Analysis of the bending of circular piezoelectric plates with functionally graded material properties by a MLPG method

A meshless method based on the local Petrov–Galerkin approach is proposed for plate bending analysis with functionally graded piezoelectric material properties. Material properties are considered to be continuously varying along the plate thickness. The axial symmetry of geometry and boundary conditions for a circular plate reduces the original three-dimensional (3-D) boundary value problem into a two-dimensional (2-D) problem on the axial cross section. Both mechanical and thermal loads with stationary and transient dynamic conditions are considered in this paper. The local weak formulation is employed on circular subdomains on the axial cross section. Subdomains surrounding nodes are randomly spread over the analyzed domain. The test functions are taken as unit step functions in the derivation of the local integral equations (LIEs). The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns. That system is solved numerically by the Houbolt finite-difference scheme as a time-stepping method.