静动力弹塑性分析的杆系离散单元计算理论研究

杆系离散单元法的现有研究成果均假定接触本构模型的切向弹簧仅用于描述剪力引起的纯剪切变形，这与弯曲梁理论下剪力引起的变形情况不相符。该文针对该问题重新定义了切向弹簧，并根据能量等效原理系统推导了不考虑或考虑剪切变形工况接触本构模型的切向接触刚度系数计算公式。在此基础上，提出了杆系离散单元精细塑性铰法以描述结构的塑性开展问题，推导了颗粒间的弹塑性接触本构模型。采用自编程序对两个大型网壳结构分别进行了静、动力弹塑性行为分析，验证了接触本构模型正确性和精细塑性铰法的适用性。该文将杆系离散单元法的基本计算理论系统化，并补充了杆系离散单元法的弹塑性计算理论，为结构静、动力分析提供了新思路。

STUDY ON CALCULATION THEORY OF MEMBER DISCRETE ELEMENT FOR STATIC AND DYNAMIC ELASTOPLASTIC ANALYSES

In existing research regarding the Member Discrete Element Method (MDEM), an assume must be satisfied that the tangential spring of contact constitutive model is only used to reflect pure shearing deformation caused by shear force. However, the deformation obtained by the above assume is inconsistent with that caused by shear force according to the bending beam theory. To address this issue, the tangential spring of the contact constitutive model was redefined, and the calculation formula of the tangential contact stiffness coefficient with or without considering shear deformation was systematically derived based on the principle of energy equivalence. On this basis, the refined plastic hinge method of the MDEM was proposed to describe structural plastic development, and the elastic-plastic contact constitutive model between particles was deduced. The static and dynamic elastoplastic behavior analyses of two large-scale reticulated shell structures were carried out by MDEM programming, and the correctness of the contact constitutive model and the applicability of the refined plastic hinge method were verified. It systematizes the basic calculation theory and supplements the elastoplastic theory of the MDEM. A new idea is provided for the static and dynamic analysis of structures.