LAUSR

Abstract Meshless local Petrov–Galerkin analysis of functionally graded plates based on a general third-order shear deformation plate theory with a modified couple stress effect is presented. Governing equations of problem are a fourth-order partial differential equations system which derived in terms of eleven generalized displacement variable, by applying the principle of virtual displacements. The moving least-squares approach is used for approximation of unknown variables and the Gauss weight function is employed as test function for obtaining local weak form. The Gauss–Legendre quadrature method is utilized for numerical integration of weak equations. Static bending results of a simply-supported plate is obtained for various power law index and length scale parameter, and is compared to analytical solutions that shows high accuracy in results.