Bending and free vibration analysis of functionally graded plates made of porous materials according to a novel the semi-analytical method

A scaled boundary finite element method (SBFEM) framework is introduced for the bending and free vibration analyses of functionally graded material (FGM) porous plates based on the three-dimensional (3D) elastic theory. Both the principle of virtual work and Green's theorem are adopted to derive the SBFEM governing equation. Assuming Young's modulus and material density of the FGM porous plate vary along the plate thickness. Even and uneven porosity distribution are performed. Translating the 2D mesh along the thickness (radial direction) can be obtained the 3D plate geometry by leaving the scaling center at infinity. Consequently, the spatial dimension of the model is reduced, and the computational efficiency is significantly improved. The 2D high-order spectral element is applied to discretize the middle plane of plate due to its superior accuracy and convergence. The radial solution can be expressed analytically by matrix exponential function and solved by precise integration method (PIM). Finally, an uncomplicated and significant stiffness matrix is obtained. Furthermore, combined with the lumped mass matrix, the free vibration problem can be transformed into an eigenvalue problem. The applicability an accuracy of this approach for the static and free vibration analyses of FGM porous structures are demonstrated through variable numerical examples.

Automated summary

This paper presents a new finite element method for analyzing the bending and free vibration problems of functionally graded material porous plates. By utilizing even and uneven porosity distributions, as well as converting from 2D to 3D geometry, the computational efficiency and accuracy can be significantly improved.