Bending analysis of thin functionally graded plate under in-plane stiffness variations

Abstract

The paper developed a new analytical solution for elastic deformation of thin rectangular functionally graded (FG) plates with in-plane stiffness (Young's modulus) variation, which has important applications in various thin-walled structures. Also the problem was solved numerically using the graded finite element method (FEM). The relevant governing equations of elasticity were solved assuming static analysis and power law distribution of the material stiffness. The plate deflections and stresses from the well-known through-the-thickness stiffness variation solution were used to verify the graded finite element method. The analytical solutions for the displacements and stresses were derived for in-plane stiffness variations. The finite element (FE) solutions were obtained both using linear hexahedral solid elements and shell elements with spatially graded stiffness distribution, implemented in the ABAQUS FE software. These solutions were verified against the finite element (FE) solutions, and are in very good agreement for various stiffness gradients. The analytical solution based on CPT was compared with that provided by higher shear deformation theory (HSDT) and graded solid element FE solution.The results obtained demonstrate that the direction of material stiffness gradient and the nature of its variation have significant effects on the mechanical behavior of FG plate. Moreover, the good agreement found between the exact solution and the numerical simulation demonstrates the effectiveness of graded solid elements in the modeling of FG plate deflection under bending. The types of analytical solutions obtained can be used to obtain deflections and stresses in thin structures with specified stiffness gradients induced by manufacturing processes, such as multi-material 3D printing.