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Abstract

This paper presents the effect of noise on surrogate based stochastic natural frequency analysis of composite laminates. Surrogate based uncertainty quantification has gained immense popularity in recent years due to its computational efficiency. On the other hand, noise is an inevitable factor in every real-life design process and structural response monitoring for any practical system. In this study, a novel algorithm is developed to explore the effect of noise in surrogate based uncertainty quantification approaches. The representative results have been presented for stochastic frequency analysis of spherical composite shallow shells considering Kriging based surrogate model. The finite element formulation for laminated composite shells has been developed based on Mindlin’s theory considering transverse shear deformation. The proposed approach for quantifying the effect of noise is general in nature and therefore, it can be extended to explore other surrogates under the influence of noise.

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... The aspect of delamination in composites has also received adequate attention in the deterministic domain . Stochastic analysis of composite and sandwich structures considering sourceuncertainty is found to be studied by many researchers including the aspects of multi-scale analysis, 3 optimization and reliability assessment [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. However, the compound effect of delamination and sourceuncertainty has not been investigated yet for the dynamic responses of composite structures. ...
... represents the transformed reduced stiffness [59] while o t z denotes the z-co-ordinate of mid- ...
... For presenting numerical results, it is considered as 10% and  10º for material properties and ply orientation angle respectively according to industry standard, unless otherwise indicated. Figure 3 shows the hybrid surrogate uncertainties involved in the system [59]. While formation of the surrogate model, gaussian white noise with a specific level (s) is induced in the set of output responses as ...
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The coupled effect of manufacturing uncertainty and a critical service-life damage condition (delamination) is investigated on the natural frequencies of laminated composite plates. In general, delamination is an unavoidable phenomenon in composite materials encountered often in real-life operating conditions. We have focused on the characterization of dynamic responses of composite plates considering source-uncertainty in the material and geometric properties along with various single and multiple delamination scenarios. A hybrid high dimensional model representation based uncertainty propagation algorithm coupled with layer-wise stochastic finite element model of composites is developed to achieve computational efficiency. The finite element formulation is based on Mindlin's theory considering transverse shear deformation. Numerical results are presented for the stochastic natural frequencies of delaminated composites along with a comprehensive deterministic analysis. Further, an inevitable effect of noise is induced in the surrogate based analysis to explore the effect of various errors and epistemic uncertainties involved with the system.
... Then, the method has been applied to solve uncertainty analysis problems in different areas of engineering e.g., mechanics of solid [16,17], fluid mechanics [18][19][20][21], structural dynamics [22,23], fluid-structure interaction [24,25], etc. A volume of literature is available on the application of SFEM in the uncertainty analysis of laminate composite plates [26][27][28][29][30][31]. ...
... To generate a polynomial chaos series, we refer to Ghanem and Spanos [10]. For ease of understanding, a 2nd order PC expansion using three inputs (see Eqs. (30) and (32)) is shown in expanded form as Eq. (33) and a simplified form as Eq. ...
Article
This article quantifies uncertainty in the dynamic responses of marine cycloidal propeller (MCP) blade by Stochastic Finite Element Method (SFEM) during crash-stop ship maneuver. Stopping a ship in an emergency is known as crash-stop astern maneuver. A MCP contains a horizontal circular metallic disc on which six aerofoil blades are hung vertically. All blades are made up of carbon fiber-reinforced composite laminates. Uncertainty in ship speed and composite material properties are propagated to find out the statistical response of natural frequencies, displacement, and stresses on the blade. SFEM is a combination of Stochastic Response Surface Method (SRSM) and Finite Element Method (FEM). SRSM is a collocation-based non-intrusive polynomial chaos expansion to transform any random distribution into a stochastic response surface equation (surrogate model). During ship maneuvering motion, the whole unit rotates about a vertical axis at the centre. For each rotation of the disc, all blades undergo periodic oscillations. The SRSM for uncertainty propagation is computationally more efficient than the standard Monte Carlo Simulation (MCS) technique without compromising the accuracy of the results. It is observed that uncertainty in vibration responses of MCP blade is significant and worth study.
... Fibre-reinforced composites usually have complex microstructures and their manufacturing processes are not trivial, which naturally makes them susceptible to variations in their microstructure, geometry and material properties. These variations can be interpreted as uncertainties, which may be the cause of variation in their mechanical properties [1]. ...
... The ease of handling, lack of requirement for heavy lifting and handling equipment, and corrosion resistance are some other factors that are advantageous in the repair, retrofitting, and rehabilitation of civil engineering structures. Because of continuous research and development on new composite materials [3][4][5][6], the use of such materials is found to be advantageous in terms of weight sensitivity and cost effectiveness. ...
Article
A numerical analysis investigation, using finite element model (FEM) and modified compression field theory (MCFT), was conducted to evaluate the shear capacity and behavior of circular concrete piles reinforced with steel and FRP bars by considering shear behavior, shear strength, and deflection shape. The FEM and MCFT models were verified against the experimental results of full-scale circular concrete speciemns previously tested by the authors. Load-deformation response curve, load-strain for the concrete and reinforced rebars were predicted using finite element analysis were compared to experimental results. The FEM outcomes showed that the model was able to capture the behavior of the specimens with good accuracy. While, the modified compression field theory using Response 2000 (R2K) software provided good predictions of the shear strength with an average value of V exp /V Response2000 for specimens is 1.17. Subsequently, a parameric study was performed to study the effect of member's depth (300, 400, and 600 mm), longitudinal reinforcement ratio (1.5, 2.5, and 3.5%), and reinforcing bars material (Steel, Glass-FRP, Carbon-FRP) on the behaviour of circular concrete piles.
... The ease of handling, lack of requirement for heavy lifting and handling equipment, and corrosion resistance are some other factors that are advantageous in the repair, retrofitting, and rehabilitation of civil engineering structures. Because of continuous research and development on new composite materials [3][4][5][6], the use of such materials is found to be advantageous in terms of weight sensitivity and cost effectiveness. ...
