A semi-analytical approach for the flexural analysis of in-plane functionally graded magneto-electro-elastic plates

摘要

This paper carries out the semi-analytical flexural analysis of functionally graded magneto-electro-elastic plates with material coefficients mathematically expressed as arbitrary functions in terms of the in-plane coordinates utilizing the scaled boundary finite element method (SBFEM) in association with the precise integration method (PIM). The introduced technique can be exploited to explore the deformable behaviors of magnetoelectro-elastic plates with various geometrical shapes, thickness-to-span ratios and boundary constraints. Only five variables including elastic displacement components through the x ,y and z directions, electric potential and magnetic potential are served as the primary unknowns without importing a priori assumptions on variations of the 3D multi-physical quantities. Furthermore, the mechanical, electric, and magnetic fields along the transverse direction of the plate can be analytically formulated. Moreover, the developed methodology only demands to discretize a surface of plate, which is profitable to simplify the 3D plate structure into a 2D problem and lower the calculation effort. Aided by the transformation between the scaled boundary and Cartesian coordinate system, the principle of virtue work and the dual vector technique, the SBFEM governing matrix equation for the in-plane functionally graded magneto-electro-elastic plate is depicted as a first order ordinary differential one and its corresponding general solution is analytically modelled as an exponential matrix according to the z-coordinate. As a convenient and highly accurate approach by dint of the 2N algorithm, the PIM is employed to construct the stiffness equation from the exponential matrix and compute the mechanical, electric and magnetic components. Finally, several numerical examples are provided to verify the high accuracy, applicability and effectiveness of the proposed method and manifest the effects of boundary conditions, thickness-to-span ratios and external loading forms on distributions of the multi-physical coupling quantities in functionally graded magneto-electro-elastic plates with in-plane material stiffness.