Analysis of porosity effect on free vibration and buckling responses for sandwich sigmoid function based functionally graded material plate resting on Pasternak foundation using Galerkin Vlasov’s method

Abstract

The objective of the present paper is to study the effect of porosity on vibration and buckling responses for sandwich plate supported with different boundary conditions at the edges. The formulation is performed for recently developed sandwich plate using new modified sigmoid function based functionally graded material plate of different symmetric and asymmetric configurations. Three different types of porosity are considered viz. even, uneven but symmetric, and uneven but non-symmetric. A new uneven non-symmetric porosity model is used in which micro-voids are varied in accordance with material property variation in the thickness direction in order to capture the accurate distribution of voids on the plate. The variational principle is employed to derive equilibrium equations. A closed form solution is obtained using the assumed solution with shape functions satisfying the edge boundary conditions using Galerkin Vlasov's method. Free vibration

Static and vibration response analysis of sigmoid function-based functionally graded piezoelectric non-uniform porous plate

“…These transverse force resultants modifying the FGP plate transverse shear stiffness and SCF depends on the geometrical and material properties. The assumed boundary conditions are involved in the equation (Chen et al, 2016; Singh and Harsha, 2021). The equations include stress component in terms of strains components, electric field, and the thermal field.…”

“…Recent development in the fields of functionally graded material structure with porosity with even or uneven distribution. Various researchers (Chen et al, 2015(Chen et al, , 2016Ebrahimi and Barati, 2017;Ferreira et al, 2006;Mantari and Soares, 2012;Rezaei and Saidi, 2016;Singh and Harsha, 2021;Su et al, 2018;Zhao et al, 2019;Zhu et al, 2020) have developed different models or studies to implement static, linear, or nonlinear vibration and buckling analysis on the different types of FGM beams, plates, and shells. These analyses have taken a different type of material variation law, that is, P-, E-, and S-law, for defining the material properties.…”

Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate

“…2(b) also presents the effect of position coefficient β on the variation of Young's modulus for n = 0.5. The volume fractions of every single layer are defined as follows [51,52]:…”

Buckling Response of Functionally Graded Porous Plates Due to a Quasi-3D Refined Theory

“…Xu et al [29] reported the buckling response of the FG porous core with laminated skins resting on an elastic base. Singh and Harsha [30] used a modified sigmoid model to examine the buckling of FG sandwich porous plates for three different types of porosity distributions. Mojahedin et al [31] investigated the buckling response of radially loaded clamped FG circular porous plates.…”