Article
A numerical analysis investigation, using finite element model (FEM) and modified compression field theory (MCFT), was conducted to evaluate the shear capacity and behavior of circular concrete piles reinforced with steel and FRP bars by considering shear behavior, shear strength, and deflection shape. The FEM and MCFT models were verified against the experimental results of full-scale circular concrete speciemns previously tested by the authors. Load-deformation response curve, load-strain for the concrete and reinforced rebars were predicted using finite element analysis were compared to experimental results. The FEM outcomes showed that the model was able to capture the behavior of the specimens with good accuracy. While, the modified compression field theory using Response 2000 (R2K) software provided good predictions of the shear strength with an average value of V exp /V Response2000 for specimens is 1.17. Subsequently, a parameric study was performed to study the effect of member's depth (300, 400, and 600 mm), longitudinal reinforcement ratio (1.5, 2.5, and 3.5%), and reinforcing bars material (Steel, Glass-FRP, Carbon-FRP) on the behaviour of circular concrete piles.
... The ease of handling, lack of requirement for heavy lifting and handling equipment, and corrosion resistance are some other factors that are advantageous in the repair, retrofitting, and rehabilitation of civil engineering structures. Because of continuous research and development on new composite materials [3][4][5][6], the use of such materials is found to be advantageous in terms of weight sensitivity and cost effectiveness. ...
Article
A numerical analysis investigation, using finite element model (FEM) and modified compression field theory (MCFT), was conducted to evaluate the shear capacity and behavior of circular concrete piles reinforced with steel and FRP bars by considering shear behavior, shear strength, and deflection shape. The FEM and MCFT models were verified against the experimental results of full-scale circular concrete speciemns previously tested by the authors. Load-deformation response curve, load-strain for the concrete and reinforced rebars were predicted using finite element analysis were compared to experimental results. The FEM outcomes showed that the model was able to capture the behavior of the specimens with good accuracy. While, the modified compression field theory using Response 2000 (R2K) software provided good predictions of the shear strength with an average value of V exp /V Response2000 for specimens is 1.17. Subsequently, a parameric study was performed to study the effect of member's depth (300, 400, and 600 mm), longitudinal reinforcement ratio (1.5, 2.5, and 3.5%), and reinforcing bars material (Steel, Glass-FRP, Carbon-FRP) on the behaviour of circular concrete piles.
... However, the downside of the standard Monte Carlo method is its slow convergence and a large number of realizations (~10 4 ) are required to attain the desired accuracy. To mitigate the computationally expensive nature of MCS, the possible avenues could be parallelization of the Monte Carlo simulations [51] or utilization of surrogate modeling approaches [52,53]. Even though parallelization may be able to reduce the time for Monte Carlo Simulations, it still requires high computational effort. ...
Article
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This paper presents an experimental investigation supported by data-driven approaches concerning the influence of critical stochastic effects on the dynamic fracture toughness of glass-filled epoxy composites using a computationally efficient framework of uncertainty quantification. Three different shapes of glass particles are considered including rod, spherical and flaky shapes with coupled stochastic variations in aspect ratio, dynamic elastic modulus and volume fraction. An artificial neural network based surrogate assisted Monte Carlo simulation is carried out here in conjunction with advanced experimental techniques like digital image correlation and scanning electron microscopy to quantify the uncertainty and sensitivity associated with the dynamic fracture toughness of composites in terms of stress intensity factor under dynamic impact. The study reveals that the pre-crack initiation time regime shows the most prominent effect of uncertainty. Additionally, rod shape and the aspect ratio are the most sensitive filler type and input parameter respectively for characterizing dynamic fracture toughness. Here the quantitative results based on large-scale data-driven approaches convincingly demonstrate using a computational mapping between the stochastic input and output parameter spaces that the effect of uncertainty gets pronounced significantly while propagating from the compound source level to the impact responses. Such outcomes based on experimental data essentially bring us to the realization that quantification of uncertainty is of utmost importance for developing a reliable and practically relevant inclusive analysis and design framework for the dynamic fracture of particulate composites. With limited literature available on the determination of fracture toughness considering inertial effects, the present work demonstrates a novel and insightful experimental approach for uncertainty quantification and sensitivity analysis of dynamic fracture toughness of particulate polymer composites based on surrogate modeling.
... Le prédicteur fourni par le krigeage est donc associé à une estimation de l'erreur locale (variance) de la prédiction. Le KRI a servi dans des problèmes d'optimisation [120][121], et dans de nombreux problèmes de sciences de l'ingénieur comme en mécanique [122] mais aussi en CEM [123]. Il existe de nombreuses variantes : adaptative [67], le Co-krigeage [124][125] [126], Poisson-krigeage [127], krigeage bayésien [128], en association avec la méthode fiabiliste de subset simulation [129]. ...
Thesis
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Une Interférence Electromagnétique Intentionnelle (IEMI) agressant un équipement électronique peut provoquer une défaillance de ce dernier. L’étude des effets d’une IEMI commence par l’évaluation du risque de défaillance afin de mettre en place les protections adéquates. Malheureusement, une prédiction déterministe d’une défaillance est impossible car les caractéristiques de l’équipement et de l’agression sont très incertaines. La stratégie proposée consiste à modéliser la contrainte générée par l’agression, ainsi que la susceptibilité de l’équipement, comme des variables aléatoires. Ensuite, trois étapes sont nécessaires. La première concerne l’estimation de la distribution probabiliste de la variable aléatoire de susceptibilité, la seconde porte sur celle de la contrainte, pour enfin, dans une troisième étape, en déduire la probabilité de défaillance. Pour la première étape, nous utilisons des méthodes d’inférence statistique sur un petit échantillon de seuils de susceptibilités mesurés. Nous comparons deux types d’inférence paramétrique : bayésienne et celle du maximum de vraisemblance. Nous concluons qu’une approche pertinente pour l'analyse du risque CEM consiste à utiliser les intervalles de confiance ou de crédibilité des estimations des paramètres pour encadrer la probabilité de défaillance, quelle que soit la méthode d’inférence choisie. Pour la deuxième étape, nous explorons les techniques de recherche de valeurs extrêmes tout en réduisant le nombre de simulations nécessaires. En particulier, nous proposons la technique de la stratification contrôlée par un métamodèle de krigeage. Nous montrons que cette technique améliore drastiquement les performances par rapport à l’approche classique (simulation Monte Carlo). De plus, nous proposons une implémentation particulière de cette technique afin de maitriser le coût de calcul. Enfin, la troisième étape est la plus simple une fois les deux premières franchies puisque, par définition, une défaillance survient lorsque la contrainte est supérieure à la susceptibilité. A partir d’un cas test final comportant la simulation de l’agression d’un équipement et de données de susceptibilité de cet équipement, nous calculons un encadrement de la probabilité de défaillance en recourant aux méthodes développées pendant cette thèse. En particulier, nous montrons que l’utilisation conjointe de la stratification contrôlée par le krigeage et de l’inférence de la distribution de la susceptibilité permet effectivement d’encadrer l’estimation de la vraie probabilité de défaillance.
