Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method

The nonlinear response of functionally graded ceramic–metal plates (FGPs) under mechanical and thermal loads is investigated using the mesh-free kp-Ritz method. The nonlinear formulation is based on the first-order shear deformation plate theory and the von Kármán strains, which deal with small strains and moderate rotations. The material properties of FGPs are assumed to be graded through the thickness direction according to a power law distribution of the volume fraction of the constituents. The approximation of the displacement field is expressed in terms of a set of mesh-free kernel particle functions. The bending stiffness of the plates is evaluated using a stabilized conforming nodal integration method, and the membrane and shear stiffnesses are computed using direct nodal integration to eliminate shear locking. The nonlinear behavior of the deflection and axial stress is studied for FGPs under thermal and mechanical loading, and the influences of the volume fraction exponent, boundary condition, and material properties on the nonlinear response of FGPs are examined.