采用有限质点法的薄壳动力非线性行为分析

基于有限质点法原理和K-L经典薄壳理论，构造具有大位移大转动分析能力的薄壳离散质点模型，推导表述基本控制方程与公式. 对于质点位移以及壳元的变形和内力，均按照面内拉压和面外弯扭两部分进行拆分与叠加，并通过物理方式的虚拟运动依次分离出与薄膜刚度和弯曲刚度相关的纯变形，进而在局部变形坐标系下求解面外变形相对应的质点内力和内力矩，建立质点切平面外转角的变步长显式时间积分式，并对质点质量、时间步长、阻尼等关键参数取值给出建议. 在此基础上引入材料非线性应力修正算法，实现对薄壳弹塑性大应变动力非线性行为的模拟，并通过典型算例验证方法及程序的有效性和正确性.

Nonlinear dynamic analysis of shells using finite particle method

A discrete particle model of thin shells with large displacement and large rotation analysis capability was constructed based on the principle of finite particle method and K-L classical thin shell theory, and the fundamental governing equations and formulas were derived. For the particle displacement and the deformation and internal force of the shell element, the two parts corresponding to the in-plane tension and the out-of-plane bending and twisting were split and superimposed, respectively. The pure deformation related with the membrane rigidity and bending rigidity was sequentially separated by using a physical modeling procedure involving fictitious motions. Then in the local deformation coordinate system, the internal forces and moments were solved, and the explicit time integral formula with variable step sizes for calculation of the out-of-plane rotation was established. The determinations of several key parameters were also given, including particle mass, time step and damping. Moreover, an stress correction algorithm for solving material nonlinearity was introduced to simulate the dynamic nonlinear behavior of a thin shell with large elastic-plastic strain. The efficiency and validity of the presented method and the self-developed program are verified by several benchmark examples of nonlinear shell dynamics.