... Owing to its numerous advantages, metamodels have recently received significant attention in structural engineering applications ranging from prediction [1,2] and uncertainty quantification [3][4][5][6][7][8] to single-objective [9,10] and multi-objective optimization [11,12]. Among all such metamodels, polynomial regression (PR) is perhaps the most widely used approach. ...
Article
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High-fidelity multi-scale design optimization of many real-life applications in structural engineering still remains largely intractable due to the computationally intensive nature of numerical solvers like finite element method. Thus, in this paper, an alternate route of metamodel based design optimization methodology is proposed in multi-scale framework based on a symbolic regression implemented using genetic programming (GP) coupled with D-optimal design. This approach drastically cuts the computational costs by replacing the finite element module with appropriately constructed robust and efficient metamodels. Resulting models are compact, have good interpretability and assume a free-form expression capable of capturing the non-linearly, complexity and vastness of the design space. Two robust nature-inspired optimization algorithms, viz. multi-objective genetic algorithm (MOGA) and multi-objective particle swarm optimization (MOPSO), are used to generate Pareto optimal solutions for several test problems with varying complexity. TOPSIS, a multi-criteria decision-making approach is then applied to choose the best alternative among the Pareto optimal sets. Finally, the applicability of GP in efficiently tackling multi-scale optimization problems of composites is investigated, where a real-life scenario is explored by varying fractions of pertinent engineering materials to bring about property changes in the final composite structure across two different scales. The study reveals that a micro-scale optimization leads to better optimized solutions, demonstrating the advantage of carrying out a multi-scale optimization without any additional computational burden.
... Stochastic natural frequency of noise-induced support vector regression (SVR) model for laminated composite curved panels is analysed by Dey et al. [49]. The effect of noise in surrogate model is quantified by Mukhopadhyay et al. [50], whereas Dey et al. [44] presented the effect of noise using polynomial neural network approach in uncertainty quantification of natural frequency, and Chakraborty [51] predicted delamination in laminated composite using ANN approach. Lee et al. [52] determined the equivalent material properties of glass/epoxy composite by applying the homogenization method, and stochasticity in the equivalent material properties are assessed by MCS and found that variation in individual material properties has a significant effect on the equivalent material properties. ...
Article
The present paper portrays the mapping for stochasticity in low-velocity impact responses of functionally graded material (FGM) plates by employing multivariate adaptive regression splines (MARS) surrogate model in conjunction with finite element (FE) approach. The unavoidable stochastic variabilities (caused due to numerous errors involved in manufacturing processes) in material properties of FGM plates are considered in order to map the effect of elemental variabilities on global response of the structure. The material properties of FGM plates are considered to follow the rule of mixture in conjunction to power law. The Newmark’s time integration scheme and modified Hertzian contact law are employed to solve the time-dependent equation. The present FE formulation is based on an eight noded isoparametric element in which each element has five degrees of freedom. The effects of variability in temperature and power-law exponent on stochastic low-velocity impact responses are also portrayed. The maximum contact force, plate and impactor displacement are considered as the response parameters. The present MARS model is coupled with the finite element to achieve the higher efficiency with adequate accuracy as compared to the FE-based full-scale Monte Carlo simulation. The statistical results illustrate that the stochasticity in material properties significantly influences the low-velocity impact responses of FGM plates.
... There is nothing as ideal in this world and hence to fully eliminate the epistemic uncertainties is next to impossible. To make the results and simulation more realistic, a part of epistemic uncertainty is incorporated as noise in the performance functions [68,69]. ...
Article
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This article presents a computational reliability analysis of reinforced soil-retaining structures (RSRS) under seismic conditions. The internal stability of RSRS is evaluated using the horizontal slice method (HSM) with modified pseudo-dynamic seismic forces. Two different failure modes of RSRS are identified and their reliability indices are computed using the first-order reliability method (FORM). The critical probabilistic failure surface is identified using a three-tier optimization scheme. Reliability index of the system is computed by considering the modes of failure to be connected in series. The tension mode is found to be the most critical mode of failure. The present study identifies that the wall height (H), shear wave velocity of the soil (Vs), and predominant frequency of the input motion (ω) govern the response of RSRS. Reliability indices depend on a parameter termed as the normalized frequency (ωH/Vs) and their values decrease with an increase in the value of ωH/Vs. Increase in the damping ratio of soil, increases the value of reliability indices, especially for ωH/Vs values, which are close to π/2. The FORM suffers from few critical shortcomings such as linear assumption of limit state surface at the most probable point of failure and its ability to consider only the statistical uncertainties excluding the effect of epistemic uncertainties. This calls for sampling-based numerical techniques such as Monte-Carlo simulation (MCS) which gives more comprehensive understanding of the problem under consideration in a probabilistic framework. Thus, a computationally efficient surrogate-assisted MCS is carried out to validate the present formulation and provide numerical insights by capturing the system dynamics over the entire design domain. Adoption of the efficient surrogate-assisted approach allowed us to quantify the epistemic uncertainty associated with the system using Gaussian white noise (GWN). Subsequently, its effects on the system reliability index and probabilistic behavior of the critical parameters are presented. The numerical results clearly indicate that it is imperative to take into account the probabilistic deviations of the critical performance parameters for RSRS to ensure adequate safety and serviceability under operational condition while quantifying the reliability of such systems.
... investigated on the stochasticity in structural integrity and material distribution in mechanical properties of metamaterials, while in high stochastic dimension and modelling error, probabilistic model of random field is constructed, identified and presented for computational structural dynamics by Batou and Soize (2013). The effect of noise in a surrogate model is quantified by Mukhopadhyay et al. (2016), whereas Dey et al. (2016b) presented the effect of noise using polynomial neural network approach in uncertainty quantification of natural frequency and Chakraborty (2005) predicted delamination in laminated composite using artificial neural network approach. Few researchers used modal stability procedure-based Monte Carlo simulation (MCS) approach for stochastic analysis (Druesne et al., 2016;Yin et al., 2018), whereas some researchers used surrogate-based MCS approach for stochastic analysis (Karsh et al., 2018a(Karsh et al., , 2018b(Karsh et al., , 2018c(Karsh et al., , 2019Kumar et al., 2019;Mukhopadhyay et al., , 2018 to reduce the computational time and cost. ...
