A simple boundary method is developed for the solution of isotropic thick plates with in-plane arbitrarily variable material properties or thickness. Equilibrated basis functions which have proved to be effective in a variety of problems, are adopted for the bending problem of thick plates. The bases are created through a weighted residual approach over a fictitious rectangular domain so as to approximately satisfy the partial differential equation of the problem. This omits the necessity of the bases to analytically satisfy the equilibrium, thus simplifying the application of the method. Boundary conditions are applied to the approximate solution through a collocation technique, which considerably reduces its computational expenses. Mindlin’s first order and Levinson’s third-order shear deformation theories are adopted for the formulation. To accommodate more complicated geometries, a simple domain decomposition approach is also developed.

针对平面内任意变化的材料特性或厚度的各向同性厚板的解决方法，开发了一种简单的边界方法。对于厚板的弯曲问题，采用了已证明在多种问题中有效的平衡基函数。通过在虚拟矩形域上通过加权残差法创建基数，以近似满足问题的偏微分方程。这省略了碱分析地满足平衡的必要性，从而简化了该方法的应用。通过并置技术将边界条件应用于近似解，从而大大减少了计算量。该公式采用Mindlin的一阶和Levinson的三阶剪切变形理论。