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This paper aims to carry out comprehensively the static bending, free vibration, and buckling analyses of two-layer FGM plates with shear connectors resting on elastic foundations, where two-layer FGM plates resting on Winker's-Pasternak elastic foundations taking into account relative sliding movements are analyzed by using the combination of Navier's solution and finite element method based on nth-order shear deformation plate theory. The plate is made up of two layers of FG materials joined by metal shear connectors. Lagrange and Hermitian shape functions are used to establish stiffness matrices, mass matrices, geometric stiffness matrices, and element force vectors. The suggested method and mechanical model are accurate when compared to the computed data from this research and reputable literature. The computed data accurately describes the mechanical response of the structure. Then a series of parameter investigations are conducted to capture the effects of the structure's geometrical and material features on the mechanical behavior of two-layer FG plates. The numerical results of this study may be utilized as a basis for future research, applications, and design of similar structures in mechanical and civil engineering practice. This is also a critical foundation for studying the dynamic behavior of structures with shear connectors.

This paper aims to carry out comprehensively the static bending, free vibration, and buckling analyses of two-layer FGM plates with shear connectors resting on elastic foundations, where two-layer FGM plates resting on Winker's-Pasternak elastic foundations taking into account relative sliding movements are analyzed by using the combination of Navier's solution and finite element method based on nth -order shear deformation plate theory. The plate is made up of two layers of FG materials joined by metal shear connectors. Lagrange and Hermitian shape functions are used to establish stiffness matrices, mass matrices, geometric stiffness matrices, and element force vectors. The suggested method and mechanical model are accurate when compared to the computed data from this research and reputable literature. The computed data accurately describes the mechanical response of the structure. Then a series of parameter investigations are conducted to capture the effects of the structure's geometrical and material features on the mechanical behavior of two-layer FG plates. The numerical results of this study may be utilized as a basis for future research, applications, and design of similar structures in mechanical and civil engineering practice. This is also a critical foundation for studying the dynamic behavior of structures with shear connectors. [ABSTRACT FROM AUTHOR]

Based on the modified couple stress theory and the Timoshenko beam theory, the free vibration and buckling mechanics model for 2D functionally graded microbeams with variable cross sections was established by means of the variational principle. The model contains the intrinsic material length scale parameters of the metal and ceramic components, which can predict the size effects of microbeams. The Ritz method was used to obtain the numerical solution of the vibration frequencies and critical buckling loads of the microbeams under arbitrary boundary conditions. Numerical examples reveal that, when the thickness of the microbeam decreases, the dimensionless 1st-order frequency and the dimensionless critical buckling load will increase, and the scale effect will grow larger. The effect of the taper ratio on the dimensionless 1st-order frequency of the microbeam is closely related to the boundary conditions. At the same time, the effects of the taper ratios of the thickness and the width are also significantly different. The dimensionless 1st-order frequencies of microbeams increase with the material length scale parameter ratios of ceramic and metal, and the degrees of increase are different under different boundary conditions. The thick-direction and axial material gradient indexes also have significant influences on the free vibration and buckling behavior of the microbeam. [ABSTRACT FROM AUTHOR]

Since the two-directional functionally graded (2D-FG) materials can satisfy the new requirements raised based on the elimination of the stress concentration, delamination and cracking problems accompanying with the low cost and lightweight on the structures without sacrificing the stiffness and strength, the structural analyses of these structures become more important than ever. Moreover, the usage of the micro-electromechanical systems composed of 2D-FG materials has been increasing in automotive, military, space, biomedical, and nuclear energy industries. Within this study, the free vibration and buckling behaviors of 2D-FG porous microbeams are investigated based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory and using finite element method. The effects of the thickness to material length scale parameter (MLSP) accompanying with the micro-porosity volume fraction ratio, boundary condition, aspect ratio, and gradient index on the dimensionless fundamental frequencies and dimensionless critical buckling loads of the 2D-FG porous microbeams are investigated. Moreover, with assumption of the variable material length scale parameters (VMLSP), the computed results are compared with ones obtained by employing constant MLSP. It is found that VMLSP increases the stiffness of the 2D-FG porous microbeams and effects the free vibration and buckling responses of these structures. [ABSTRACT FROM AUTHOR]

To acquire exact solutions of double-functionally graded Timoshenko beam system on Winkler-Pasternk elastic foundation, which are benchmarks of double-beam systems in the field of engineering, motion differential equations of double-beam system are derived using Hamilton’s principle. In this paper, the exact dynamic stiffness matrix of double-functionally graded Timoshenko beam system on Winkler-Pasternak under axial loading are established and the damping of the connecting layer is also taken into consideration. The exact natural frequency and buckling load are obtained using Wittrick-William algorithm. To comprehensively analyze dynamic characteristics of double beam system, the effect of gradient parameter, foundation parameters, axial loading and connecting stiffness on the frequency and buckling load is compared, and the influence of damping factor is also investigated. Finally, dynamic response of double-beam system is studied using Fourier transformation. [ABSTRACT FROM AUTHOR]