Article
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Purpose – The purpose of this paper is to investigate the first three stochastic natural frequencies of skewed sandwich plates, considering uncertain system parameters. To conduct the sensitivity analysis for checking the criticality of input parameters. Design/methodology/approach – The theoretical formulation is developed based on higher-order zigzag theory in accordance with the radial basis function (RBF) and stochastic finite element (FE) model. A cubic function is considered for in-plane displacement over thickness while a quadratic function is considered for transverse displacement within the core and remains constant in the facesheet. RBF is used as a surrogate model to achieve computational efficiency and accuracy. In the present study, the individual and combined effect of ply-orientation angle, skew angle, number of lamina, core thickness and material properties are considered for natural frequency analysis of sandwich plates. Findings – Results presented in this paper illustrates that the skewness in the sandwich plate significantly affects the global dynamic behaviour of the structure. RBF surrogate model coupled with stochastic FE approach significantly reduced the computational time (more than 1=18 times) compared to direct Monte Carlo simulation approach. Originality/value – The stochastic results for dynamic stability of sandwich plates show that the inevitable source uncertainties present in the input parameters result in significant variation from the deterministic value demonstrates the need for inclusive design paradigm considering stochastic effects. The present paper comprehensively establishes a generalized new RBF-based FE approach for efficient stochastic analysis, which can be applicable to other complex structures too.
... The uncertainties incurred during the layup process are due to the misalignment of ply-orientation. Typical uncertainties incurred from the curing process are intralaminate voids, incomplete curing of resin, excess resin between plies, excess matrix voids and porosity and variation in ply thickness [65][66][67][68][69]. ...
Article
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The stochastic buckling behaviour of sandwich plates is presented considering uncertain system parameters (material and geometric uncertainty). The higher-order-zigzag theory (HOZT) coupled with stochastic finite element model is employed to evaluate the random first three buckling loads. A cubic in-plane displacement variation is considered for both face sheets and core while quadratic transverse displacement is considered within the core and assumed constant in the faces beyond the core. The global stiffness matrix is stored in a single array by using skyline technique and stochastic buckling equation is solved by simultaneous iteration technique. The individual as well as compound stochastic effect of ply-orientation angle, core thickness, face sheets thickness and material properties (both core and laminate) of sandwich plates are considered in this study. A significant level of computational efficiency is achieved by using artificial neural network (ANN) based surrogate model coupled with the finite element approach. Statistical analyses are carried out to illustrate the results of stochastic buckling behaviour. Normally in case of various engineering applications, the critical buckling load with the least Eigen value is deemed to be useful. However, the results presented in this paper demonstrate the importance of considering higher order buckling modes in case of a realistic stochastic analysis. Besides that, the probabilistic results for global stability behaviour of sandwich structures show that a significant level of variation with respect to the deterministic values could occur due to the presence of inevitable source-uncertainty in the input parameters demonstrating the requirement of an inclusive design paradigm considering stochastic effects.
... The aspect of considering uncertainty in the analysis and design of composite structures are becoming increasingly recognised in last few years. Probabilistic approaches are found to be predominantly used to quantify the effect of uncertainty in composite structures following intrusive [Lal and Singh (2010), Scarth and Adhikari (2017), Zhou et al. (2017)] as well as non-intrusive [Shaw et al. (2010), Dey et al. (2016aDey et al. ( , 2018, Umesh and Ganguli (2013), , Karsh et al. (2018), Sakata et al. (2008), , 2017c, 2018, Mukhopadhyay and Adkhikari (2016b); Mukhopadhyay et al. (2016c)] methods. The prerequisite of carrying out a probabilistic analysis is to 3 Fig. 1 Fuzzy multi-scale analysis of composite laminates considering the coupled effect of material and geometric uncertainty (a) Typical distribution of a typical material property y (such as E 1 ) along a cross-sectional view (X-Z plane) of two laminae for a particular realization in case of the conventional approach where spatial variation of y is ignored (b) Typical distribution of a material property y along a cross-sectional view (X-Z plane) of two laminae for a particular realization in case of the present approach considering spatial variation of material properties (c) Typical representation of a fuzzy based analysis have the statistical distribution of stochastic input parameters available. ...
Article
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This article presents a non-probabilistic fuzzy based multi-scale uncertainty propagation framework for studying the dynamic and stability characteristics of composite laminates with spatially varying system properties. Most of the studies concerning the uncertainty quantification of composites rely on probabilistic analyses, where the prerequisite is to have the statistical distribution of stochastic input parameters. In many engineering problems, these statistical distributions remain unavailable due to the restriction of performing large number of experiments. In such situations, a fuzzy-based approach could be appropriate to characterize the effect of uncertainty. A novel concept of fuzzy representative volume element (FRVE) is developed here for accounting the spatially varying non-probabilistic source-uncertainties at the input level. Such approach of uncertainty modelling is physically more relevant than the prevalent way of modelling non-probabilistic uncertainty without considering the ply-level spatial variability. An efficient radial basis function based stochastic algorithm coupled with the fuzzy finite element model of composites is developed for the multi-scale uncertainty propagation involving multi-synchronous triggering parameters. The concept of a fuzzy factor of safety (FFoS) is discussed in this paper for evaluation of safety factor in the non-probabilistic regime. The results reveal that the present physically relevant approach of modelling fuzzy uncertainty considering ply-level spatial variability obtains significantly lower fuzzy bounds of the global responses compared to the conventional approach of non-probabilistic modelling neglecting the spatially varying attributes.
... The analysis had been performed with finite element methodology and probability theory was used to incorporate the uncertainties in the material properties. Mukhopadhyay et al. [246] investigated the effect of noise on stochastic free vibration response on the composite laminated shallow shall structures. Authors used surrogate based methodology to quantify Authors used surrogate based methodology to quantify the uncertainties in material properties. ...
