Three-dimensional static analysis of Levy-type functionally graded plate with in-plane stiffness variation

Abstract

A three-dimensional analytical solution is developed for a longitudinally functionally graded plate subjected to Levy-type boundary conditions. A linear variation of material compliances is taken along the x-direction. The recently developed mixed-field multiterm extended Kantorovich method is applied to solve the governing equations in mixed form. A set of non-homogeneous ordinary differential equations (ODEs) with varying coefficients are obtained along the x-direction, which is solved by using the recently developed modified power series method. Another set of ODEs with constant coefficient is obtained along the z-direction, which is solved analytically. For the first time, numerical results for a two layered plate having a different in-plane material variation in each layer are presented along with single layer plate results. Benchmark results are presented which can be used to validate approximate two-dimensional solutions and 3D numerical results.