The accuracy of the proposed design equation is established by comparison with a number of experimental and finite element results reported by other researchers.
Most algorithms for the least-squares estimation of non-linear parameters have centered about either of two approaches. On the one hand, the model may be expanded as a Taylor series and corrections to the several parameters calculated at each iteration on the assumption of local linearity. On the other hand, various modifications of the method of steepest-descent have been used. Both methods not infrequently run aground, the Taylor series method because of divergence of the successive iterates, the steepest-descent (or gradient) methods because of agonizingly slow convergence after the first few iterations. In this paper a maximum neighborhood method is developed which, in effect, performs an optimum interpolation between the Taylor series method and the gradient method, the interpolation being based upon the maximum neighborhood in which the truncated Taylor series gives an adequate representation of the nonlinear model. The results are extended to the problem of solving a set of nonlinear algebraic e
The Marquardt algorithm for nonlinear least squares is presented and is incorporated into the backpropagation algorithm for training feedforward neural networks. The algorithm is tested on several function approximation problems, and is compared with a conjugate gradient algorithm and a variable learning rate algorithm. It is found that the Marquardt algorithm is much more efficient than either of the other techniques when the network contains no more than a few hundred weights.
Approximations by super positions of a sigmoidal function
- J Cybenko
Cybenko J. 1989. Approximations by super positions of a sigmoidal function.
Math Control Signals Syst. 2:303-314.