Article
The main objective of the present paper is to draw the attention of researchers towards the analyses of composite structures in non-deterministic environment. The various distinguishing features of the stochastic finite element methodologies for the analysis of composite structures have been discussed. A thorough literature review has been carried out while emphasizing on the bending, buckling, vibration analysis and failure analysis of composite structures by considering the uncertain behavior of material properties, mechanical loadings and others. This paper also presents an overview of various micromechanical models in the deterministic and stochastic domains, plate theories and impact of uncertainties on the processing techniques of various composite structures. The future research directions have been discussed which will be prolific to the material, design, civil, mechanical and aerospace engineers.
... Hence, the entire solution often becomes computationally quite intensive. Carrying out thousands of such simulations becomes practically impossible unless the system is coupled with an efficient surrogate model [77][78][79][80][81][82]. The radial basis function (RBF) model is utilised to form a representative surrogate of the true model forecasting the output parameters from unknown set of input parameters as close as possible. ...
Article
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This paper investigates the stochastic behaviour of hydrodynamic journal bearings by solving the Reynolds equation with random parameters numerically based on finite difference method. The steady state and dynamic characteristics are quantified considering random variabilities in eccentricity and surface roughness that can closely simulate the uncertain service conditions and inevitable manufacturing imperfections. Based on efficient radial basis function, a Monte Carlo simulation (MCS) algorithm is developed in conjunction with the governing equations for quantifying stochastic characteristics of the crucial performance parameters concerning hydrodynamic bearings. Relative sensitivity to stochasticity for different performance parameters is analysed. Physically insightful new results are presented in a probabilistic framework, wherein it is observed that the stochasticity has pronounced influence on the performance of bearing.
... Recently researchers (Patil et al., 2017;Deierling and Zhupanska, 2018;Gopinath and Batra, 2018;Zhu et al., 2018;Zhou et al., 2020;Mukhopadhyay et al., 2016) investigated the effective properties of composites using methods based on homogenization and RVE/unit cell technique. Patil et al. (2017) predicted the effective properties of heterogeneous materials by applying the extended as well as multiscale FE method (XFEM and MsFEM) in which the particles and voids were incorporated into the matrix. ...
Article
This article presents different micromechanical modelling techniques based on analytical and numerical approaches to determine the effective elastic and piezoelectric (piezoelastic) properties of graphene-based composite materials. Different types, orientations and shapes as well as different geometrical parameters of fiber reinforcement are considered for estimating the effective properties. The effective properties of composite are predicted with and without considering the strong covalent bond which provides interaction and in-plane stability of 2Dcrystalline graphene or strong van der Wall forces formed between graphene layers and the matrix. It is revealed that the axial, transverse and shear effective piezoelastic properties of graphene reinforced piezoelectric composite (GRPC) are significantly enriched due to the incorporation of graphene into the epoxy matrix. The importance of incorporating graphene as nanofillers/interphase into the conventional epoxy matrix to form an advanced composite and its effective properties are illustrated while these results show excellent agreement with previously reported experimental estimates. These results reveal that due to incorporation of graphene nanofillers, there is a significant enhancement in effective properties of composite. The results would also help to recognize the most important material properties with respect to different shapes and orientation of reinforcements which influences the performance of system significantly. To confirm safety, robustness and sustainability of the structure, it is the most prior requirement to determine the effective properties of composites considering different parameters for the different static and structural analyses.
... The ease of handling, lack of requirement for heavy lifting and handling equipment, and corrosion resistance are some other factors that are advantageous in the repair, retrofitting, and rehabilitation of civil engineering structures. Because of continuous research and development on new composite materials [3][4][5][6], the use of such materials is found to be advantageous in terms of weight sensitivity and cost effectiveness. ...
... But for safe and economical design of these hybrid FG-sandwich structures, it is very necessary to consider these uncertainties [10,11,16,[64][65][66]. Probabilistic approaches for predicting uncertainty-based dynamic responses in case of complex structures like composite plates and shells have gained extreme attention from the researchers [9,17,51,52]. Uncertainty in the field of dynamic stability of composites was studied [15,[26][27][28][29][30][31]. ...
Chapter
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The present chapter investigates the moment-independent sensitivity analysis for hybrid sandwich structures (having cylindrical shell geometry) subjected to low-velocity impact. These hybrid structures are extensively used in lightweight applications where thermal exposure/resistance is of prime importance. Here, the FG facesheet is placed at the upper layer of core whereas laminated composite facesheet is kept at lower layer so that the structure can sustain high-temperature exposure at reduced weight because of laminated composite facesheet at the inner layer of the core. The probabilistic study is performed for the transient impact response of the structure which in turn utilized to assess the sensitiveness of the parameters. The computational efficiency is achieved by implementing polynomial chaos expansion (PCE) metamodel in conjunction with Monte Carlo simulation (MCS). The results illustrate the parameters which significantly affect the transient impact response of the structure.
... There are also some studies belonging to Dey et. al. [12,13] those deal with the uncertainty in composites via a surrogate based approach. Nguyen et. ...
Article
Statistical Moment (SM) based modelling is a quite straightforward approach in stochastic modelling of uncertain structures. However, the method still has deficiencies including determination of SMs of natural frequencies of vibratory structures, and it has not been tested yet for realistic structures. This study aims such verification by employing high-degree statistical moments in stochastic equations. In this respect, SM approach is applied for two different uncertainty cases. In the first case, uncertain parameters are experimentally reproduced from the batch of laminated composite beams. Then, those uncertainties are fed to SM equations used in finite element model to obtain descriptive statistical quantities (mean, variance, skewness, and kurtosis) of stochastic natural frequencies. Next, Pearson model is utilized to obtain probability density function of the natural frequency by using standardized SMs. Beside this, uncertain fundamental natural frequency of fifty samples of composite beams is measured by experimental modal tests. All SM based predictions and modal test results are also compared with numerical Monte Carlo Simulations. The latter case examines composite beams having nonnormal uncertain thickness. Since the results are in good harmony with each other, it is concluded that high-order SM based approach may effectively be used in uncertainty modelling of realistic structures.
... A significant number of relatively recent works concentrate on the aspect of material and geometric uncertainty of the micro and macro mechanical parameters of composites including the aspect of different forms of defects [46][47][48][49][50][51][52][53][54][55][56]. Machine learning assisted approaches have attracted the attention of researchers lately for achieving computational efficiency and obtaining better insights [57][58][59][60][61][62][63]. The aspect of sensitivity analysis for laminated composites has been addressed by a limited number of studies, albeit considering the performance parameters individually [64][65][66][67]. ...
