基于S-R和分解定理的无网格法在功能梯度板中的应用

为了研究功能梯度板的非线性变形问题, 以 S-R 和分解定理为基础, 从虚功率原理出发, 结合更新拖带坐标系法、无网格 Galerkin 法, 推导出用于求解三维几何非线性问题的离散方程. 利用 MATLAB 编写无网格法程序, 对功能梯度板的非线性弯曲问题进行求解, 并研究板的体积分数指数和宽厚比对板弯曲的影响. 将计算结果与已有成果进行了比较, 验证了三维 S-R 无网格法求解功能梯度板大变形问题的合理性.

Application of a meshless method based on the S-R decomposition theorem in functionally graded plates

To study the nonlinear deformation problem of functionally graded plates, this study uses the S-R decomposition theorem combined with the updated comoving coordinate system method and meshless Galerkin method to derive a discrete equation for solving three-dimensional geometric nonlinear problems. The meshless method is programmed by MATLAB. The nonlinear bending problem of the functionally graded plate is first solved, and the effects of the volume fraction index and width-thickness ration on the bending of plates are studied. Results are compared with existing results, and the rationality of solving the large deformation problem of functionally graded plates using the three-dimensional S-R meshless method is verified.