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The main objective of this study is to develop a numerical model based on Isogeometric Analysis to study the dynamic behavior of multi-directional functionally graded plates with variable thickness.

A numerical study was conducted on the dynamic behavior of multi-directional functionally graded plates. Rectangular and circular plates with variable thickness are taken into investigation. The third-order shear deformation plate theory of Reddy is used to describe the displacement field, while the equation of motion is developed based on the Hamilton's principle. Isogeometric Analysis approach is employed as a discretization tool to develop the system equation, where NURBS basis functions are used. The famous Newmark method is used to solve time-dependent problems.

The results obtained from this study indicated that the thickness gradation has a more considerable effect than in-plane variation of materials in MFGM plates. Additionally, the influence of the damping factor is observed to affect the vibration amplitude of the plate. The results obtained from this study could be used for future investigations, where the viscous elasticity and other dynamic factors are considered.

Although there have been a number of studies in the literature devoted to analyzing the linear static bending and free vibration of FGM and MFGM plates with variable thickness, the study on dynamic response of FGM and MFGM plate is still limited. Therefore, this study is dedicated to the investigation of the dynamic behavior of multi-directional functionally graded plates.

The optimization of variable thickness plates and shells is studied. In particular, three types of shell are considered: hyperbolic paraboloid, conoid and cylindrical shell. The main objective is to investigate the optimal thickness distributions as the geometric form of the structure changes from a plate to a deep shell. The optimal thickness distribution is found by use of a structural optimization algorithm which integrates the Coons patch technique for thickness definition, structural analysis using 9‐node Huang‐Hinton shell elements, sensitivity evaluation using the global finite difference method and the sequential quadratic programming method. The composition of the strain energy is monitored during the optimization process to obtain insight into the energy distribution for the optimum structures. Several benchmark examples are considered illustrating optimal thickness variations under different loading, boundary and design variable linking conditions.

The purpose of this study is to propose a generalized integral transform technique (GITT) to investigate the bending behavior of rectangular thin plates with linearly varying thickness resting on a double-parameter foundation.

The bending of plates with linearly varying thickness resting on a double-parameter foundation is analyzed by using the GITT for six combinations of clamped, simply-supported and free boundary conditions under linearly varying loads. The governing equation of plate bending is integral transformed in the uniform-thickness direction, resulting in a linear system of ordinary differential equations in the varying thickness direction that is solved by a fourth-order finite difference method. Parametric studies are performed to investigate the effects of boundary conditions, foundation coefficients and geometric parameters of variable thickness plates on the bending behavior.

The proposed hybrid analytical-numerical solution is validated against a fourth-order finite difference solution of the original partial differential equation, as well as available results in the literature for some particular cases. The results show that the foundation coefficients and the aspect ratio b/a (width in the y direction to height of plate in the x direction) have significant effects on the deflection of rectangular plates.

The present GITT method can be applied for bending problems of rectangular thin plates with arbitrary thickness variation along one direction under different combinations of loading and boundary conditions.

This paper aims to contribute novel insights into the analysis of thin functionally graded material (FGM) plates with variable thickness, considering both temperature-dependent and independent material properties, focusing on critical linear buckling temperature rise and the effect of critical linear moisture for various moisture concentrations.

The study derives stability and equilibrium equations for thin rectangular FGM plates under hygrothermal loading, employing classical plate theory (CPT). Buckling behavior is examined using Galerkin’s method to obtain pre-buckling force resultants.

The findings highlight significant increases in critical buckling temperature with aspect ratio, distinct temperature sensitivity between materials and increasing moisture susceptibility with larger aspect ratios. These insights inform material selection and design optimization for FGM plates under hygrothermal loading, enhancing engineering applications.

This research primarily focuses on hypothetical scenarios and mathematical model development and analysis.

This paper presents original contributions in the field by addressing the hygrothermal buckling analysis of thin FGM rectangular plates with variable thickness, utilizing CPT, thereby enriching the understanding of structural behavior in varying environmental conditions.

The resistance of steel plate shear walls (SPSW) under explosive loads is evaluated using nonlinear FE analysis and surrogate methods. This study uses the conventional weapons effect program (CONWEP) model for the explosive load and the Johnson-Cook model for the steel plate. Based on the Taguchi method, 25 samples out of 100 samples are selected for a parametric study where we predict the damaged zones and the maximum deflection of SPSWs under explosive loads. Then, this study uses a multiple linear regression (MLR), multiple Ln equation regression (MLnER), gene expression programming (GEP), adaptive network-based fuzzy inference (ANFIS) and an ensemble model to predict the maximum detection of SPSWs. Several statistical parameters and error terms are used to evaluate the accuracy of the different surrogate models. The results show that the cross-section in the y-direction and the plate thickness have the most significant effects on the maximum deflection of SPSWs. The results also show that the maximum deflection is related to the scaled distance, i.e. for a value of 0.383. The ensemble model performs better than all other models for predicting the maximum deflection of SPSWs under explosive loads.

The SPSW under explosive loads is evaluated using nonlinear FE analysis and surrogate methods. This study uses the CONWEP model for the explosive load and the Johnson-Cook model for the steel plate. Based on the Taguchi method, 25 samples out of 100 samples are selected for a parametric study where we predict the damaged zones and the maximum deflection of SPSWs under explosive loads. Then, this study uses a MLR, MLnER, GEP, ANFIS and an ensemble model to predict the maximum detection of SPSWs. Several statistical parameters and error terms are used to evaluate the accuracy of the different surrogate models. The results show that the cross-section in the y-direction and the plate thickness have the most significant effects on the maximum deflection of SPSWs. The results also show that the maximum deflection is related to the scaled distance, i.e. for a value of 0.383. The ensemble model performs better than all other models for predicting the maximum deflection of SPSWs under explosive loads.