Article
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The present paper proposes a surrogate-assisted moment-independent stochastic sensitivity analysis of laminated composite plates for establishing a unified measure in the case of multi-objective performances. With the advancements in artificially engineered structural systems spanning across different length scales, it has become more common to design composite structures for multi-objective performances like the criteria of deflection, buckling and vibration of multiple modes, different impact parameters, and failure. Normally sensitivity analysis is carried out separately and individually for different such performance parameters. This paradigm is no more suitable for advanced multi-functional structures like composite laminates. In this article, we propose an efficient unified sensitivity analysis approach based on weighted relative importance of different performance parameters by introducing the notion of engineering judgment. A moment-independent sensitivity analysis is proposed here based on finite element modeling of composites in conjunction with the Least Angle Regression assisted Polynomial Chaos Expansion (PCE) to achieve computational efficiency without compromising the outcome. Such surrogate-assisted finite element approaches are particularly crucial for computationally intensive multi-objective systems like composites. The layer-wise unified sensitivity quantification of laminated composites considering multi-functional objectives, as presented here, would lead to more optimized designs and better quality control while manufacturing the complex advanced structural systems.
... Instead, surrogate model approaches, which are constructed based on a limited set of actual input/output data points, are a suitable method when dealing with such complex problems. Several surrogate models have been reported in the literature to evaluate uncertainties in composite laminates, such as Kriging method, 18,19 radial basis function, 20 polynomial chaos expansion (PCE), 15,21,22 and artificial neural network. 23,24 State-of-the-art reviews on the surrogate models for evaluating the uncertainty in structural responses of composite laminates can be found in reference. ...
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... Therefore, reliability analysis along with progressive damage analysis of composite structures is a challenging approach. Recently, surrogate models (also known as metamodels) have been used as a useful tool for enabling uncertainty quantification in presence of a large number of costly model evaluations, as it replaces an expensive high-fidelity model with a cheap whilst trained surrogate model [18][19][20]. Mukhopadhyay et al. [21] have presented a precious and concise review on surrogate-based uncertainty quantification algorithms. In addition to this, for stochastic natural frequency analysis of composite laminates, they carried out a comparative analysis for evaluation of different surrogate models from the viewpoint of computational efficiency and accuracy. ...
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Progressive damage analysis of composite structures in the presence of uncertainties is a computationally-expensive and highly-complex process. This work tackles these issues by developing efficient finite element (FE)-based surrogate models that are constructed with artificial neural network (ANN) models and design of experiment (DOE) methods. The proposed framework for building surrogate models (metamodels) can capture various multi-scale uncertainties. In addition, to alleviate the computational burden in non-deterministic analyses, a novel strategy is proposed using the Plackett-Burman method to determine sources of uncertainties that have significant impacts in scattering the response. The response surface methodology (RSM), in cooperation with FE analysis, is used to create datasets. The RSM-based and ANN-based metamodels are constructed by using these datasets. Both are tested on unseen data. Key results show that for complex models, ANN-based metamodels have better accuracy than RSM-based ones in prediction. The high accuracy built surrogate models are used for stochastic, probabilistic and reliability analysis of filament wound composite tubes. As a result, this multi-scale surrogate-based framework significantly decreases the computational time and cost of the analyses. Reliability analysis demonstrates that the statistical correlation between ply properties is significant, and it must be considered for accurate evaluation.
... They demonstrated that the approach is significantly faster than using ANN-based surrogates, without sacrificing any predictive capabilities. Mukhopadhyay et al. (2016) presented the impact of noise on stochastic natural frequency analyses based on surrogate models of composite laminates. They developed an algorithm for exploring the impact of noise in surrogate-based UQ methods and verified the approach for stochastic frequency analyses of spherical shallow shells using a surrogate model based on Kriging. ...
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The utilization of surrogate models to approximate complex systems has recently gained increased popularity. Because of their capability to deal with black-box problems and lower computational requirements, surrogates were successfully utilized by researchers in various engineering and scientific fields. An efficient use of surrogates can bring considerable savings in computational resources and time. Since literature on surrogate modelling encompasses a large variety of approaches, the appropriate choice of a surrogate remains a challenging task. This review discusses significant publications where surrogate modelling for finite element method-based computations was utilized. We familiarize the reader with the subject, explain the function of surrogate modelling, sampling and model validation procedures, and give a description of the different surrogate types. We then discuss main categories where surrogate models are used: prediction, sensitivity analysis, uncertainty quantification, and surrogate-assisted optimization, and give detailed account of recent advances and applications. We review the most widely used and recently developed software tools that are used to apply the discussed techniques with ease. Based on a literature review of 180 papers related to surrogate modelling, we discuss major research trends, gaps, and practical recommendations. As the utilization of surrogate models grows in popularity, this review can function as a guide that makes surrogate modelling more accessible.
... The ease of handling, lack of requirement for heavy lifting and handling equipment, and corrosion resistance are some other factors that are advantageous in the repair, retrofitting, and rehabilitation of civil engineering structures. Because of continuous research and development on new composite materials [3][4][5][6], the use of such materials is found to be advantageous in terms of weight sensitivity and cost effectiveness. ...
