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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.

The purpose of this study is to investigate the bending analysis of metal (Ti-6Al-4V)-ceramic (ZrO₂) functionally graded material (FGM) sandwich plate with material property gradation along length and thickness direction under thermo-mechanical loading using inverse trigonometric shear deformation theory (ITSDT). FGM sandwich plate with a ceramic core and continuous variation of material properties has been modelled using Voigt’s micro-mechanical model following the power law distribution method. The impact of bi-directional gradation of material properties over the bending response of FGM plate under thermo-mechanical loading has been investigated in this work.

In this study, gradation of material properties for FGM plates is considered along length and thickness directions using Voigt’s micromechanical model following the power law distribution method. This type of FGM is called bi-directional FGMs (BDFGM). Mechanical and thermal properties of BDFGM sandwich plates are considered temperature-dependent in the present study. ITSDT is a non-polynomial shear deformation theory which requires a smaller number of field variables for modelling of displacement function in comparison to poly-nominal shear deformation theories which lead to a reduction in the complexity of the problem. In the present study, ITSDT has been utilized to obtain the governing equations for thermo-mechanical bending of simply supported uni-directional FGM (UDFGM) and BDFGM sandwich plates. Analytical solution for bending analysis of rectangular UDFGM and BDFGM sandwich plates has been carried out using Hamilton’s principle.

The bending response of the BDFGM sandwich plate under thermo-mechanical loading has been analysed and discussed. The present study shows that centre deflection, normal stress and shear stress are significantly influenced by temperature-dependent material properties, bi-directional gradation exponents along length and thickness directions, geometrical parameters, sandwich plate layer thickness, etc. The present investigation also reveals that bi-directional FGM sandwich plates can be designed to obtain thermo-mechanical bending response with an appropriate selection of gradation exponents along length and thickness direction. Non-dimensional centre deflection of BDFGM sandwich plates decreases with increasing gradation exponents in length and thickness directions. However, the non-dimensional centre deflection of BDFGM sandwich plates increases with increasing temperature differences.

For the first time, the FGM sandwich plate with the bi-directional gradation of material properties has been considered to investigate the bending response under thermo-mechanical loading. In the literature, various polynomial shear deformation theories like first-order shear deformation theory (FSDT), third-order shear deformation theory (TSDT) and higher-order shear deformation theory (HSDT) have been utilized to obtain the governing equation for bending response under thermo-mechanical loading; however, non-polynomial shear deformation theory like ITSDT has been used for the first time to obtain the governing equation to investigate the bending response of BDFGM. The impact of bi-directional gradation and temperature-dependent material properties over centre deflection, normal stress and shear stress has been analysed and discussed.

The purpose of this study is to propose generalised integral transform technique (GITT) to obtain the exact solutions for bending of clamped parallelogram plate resting on elastic foundation.

The GITT is used to solve the bending problem of the full clamped parallelogram plate under an elastic foundation. The auxiliary problem was developed and the corresponding eigenfunction and eigenvalue were calculated simultaneously. The original partial differential governed equation has been represented by the transformed ordinary differential equation system and solved by the subroutine DBVPFD from International Mathematics and Statistics Library.

The GITT has been proven to be an efficient approach to solve the bending problem of the plate with different loads, boundary conditions and elastic foundations. The parametric study indicates that the elastic foundation modulus has significant contribution in reducing the vertical deflections and moments for both rectangular and parallelogram plates. With the increasing of aspect ratio (a/b) and the elastic foundation modulus, the trends of the deflection and moment reduction decreased significantly.

The present hybrid analytical-numerical methodology was first used to solve the mechanics problem of the clamped parallelogram plate resting on elastic foundation. Excellent convergence and high accuracy was observed by comparing with the published results. It exhibits potential application to investigate the mechanics problem of the composite plate with different boundary conditions in the shipbuilding and civil engineering.

It has been revealed that application of the differential form of Eringen’s nonlocal elasticity theory to some cases (e.g. cantilevers) leads to paradoxical results, and recourse must be made to the integral version of Eringen’s nonlocal model. The purpose of this paper, within the framework of integral form of Eringen’s nonlocal theory, is to study the bending behavior of nanoscale plates with various boundary conditions using the isogeometric analysis (IGA).

The shear deformation effect is taken into account according to the Mindlin plate theory, and the minimum total potential energy principle is utilized in order to derive the governing equations. The relations are obtained in the matrix-vector form which can be easily employed in IGA or finite element analysis. For the comparison purpose, the governing equations are also derived based on the differential nonlocal model and are then solved via IGA. Comparisons are made between the predictions of integral nonlocal model, differential nonlocal model and local (classical) model.

The bending analysis of nanoplates under some kinds of edge supports indicates that using the differential model leads to paradoxical results (decreasing the maximum deflection with increasing the nonlocal parameter), whereas the results of integral model are consistent.

A new nonlocal formulation is developed for the IGA of Mindlin nanoplates. The nonlocal effects are captured based on the integral model of nonlocal elasticity. The formulation is developed in matrix-vector form which can be readily used in finite element method. Comparisons are made between the results of differential and integral models for the bending problem. The proposed integral model is capable of resolving the paradox appeared in the results of differential model.

This study aims to propose a numerical modeling procedure for response analysis of elastic body floating in water and submitted to regular waves. An equivalent simplified mechanical single-degree-of-freedom system allowing to reproduce the heave movements is first developed, then the obtained lumped characteristics are used for elastic analysis of the floating body in heave motion.

