Numerical investigation of porous bi-directional functionally graded plates with variable thickness using a Trefftz-based approach

In this paper, flexural behavior of functionally graded (FG) and bi-directional functionally graded (BDFG) porous composite plates with variable thickness is analyzed by developing a novel meshfree method based on Trefftz attitude. Classical, first- and third-order shear deformation theories are applied to the formulation. The developed Trefftz-based method creates exclusive basis functions capable of satisfying the equilibrium by means of weighted residual imposition of the equation, thus enhancing the accuracy of the results. The solution function has complete continuity, which paces up its convergence. The integration is performed analytically independent of the domain shape, thus removing the need for numerical quadrature throughout the solution procedure. For more versatility, a domain decomposition approach is developed with up-to-desired order of continuity, leading to considerable mesh reduction compared with mesh-based methods. Derived in one step, the overall multi-domain solution does not need repetitive approaches to converge. Because of independent satisfaction of the equilibrium by the basis functions, the boundary and continuity conditions may be imposed in point-wise style, removing the cumbersome boundary integration. Simultaneous in-plane and transverse graded variation of the material properties and porosity is considered. Verification of new results by 3D finite element solution reveals high accuracy and efficiency of the method. Comprehensive parametric study is also performed for FG and BDFG porous plates with various distributions and variable thickness.