流形元法与结构模拟分析

本文在原有一阶流形元法的基础上推导了二阶流形元法数值计算模型,并开发了可以模拟沿结合面开裂、沿数学网格开裂,裂缝沿任意可能方向扩展及考虑裂隙渗流对变形的耦合作用分析裂隙边坡的稳定性程序。作为应用实例,计算了受刚性板挤压的圆柱体的接触应力、悬臂梁的大变形、不连续块体边坡崩塌破坏、拱座的破坏失稳及移动中梁的破坏问题。结果表明,流形元法可以以较高的精度分析一般结构的变形及应力、接触应力及大变形问题,并能很好地模拟不连续介质的破坏及块体的运动。

Structure analysis by second-orderManifold Method

The Manifold Method is a newly developed numerical procedure. By a unique arrangement of numerical meshes and treatment to contact , the method is able not only to accurately analyze the structure displacement and stress distribution as can be done by applying Finite Element Method, but also to simulate the deformation of structures with many discontinuities and block movement as can be done by using Discontinuous Deformation Analysis. Based on the original first order Manifold Method, the author developed a second-orderManifold Method togetherwith corresponding computat ional code. Application examples included analysis of contact stress of a cylinder compressed between rigid plates, large deformation problem of a cantilever beam and failure of a side slope with discontinuities. The results showed that the second-order Manifold Method was capable of analyzing structure deformation, stress, contact problems and large-scale deformation problems with relatively high accuracy. It would provide also the failure process and block movement with acceptable accuracy.