First, a two-dimensional numerical model of a rigid floating body in a wave tank is implemented under DualSPHysics, an open source computational fluid dynamics (CFD) code based on smoothed particle hydrodynamics method. Then, the obtained results are exploited to derive an equivalent mechanical mass-spring-damper model. Finally, estimated equivalent characteristics are used in a structural finite element modeling of the considered body assuming elastic behavior.

Obtained results concerning the floating body displacements are represented and validated using existing experimental data in the literature. Wave forces acting on the body are also evaluated. It was found that for regular waves, it is possible to replace the complex CFD refined model by an equivalent simplified mechanical system which makes easy the use of structural finite element analysis.

The originality of this work lies in the proposed procedure to evaluate the mechanical properties of the equivalent elastic system. This allows to couple two different software tools and to take advantages of their features.

The purpose of this paper is to parametrically investigate the vibration and damping characteristics of a functionally graded (FG) inhomogeneous and porous curved sandwich beam with a frequency-dependent viscoelastic core.

The FG material properties in this study are assumed to vary through the beam thickness by power law distribution. Additionally, FG layers have porosities, which are analyzed individually in terms of even and uneven distributions. First, the equations of motion for the free vibration of the FG curved sandwich beam were derived by Hamilton's principle. Then, the generalized differential quadrature method (GDQM) was used to solve the resulting equations in the frequency domain. Validation of the proposed FG curved beam model and the reliability of the GDQ solution was provided via comparison with the results that already exist in the literature.

A series of studies are carried out to understand the effects on the natural frequencies and modal loss factors of system parameters, i.e. beam thickness, porosity distribution, power law exponent and curvature on the vibration characteristics of an FG curved sandwich beam with a ten-parameter fractional derivative viscoelastic core material model.

This paper focuses on the vibration and damping characteristics of FG inhomogeneous and porous curved sandwich beam with frequency dependent viscoelastic core by GDQM – for the first time, to the best of the authors' knowledge. Moreover, it serves as a reference for future studies, especially as it shows that the effect of porosity distribution on the modal loss factor needs further investigation. GDQM can be useful in dynamic analysis of sandwich structures used in aerospace, automobile, marine and civil engineering applications.

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 is given. The bibliography at the end of the paper contains 1,726 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 1996‐1999.

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 purpose of this study was to investigate the changes in solder joint stress when subjected to mechanical bending. The analytical theory pertaining to the stresses in the solder joint between the components (including the molding compound, the chip and the substrate) was described, and the printed circuit board (PCB) with a discontinuity function when the PCB assembly is subjected to mechanical bending was developed. Thus, the findings reported here may lead to a better understanding of the solder joint failure based on the Physics of Failure model.

This paper discusses the analytical model for calculating the stress in solder joints, as well as presents a simulation model that can be used for calculating the strain energy density of solder joint. First, the multilayer plate theory is used in discussing the composite material for the component, including the molding compound, the silicon chip and the substrate, or the PCB, including the copper layers, the fiber and the epoxy. Finally, the complete structure of the analytical model developed as a part of this current work is presented.

For the analytical model of multilayer structures in which the interconnection layer is discrete, mechanical bending has been modeled with respect to varying silicon chip length. The analytical model that describes the stress of the outermost solder joint experiences is chosen, as this is the typical solder joint failure. The analytical model can be applied to discrete solder joints, which are evaluated by calculating the matrix form. Owing to its use of the matrix equation, the analytical model can be highly combinatorial and thus more capable of calculating the solution.

The analytical solution based on a simple concept was presented and validated using the finite element model for the stress experienced by solder joints subjected to mechanical bending. To verify that the simulation represents a real PCB case, the authors use the finite element method (FEM) to compare their case with the multilayer plate theory. Owing to the good agreement between the theory and simulation results, the authors conclude that the multilayer plate theory can be correctly applied in multilayer PCB and be used in an analytical model for the PCB assembly subjected to mechanical bending.

Owing to the good agreement between the theory and simulation results, the authors conclude that the multilayer plate theory can be correctly applied in multilayer PCB and be used in an analytical model for the PCB assembly subjected to mechanical bending.

The analytical model is validated with the FEM model and provides the way to physically examine the solder joint failure mechanism. In this paper, the analytical model is developed as a means to assess the solder joint stress subjected to mechanical bending.

The analytical model treats the solder joint as discrete and has been successfully validated against the finite element model. The complete structure model (the second analytical model) is presented to discuss the effects of varying silicon chip length on the normal stress in solder joints. When the silicon chip length exceeds to 80 per cent of the total package length, the stress of the outermost solder joint increases rapidly. The design analysis findings have suggested that the failure of the outermost solder joint subjected to mechanical bending on the PCB assembly can be reduced by analyzing the analytical model.

The purpose of this paper is to demonstrate new design concepts for 24 classes of laminate, which have been derived as part of an ongoing study on the development of a unified approach to the characterization of coupled laminates. The paper presents a description of each class of coupled laminate.

The paper gives an overview of the desired performance and requirements of a smart leading edge device, its aerodynamic design for the wind tunnel tests and the structural pre‐design and sizing of the full‐scale leading edge section which will be tested in the wind tunnel.

Coupled laminates have potential applications in the design of aero‐elastic compliant rotor blades or aircraft wing structures, by introducing tailored extension‐twist and/or shear‐extension coupling at the laminate level; or in the design of thermally activated morphing structures, by exploiting more complex coupling behaviour.

These laminates contain standard cross‐ply and/or angle‐ply combinations, although double angle‐ply laminates are also considered, and correspond to any standard fibre/matrix system with a constant ply thickness throughout.

The vast majority of the laminate described possess coupling behaviour not previously identified in the literature.