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Several approaches were used to explore the characteristics of reinforced concrete (RC) structural elements. Experimental work in the lab was extensively used as a means to examine the structural response and influence of different parameters under shear loads. Also, using numerical analysis to look into these components has been proven effective. This paper focuses on the shear conduct and response of circular beams reinforced with steel bars using the finite element (FE) model by considering the effect of reinforcement type and ratio, shear span-depth ratio (a/d), and member's size. The FE model results were confirmed with the experimental outcomes of full-scale circular RC specimens tested earlier by scientists. The outcomes from the numerical study displayed that the proposed finite element replica was capable of simulating the characteristics of the beams, tested experimentally in the lab, with credible accuracy. From the FE model, it was found that the concrete shear contribution is best described as a formula that is inversely proportional to the member's depth and directly proportional to the square root of axial stiffness of the reinforcement. Keywords: circular beams; finite element (FE); flexural reinforcement ratio; ratio; shear span-depth ratio (a/d); shear strength; size effect; steel. INTRODUCTION Circular reinforced concrete (RC) members exist in many types of structures. Many of these members usually experience severe transversal/shear loads generated from earthquakes and/or wind stresses. As a consequence, a significant amount of shear load is applied to the member's cross section (Ali et al. 2020). Realizing and grasping the behavior of the RC members during loading is paramount to construct a completely safe and efficacious structure. In the last decade, the shear strength of fiber-reinforced polymer (FRP) RC members with rectangular cross sections received considerable attention. The experimental work focused mainly on beams without web reinforcement, but limited research has addressed beams with circular cross section. Yet, no finite element model or numerical equations have investigated circular concrete members reinforced with steel or FRP reinforcement under shear loads. In general, shear design provisions can be applied to circular members by using an equivalent rectangular cross section. The accuracy of such an approach should, however, be assessed because a circular section may not contribute to shear strength in the same way as a rectangular section. Circular members usually have longitudinal reinforcement uniformly distributed around the section's perimeter. This reinforcement reduces crack propagation above the neutral axis and limits crack width, which, in turn, increases the contributions of aggregate interlock. Moreover, these bars add to the dowel mechanism in resisting the relative transverse displacement between two
... Both the methods are found to perform satisfactorily for all the three structures upto a noise level of 1.5%. Subsequently, Mukhopadhyay et al. [402,403] quantified the effect of noise on machine learning based uncertainty quantification of polymer composites. Saseendran et al. [404] analyzed the impact of noise on two ML algorithms namely, polynomial and linear regression with ridge regularization. ...
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The superior multi-functional properties of polymer composites have made them an ideal choice for aerospace, automobile, marine, civil, and many other technologically demanding industries. The increasing demand of these composites calls for an extensive investigation of their physical, chemical and mechanical behavior under different exposure conditions. Machine learning (ML) has been recognized as a powerful predictive tool for data-driven multi-physical modeling, leading to unprecedented insights and exploration of the system properties beyond the capability of traditional computational and experimental analyses. Here we aim to abridge the findings of the large volume of relevant literature and highlight the broad spectrum potential of ML in applications like prediction, optimization, feature identification, uncertainty quantification, reliability and sensitivity analysis along with the framework of different ML algorithms concerning polymer composites. Challenges like the curse of dimensionality, overfitting, noise and mixed variable problems are discussed, including the latest advancements in ML that have the potential to be integrated in the field of polymer composites. Based on the extensive literature survey, a few recommendations on the exploitation of various ML algorithms for addressing different critical problems concerning polymer composites are provided along with insightful perspectives on the potential directions of future research.
... Subsequently, Mukhopadhyay et al. [402,403] quantified the effect of noise on machine learning based uncertainty quantification of polymer composites. Saseendran et al. [404] analyzed the impact of noise on two ML algorithms namely, polynomial and linear regression with ridge regularization. ...
Preprint
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The superior multi-functional properties of polymer composites have made them an ideal choice for aerospace, automobile, marine, civil, and many other technologically demanding industries. The increasing demand of these composites calls for an extensive investigation of their physical, chemical and mechanical behavior under different exposure conditions. Machine learning (ML) has been recognized as a powerful predictive tool for data-driven multi-physical modeling, leading to unprecedented insights and exploration of the system properties beyond the capability of traditional computational and experimental analyses. Here we aim to abridge the findings of the large volume of relevant literature and highlight the broad spectrum potential of ML in applications like prediction, optimization, feature identification, uncertainty quantification, reliability and sensitivity analysis along with the framework of different ML algorithms concerning polymer composites. Challenges like the curse of dimensionality, overfitting, noise and mixed variable problems are discussed, including the latest advancements in ML that have the potential to be integrated in the field of polymer composites. Based on the extensive literature survey, a few recommendations on the exploitation of various ML algorithms for addressing different critical problems concerning polymer composites are provided along with insightful perspectives on the potential directions of future research.
... The finite element modelling (in the case of computationally intensive simulation of repetitive nature) [55,[95][96][97][98][99][100][101] can be an alternate way where inefficient analytical solutions [92][93][94] are not possible. The surrogate modelling ...
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Purpose: This paper presents the sensitivity analysis (SA) of the random natural frequency responses of hybrid multi-functionally graded sandwich (HMGS) shells for establishing a unified measure in the case of multi-objective performances. The functionally graded materials, laminated composites, and sandwich cores are employed to develop such novel structures to tailor the benefits of each component in a single structure. Methods: A novel MARS-based sensitivity analysis of these hybrid multi-functionally graded sandwich shells is developed to achieve computational efficiency without compromising the outcome. Such surrogate-assisted FE approaches are crucial for computationally intensive multi-objective systems. The basic governing equations of random natural frequency are framed based on finite element formulation. The variabilities of major influencing random input parameters (here, geometric and material properties) are carried out by employing Monte Carlo simulation (MCS). The multivariate adaptive regression spline (MARS) is adopted as a surrogate model to increase computational efficiency. Results and Conclusion: The results are portrayed to showcase the significant effects of variable input parameters (sensitivity) on random frequency responses of such novel HMGS shells. Hence, it provides the predominant random input parameters and their relative degree of importance while designing such multi-dimensional structural systems. Thus, the contribution of this article lies in both the development of a computationally efficient sensitivity analysis approach and the insightful numerical results for hybrid structures presented thereafter. The comprehensive and collective sensitivity quantification considering multi-functional objectives, as presented in this article, would lead to efficient computational modeling of complex structural systems for more optimized designs and better quality control during manufacturing.
... Though it is not possible to completely eliminate these sources of uncertainties, they can be reduced by making the better prediction models by making use of simulated noisy datasets [67]. To create the simulated noisy dataset from traditional design dataset which is used for the formation of surrogate model, a Gaussian white noise is introduced which has a specific variance level (p), in the set of responses [68], while the inputs are kept unchanged. ...
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Over the last few decades, uncertainty quantification in composite materials and structures has gained a lot of attention from the research community as a result of industrial requirements. This book presents computationally efficient uncertainty quantification schemes following meta-model-based approaches for stochasticity in material and geometric parameters of laminated composite structures. Several metamodels have been studied and comparative results have been presented for different static and dynamic responses. Results for sensitivity analyses are provided for a comprehensive coverage of the relative importance of different material and geometric parameters in the global structural responses.