The resistance of SPSW under explosive loads is evaluated using nonlinear FE analysis and surrogate methods. This study uses the CONWEP model for the explosive load and the Johnson-Cook model for the steel plate. Based on the Taguchi method, 25 samples out of 100 samples are selected for a parametric study where we predict the damaged zones and the maximum deflection of SPSWs under explosive loads. Then, this study uses a MLR, MLnER, GEP, ANFIS and an ensemble model to predict the maximum detection of SPSWs. Several statistical parameters and error terms are used to evaluate the accuracy of the different surrogate models. The results show that the cross-section in the y-direction and the plate thickness have the most significant effects on the maximum deflection of SPSWs. The results also show that the maximum deflection is related to the scaled distance, i.e. for a value of 0.383. The ensemble model performs better than all other models for predicting the maximum deflection of SPSWs under explosive loads.

The resistance of SPSW under explosive loads is evaluated using nonlinear FE analysis and surrogate methods. This study uses the CONWEP model for the explosive load and the Johnson-Cook model for the steel plate. Based on the Taguchi method, 25 samples out of 100 samples are selected for a parametric study where we predict the damaged zones and the maximum deflection of SPSWs under explosive loads. Then, this study uses a MLR, MLnER, GEP, ANFIS and an ensemble model to predict the maximum detection of SPSWs. Several statistical parameters and error terms are used to evaluate the accuracy of the different surrogate models. The results show that the cross-section in the y-direction and the plate thickness have the most significant effects on the maximum deflection of SPSWs. The results also show that the maximum deflection is related to the scaled distance, i.e. for a value of 0.383. The ensemble model performs better than all other models for predicting the maximum deflection of SPSWs under explosive loads.

This paper deals with the buckling analysis of prismatic folded plate structures supported on diaphragms at two opposite edges. The analysis is carried out using variable thickness finite strips based on Mindlin‐Reissner assumptions which allow for transverse shear deformation effects. The theoretical formulation is presented for a family of C(0) strips and the accuracy and relative performance of the strips are examined. Results are presented for a series of problems including plates and stiffened panels. In a companion paper these accurate and inexpensive finite strips are used in the context of structural shape optimization.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Shells are widely used structural systems in engineering practice. These structures have been used in the civil, automobile and aerospace industries. Many shells are designed using the finite element analysis through the conventional and costly trial and error scheme. As a more efficient alternative, optimization procedures can be used to design economic and safe structures.

This paper presents developments, integration and applications of reliable and efficient computational tools for the structural optimization of variable thickness plates and free‐form shells. Topology, sizing and shape optimization procedures are considered here. They are applied first as isolated subjects. Then these tools are combined to form a robust and reliable fully integrated design optimization tool to obtain optimum designs. The unique feature is the application of a flexible integrally stiffened plate and shell formulation to the design of stiffened plates and shells.

This work showed the use of different optimization strategies to obtain an optimal design for plates and shells. Both topology optimization (TO) and structural shape optimization procedures were considered. These two optimization applications, as separate procedures produce new designs with a great improvement when compared to the initial designs. However, the combination of stiffening TO and sizing optimization using integrally stiffened shells appears as a more attractive tool to be used. This was illustrated with several examples.

This work represents a novel approach to the design of optimally stiffened shells and overcomes the drawbacks of both topology optimization and structural shape optimization procedures when applied individually. Furthermore, the unique use of integrally stiffened shell elements for optimization, unlike conventional shell‐stiffening optimization techniques, provided a general and extremely flexible tool.

While calculating internal forces of a structure resulting from temperature it is necessary to know thermal conduction and what goes hand in hand to determine temperature distribution at various points of the analysed structures. Finite strip method (FSM) is very suitable for the analysis of thermal conduction, heating, heat and temperature distribution in engineering structures, especially rectangular of identical edge conditions. The paper presents several examples of FSM application for the analysis of conduction and heat and temperature distribution for various types of engineering structures which can appear, among others, while welding several joined elements with welds made at specified speed as linear and point welds. Bars, shields, square and rectangular plates, steel orthotropic plates, steel and combined girders (steel‐concrete), box girders subject to various loads connected with heat and temperature (loaded with temperature, non‐uniformly heated surface). The obtained results may be useful in engineering practice for determining actual temperature and load capacity in individual elements of the construction.

A general solution for the small deflexions of thin plates of slowly varying thickness under lateral loading in the form of an influence function is briefly presented. It is known that the influence function may be represented as an infinite series in terms of the eigenfunctions and eigenvalues associated with a homogeneous form of the plate differential equation. It is suggested that the series may give an acceptable approximation to the influence function when summed over a small number of terms when also the eigenfunctions and eigenvalues involved are deduced by an approximate procedure of the Rayleigh‐Ritz type. In order to test this assertion a numerical example is given for a uniform canti‐lever plate and the results are compared with experiment and with similar results deduced by an alternative theoretical procedure. Thus the calculation of a sufficient number of approximate normal vibration modes and frequencies for the plate as normally required for aeroelastic investigations may in this way be made to serve as the basis for a complete analysis of the plate. A simple approximate allowance for shear deflexion of the plate is presented and illustrated.