This paper is devoted to study the bending response, free vibration and mechanical buckling of functionally graded material (FGM) plates based on the scaled boundary finite element method (SBFEM) for the first time. On the basis of the three-dimensional (3D) theory of elasticity, the SBFEM governing equations of the FGM plate are derived from the principle of virtual work and solved analytically in the thickness direction to obtain the displacements, stresses, natural frequencies and critical buckling loads. A high order spectral element only with three degrees of freedom per node that is able to satisfy the high order continuity of the displacement fields while facilitating the numerical computation is applied. In the present method, only the bottom surface of plate structures needs to be discretized while numerical approximations in the thickness direction are no longer required, which leads to an accurate solution of the displacement in the thickness direction and a considerable reduction of the computational cost. Furthermore, the model strictly follows 3D theory of elasticity without employing any kinematic assumptions of plate theory, so that it is able to eliminate the shear locking problem for numerical simulations of FGM plates when the thickness becomes thinner. Accuracy and superior computational efficiency of the present formulations have been verified by comparing with the available analytical and numerical solutions achieved by other researchers. • SBFEM is firstly used for the mechanical analysis of FGM plates. • Bottom surface of FG plate only needs to be discretized. • Model strictly follows 3D theory of elasticity without any plate theory. • SBFEM equations of this problem are derived and solved in detail. • SBFEM achieves highly convergent and accurate for this problem. [ABSTRACT FROM AUTHOR]

• Vibration, buckling, and energy harvesting of piezoelectric nanobeams are studied. • As size dependent theory, the two-phase elasticity is utilized. • Exact solution and GDQM are presented. • Size dependent piezoelectric load is taken into account. • Results of CF piezoelectric nanobeam are obtained without any paradox. • By increasing nonlocality, maximum voltage intensifies and tip deflection reduces. Based on a paradox-free nonlocal theory—two-phase local/nonlocal elasticity—vibration, buckling, and energy harvesting of piezoelectric nanobeams are investigated for the first time. By the means of the differential form of two-phase elasticity and Hamilton's principle, governing equations and boundary conditions are obtained. The exact solution as well as a numerical solution, Generalized Differential Quadrature Method (GDQM), are presented to extract results. Also, for the sake of obtaining equations for the forced vibration and energy harvesting analysis, the Galerkin method is utilized to discretize the governing equation. Given the fact that the differential nonlocal elasticity is not able to apply the size dependency on uniform loads, for the first time, the size-dependent piezoelectric load is taken into account through the two-phase elasticity. Also, vibration and energy harvesting of a clamped free nanobeam – which is a really good case for harvesting energy and cannot be accurately studied by differential nonlocal – are investigated employing the two-phase elasticity. To validate the present formulation and solution procedures, several comparison studies are conducted. Comparison between the common differential nonlocal elasticity and two-phase theory reveals that differential nonlocal elasticity is incompetent to yield reliable results for studying the vibration and energy harvesting of piezoelectric-based materials. Therefore, to study the mechanics of piezoelectric nano structures, other nonlocal theories such as two-phase local/nonlocal elasticity should be used. This paper can be a useful basis to investigate the vibration, buckling, and energy harvesting of nano piezoelectric devices and to improve their design. [ABSTRACT FROM AUTHOR]

• Thermal vibration and buckling of nanobeams are studied with two phase elasticity. • Size dependency of elastic medium and thermal load is considered. • Exact solution, GDQM and FEM are presented. • Size effect of thermal load is more significant in higher temperatures. • In stiffer medium, neglecting of size dependency leads to higher errors. In this paper, vibration and buckling of two-phase nanobeams embedded in size dependent elastic medium and under thermal load are analyzed. Due to paradoxes of common differential nonlocal elasticity, such as neglecting the size effect of uniform loads, failure to satisfy the constitutive boundary conditions, associated to transformation of integral nonlocal equation to differential one, and incompatibility between the results of differential nonlocal with those of integral nonlocal, the size dependent effects of nanobeam, elastic medium and thermal load are taken into account simultaneously by using two-phase local/nonlocal Eringen's elasticity, for the first time. Governing equations and corresponding boundary conditions are derived using Hamilton's principle. To obtain natural vibration frequencies as well as critical buckling temperature, three different methods of solution are presented, i.e. exact solution, Generalized Differential Quadrature Method (GDQM) and Finite Element Method (FEM) which is based on the integral form of two-phase elasticity. Several comparison studies are conducted to examine the validity of the present formulation and results. The effects of applying two-phase elasticity on elastic medium and thermal load in vibration and buckling of nanobeams with different boundary conditions are investigated in details. Differences appeared in present results, especially in the cases with higher temperature and nonlocality as well as stiffer elastic medium, reveal that the size dependency of elastic medium and uniform thermal load, which is neglected by differential nonlocal, must be considered by employing two-phase elasticity. Image, graphical abstract [ABSTRACT FROM AUTHOR]