基于向量式混合质点单元薄壳非线性分析方法的膜材褶皱形变模拟研究（英文）

A vector-form hybrid particle-element method for modeling and nonlinear shell analysis of thin membranes exhibiting wrinkling

研究目的:建立一种适用于理想膜结构可进行高精度褶皱形变模拟的稳定可靠的数值分析技术及方法。创新要点:根据薄壳理论,在向量式混合质点单元方法(VFPEM)薄膜计算理论的基础上,引入弯曲内力分析模型并与其进行组合,发展了一种能够描述膜材面外变形的新型非线性薄壳计算理论,同时给出了将其应用于褶皱形变模拟的关键求解技术。研究方法:1.针对薄壳计算模型中的弯曲内力,利用移动基础架构和逆向刚体运动的概念扣除刚体转动,在只含有节点独立转动自由度的单元变形坐标系下根据虚功原理和平衡条件进行计算;2.借助于薄壳非线性屈曲模拟方法,引入合理的初始扰动作为诱发理想平面膜材中形成褶皱的有效机制;3.采用拟动力显式数值积分技术求解质点运动方程,通过追踪质点平衡位置来获得稳态的褶皱构形。重要结论:采用本文模型和方法可以模拟薄膜结构在面内荷载作用下褶皱的分布模式、具体构形信息及应力状态,计算过程不存在收敛性困难,结果准确。

The wrinkling phenomenon is a commonly-known problem in many fields of engineering applications. Using a general structural analysis framework of the vector-form hybrid particle-element method （VHPEM）, this paper presents a newly developed shell-based numerical model for the geometrically nonlinear wrinkling analysis of thin membranes. VHPEM is rooted in vector mechanics and physical perspective. It discretizes the analyzed domain into a group of finite particles linked by canonical elements, and the motions of the free particles are governed by Newton＇s second law while the constrained ones follow the pre- scribed paths. An adaptive convected material frame is adopted for a general kinematical description. Internal forces related to the non-zero bending rigidity of a membrane can be efficiently evaluated by the rotation deformation in a set of deformation coor- dinates after eliminating rigid body motions simply by a fictitious reverse motion. To overcome the numerical difficulties asso- ciated with wrinkles, a pseudo-dynamic scheme using the explicit time integration is introduced into this method. Structural nonlinearity can be easily handled without iterative operations or any other special modification. The wrinkling behavior can be readily obtained by performing a pseudo bifurcation analysis incorporated into the VHPEM. The numerical results reveal that the VHPEM has good reliability and accuracy on solving the membrane wrinkling problem.