二阶流形元法与结构变形分析

在原有一阶流形元法的基础上开发了二阶流形元法数值仿真模型和相应的计算程序，并给出了计算实例。结果表明，二阶流形元法可以以较高的精度分析一般结构的变形和接触应力问题，对大变形问题独有优势。并能很好地模拟不连续介质的破坏过程及块体破坏后的运动。

SECOND-ORDER MANIFOLD METHOD IN STRUCTURE FAILURE ANALYSIS

Manifold method (MM) is a newly developed numerical procedure. The method possesses three features. (1) It uses two sets of meshes, namely mathematics meshes and physical meshes. Mathematical meshes are used to define interpolation function. Physical meshes are used to define physical boundary and integration domain. (2) The concept of cover is utilized. Local function at each zone is defined at cover. Each cover coves an enclosed zone. Covers overlap each other and define the global function of the common zone by a weight function. (3) It uses penalty as contact treatment. A unique contact treatment method is developed. By this sort of treating the contact between blocks are able to simulate reasonably. All these features make MM not only be able to accurately analyze the structure failure and stress distribution as FEM, but also to obtain integrally the deformation and block movement of discontinuities as DDA. Based on the original first-order MM by Shi, this paper presents a second-order MM with detail computational formula, governing equations and numerical codes. Application examples include normal stress distribution and deformation problem, large-scale deformation problem and contact problem. The simulation results are compared with analytical solutions. It shows that the newly developed second-order MM is capable of analyzing structure stress distribution and contact stress problems with relatively high accuracy. A simulation example of slope failure is also given in the paper. Reasonable failure process is obtained. The extended second order manifold method has good adaptability and can be used to simulate the whole process of structure from loading and deformation to failure and movement of blocks.