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有限质点法是一种新型的数值方法,可有效求解结构或机构的大变位、大变形及其相互耦合等复杂行为,目前已经应用于无穷小机构、可展结构、接触碰撞、结构倒塌破坏、结构屈曲、索杆结构、平面固体、膜结构的找形及褶皱、结构多尺度、结构精细化等方面的研究,均取得了较好的效果。为形成从平面固体到三维固体及弹塑性等问题的完整研究体系,该文基于有限质点法推导了一种适用于三维固体非线性问题分析的四面体固体元,并将其应用于弹塑性问题的求解。通过自编程序,分别计算静力,动力等经典算例,并将该方法的计算结果和有限元法及试验结果进行了对比。结果表明,该方法能够有效地求解三维固体的弹塑性等静动力问题。
Finite element point method is a new numerical method that can effectively solve complex behaviors such as large deformation, large deformation and mutual coupling of structures or structures. It has been applied to infinitesimal structures, developable structures, contact collisions, collapse of structures, Structural buckling, rod structure, plane solid, membrane structure and the shape and folding, multi-scale structure, structure refinement and other aspects of research, have achieved good results. In order to form a complete research system from planar solid to three-dimensional solid and elasto-plasticity, a tetrahedral solid element suitable for the analysis of three-dimensional solid nonlinear problems is derived based on the finite element method and applied to elastoplastic problems Solving. Through the self-programmed program, classical examples such as static force and dynamic force are respectively calculated, and the calculated results are compared with the finite element method and the experimental results. The results show that the proposed method can effectively solve the elasto-plastic isostatic dynamic problem of three-dimensional solid.