径向基函数配点法分析三维功能梯度材料板的静力和动力问题

Meshfree radial basis collocation method (RBCM) is introduced to study the static and dynamic problems of the three dimensional (3D) functionally graded plate. Radial basis functions which possess infinite continuity are employed to be the approximation, collocation method is utilized for discretization, and least squares approach is adopted to solve the discretized equations. No mesh will be required in the discretization and resolution and therefore RBCM is a truly meshfree method. Discretization scheme of RBCM is quite simple and high accuracy can be obtained. Radial basis approximation only depends on the distance from the center which makes RBF a good candidate to solve 3D problems. Conventional collocation method introduces error accumulation on the boundaries. In this paper, the spatial domain is discretized first, and then temporal domain is discretized. Boundary conditions are imposed in each time step. Therefore, error accumulation on the boundaries can be overcome. Numerical simulations demonstrate that graded distribution of material properties will lead to nonlinear variation of the mechanical properties. The magnitude of the nonlinear variation will be different for different graded distributions.