基于向量式有限元的实体结构非线性行为分析

基于向量式有限元基本理论，推导了四节点四面体实体单元的基本理论计算式，通过参考平面的逆向运动来获得单元节点纯位移，进而通过变形坐标系获得单元节点内力。将双线性弹塑性材料本构模型引入向量式有限元实体单元，以实现考虑塑性硬化效应时实体结构的材料非线性行为分析。针对实体结构的碰撞接触行为，通过实体外表面质点和三角形网格面的单向碰撞检测来处理碰撞检测问题，采用基于中央差分的罚接触力响应方法来处理碰撞响应问题。弹塑性材料和碰撞接触均作为单独的计算分析模块引入向量式有限元实体单元。算例分析表明，所编制的向量式有限元实体单元程序可以有效实现线性和非线性材料情况下实体结构的静动力、大变形、大转动以及碰撞接触行为分析，验证了所提理论计算式和编制程序计算结果的可信度。

Nonlinear behavior analysis of entity structure based on vector form intrinsic finite element

Based on the basic theory of the vector form intrinsic finite element (VFIFE), the basic theoretic formulas of the tetrahedral entity element were derived. The derivation procedure was to get the pure nodal deformation through reverse movement of the reference plane firstly, and then got the internal nodal forces through deformation coordinate system. The bilinear elasto-plastic constitutive model was introduced into the tetrahedral entity element of VFIFE, so that the material nonlinear behavior analysis of entity structures considering strain hardening effect could be realized. For the collision-contact behavior of entity structures, a one-way collision detection method between the particle and triangular mesh surface of the outer entity surface was proposed for the collision detection, and a penalty contact force response method based on the central differential formula was presented for the analysis of collision response. Elasto-plastic material and collision-contact were both introduced into the theoretical derivation of VFIFE as separate calculation modules. Results from numerical examples show that, the static and dynamic analysis, the large deformation and large rotation analysis, and the collision contact behavior analysis for entity structures under both linear and nonlinear material condition can all be well performed by the developed program, verifying the correctness and reliability of theoretical derivation and computer program in this paper.