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Chapter
In the present chapter, multivariate adaptive regression splines (MARS) is explored as a surrogate model in conjunction to Monte Carlo simulation (MCS) to analyse the random first-ply failure loads of graphite–epoxy laminated composite plates. The five failure criteria, namely maximum strain theory, maximum stress theory, Tsai–Hill theory, Tsai–Wu theory, and Hoffman theory, are considered. The numerical validation of deterministic failure load is presented first. Thereafter, a concise investigation is carried out to examine the capability of MARS model for efficiently predicting the first-ply failure loads. Comparative results are presented using scatter plots and probability density function plots to access the prediction capability with respect to direct MCS. The current results portray the successful application of MARS as the surrogate model to achieve computational efficiency and analyse the first-ply failure loads.
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The initiation and propagation of uncertainties in structural behaviour of complex anisotropic sandwich structure has significant computational challenges. Due to limitation of experimental data, probabilistic descriptions of uncertain parameters are not practically feasible to expedite. This paper presents the prediction capability of surrogate model (polynomial neural network) to estimate the stochastic buckling behaviour of sandwich plates. The polynomial neural network (PNN) is utilized to construct the surrogate. The computational time and cost is significantly reduced by using the proposed model in conjunction to finite element model employing higher order zigzag theory (HOZT). Both material and geometric uncertainties are considered to obtain the statistical quantity of interest (QoI). The computational efficacy of PNN is validated by means of scatter plot and probability density function plot. The constructed PNN-model is found to be convergent with the results obtained by direct Monte Carlo simulation (MCS) techniques. The proposed model can be used for more complex structures in future.
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In this paper a high precision composite plate bending element has been presented and its application to the analysis of isotropic and composite folded plates has been shown to study the performance of the element. In the present element the effect of shear deformation has been considered. Numerical examples have been solved by the proposed element and the results obtained in the form of bending moment, in-plane force and deflection have been compared with the published results (where available) to show the potentiality of the element. Number of new results have been presented, which are expected to be useful in future research.
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The first known solution of the title problem is presented. The Ritz method is used, with algebraic polynomials forming the set of trial functions. The condition that all three components of displacement be zero at the four corners is straightforwardly enforced. Numerical studies show that the convergence is relatively slow, requiring more terms than for shells which are completely free. The class of problems studied includes independent, constant curvature in each of the directions parallel to the edges, yielding vibration modes which fall into one of four symmetry classes, with symmetry or antisymmetry of the displacements existing with respect to each of the two symmetry axes of the problem. Detailed results are given for the frequencies and mode shapes of the first two modes of each symmetry class for shells having square planform and circular cylindrical, spherical and hyperbolic paraboloidal curvatures. Accuracy of the results is partially established by comparison with other previously published, accurate results for the corner supported flat square plate.
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This paper describes a novel method for a stochastic analysis of a multiscale homogenization problem. An inhomogeneous material such as a composite material has a complex microstructure, and sometimes it has an uncertainty in geometry or a material property of a microstructure. This microscopic uncertainty will cause dispersion of a macroscopic homogenized material property of a composite material. In order to analyze this problem, an approximation-based stochastic analysis approach is developed.The proposed method uses a flexible approximation technique and variable transformation of a probabilistic density function. In this paper, the Kriging method is used for approximation and integral estimation of a probabilistic density function.As a numerical example, a stochastic response analysis for a homogenized elastic tensor and homogenized elastic constants of a unidirectional fiber reinforced composite material is performed using the Monte-Carlo simulation, the perturbation-based homogenization method and the proposed method. Uncertainties in material properties and geometry of a microstructure of a unidirectional fiber reinforced composite plate are taken into account. From the numerical results, validity and effectiveness of the proposed method are shown.
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A finite element analysis for studying the free vibration behaviour of generalized doubly curved laminated composite shells is presented using eight-noded curved quadrilateral isoparametric finite elements. The formulation assumes first-order shear deformation theory for thin and shallow shells, and also considers the two principal radii of curvature and the radius of cross-curvature. Some of the results obtained are compared with those present in the existing literature. Several other numerical results are presented by varying fibre orientations, lamination schemes, support spacings, aspect ratio, lower height to higher height ratio (for conoids), the thickness to radius ratio and radii of curvature ratio (for elliptic and hyperbolic paraboloids), which are relevant to the doubly curved shells.
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The Ritz method with algebraic polynomial displacement functions is used to analyze free vibrations of thin cantilevered laminated plates and shallow shells having rectangular planforms. Convergence studies are made which demonstrate that accurate results are obtained using 192 displacement terms for spherical, circular cylindrical, hyperbolic paraboloidal shallow shells and 64 terms for plates. Results are compared with those obtained experimentally and by finite element methods. It is found that the present method needs considerably less degrees of freedom than the finite element method to obtain the same accuracy and compares well with results from experiment. The effect of various parameters (material, number of layers, fiber orientation, curvature) upon the frequencies is studied.
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A Monte Carlo procedure was developed for optimizing symmetric fiber reinforced composite laminates such that the weight is minimum and the Tsai-Wu strength failure criterion is satisfied in each ply. The laminate may consist of several materials including an idealized core, and may be subjected to several sets of combined in-plane and bending loads. The procedure yields the number of plies, the fiber orientation, and the material of each ply and the material and thickness of the core. A user friendly computer code was written for performing the numerical calculations. Laminates optimized by the code were compared to laminates resulting from existing optimization methods. These comparisons showed that the present Monte Carlo procedure is a useful and efficient tool for the design of composite laminates.
Finite Element Procedures in Engineering Analysis, PHI, New Delhi. [27] Meirovitch L., (1992) Dynamics and Control of Structures Use of Kriging models to approximate deterministic computer models
  • K J Bathe
Bathe K.J., (1990) Finite Element Procedures in Engineering Analysis, PHI, New Delhi. [27] Meirovitch L., (1992) Dynamics and Control of Structures, John Wiley & Sons, New York. [28] Martin J.D., Simpson T.W., (2005) Use of Kriging models to approximate deterministic computer models, AIAA Journal, 43(4), 853–863.
Structural damage identification: a RS-HDMR approach
  • T Mukhopadhyay
  • R Chowdhury
  • A Chakrabarti
Mukhopadhyay T., Chowdhury R., Chakrabarti A. (2016) Structural damage identification: a RS-HDMR approach, Advances in Structural Engineering (In Press)