组合弹性结构的新型有限元法及其区域分解算法研究

Elastic multi-structures are widely used in many fields of the national defence and ordinary life. It is both theoretical and.practical importance to give the study on their numerical solutions. For the construction of new-type finite elements, the aim of the project is only for two-component problems, but we have obtained results for elastic multi-structures consisting of an arbitrary number of components. It is a breakthrough in the numerical analysis.of elastic multi-structures. The related TRUNC element method, mortar element method and mixed element method are also discussed, and the resulting manuscripts have been submitted. For the domain.decomposition, some important results have been achieved for the body-plate model, which will appear in Math. of Comp. We are creating a software package for our algorithms to simulate the deformation of.ocean platforms. There have appeared (or have been accepted for publication) 14 papers, including 6 SCI ones and 3 EI ones. We have completed the task of the project smoothly.

组合弹性结构广泛应用于国防和国民经济诸部门，对它的有效数值求解有很大实用价值，已有方法主要为低次、位移型有限元素法，远未完善。本项目拟研究建立求解该问题若干新型有效有限元素法并构建相应离散问题的合理区域分解求解算法。该问题子域模型物性相异，不同于常规问题。因此本项目研究还可望为有限元素法和区域分解法带来新的发展方向。