基于有限质点法的三维固体弹塑性问题求解

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。

ELASTIC-PLASTIC ANALYSIS OF 3D SOLIDS USING THE FINITE PARTICLE METHOD

The finite particle method (FPM) is new numerical method and suitable for analyzing structures and mechanisms undergoing large rigid body motion, deformation or their coupled problems. FPM has been successfully applied to infinitesimal mechanisms, deployable structures, contact, progressive collapse, buckling, cable-strut structures, 2D solid, membrane structures, multi-scale analysis and refinement analysis. In order to form a complete FPM research scheme involving 2D and 3D solids and elastic-plasticity problems, a constant strain 3D tetrahedron solid element was proposed in this study, and the formulations of internal forces were derived. Additionally, an elastic-plasticity analysis was also conducted. Several numerical examples with behavior of static, dynamic, nonlinear material properties were presented to demonstrate the performance and applicability of the proposed approach. Compared with the nonlinear finite element method (NFEM) and experiments, the results of numerical examples solved by self-designed program show that the present method is of high level of reliability and accuracy.