向量式有限元膜单元及其在膜结构褶皱分析中的应用

发布时间：2018-09-05 13:41

【摘要】：向量式有限元法是一种基于点值描述和向量力学理论的分析方法,可有效模拟结构的空间大位移、大转动行为。推导了三角形膜单元的向量式有限元基本公式,详细阐述了通过逆向运动获得单元节点纯变形位移以及在变形坐标系下求解单元节点内力的方法。在此基础上编制了膜单元的计算程序,并通过算例分析验证了理论推导的正确性及所编制程序的可靠性。进一步将向量式有限元引入膜结构的褶皱分析,采用主应力-主应变准则和修正本构矩阵方法处理膜结构的褶皱问题,对一典型膜结构在面外荷载作用下的力学行为及褶皱发展情况进行跟踪分析,成功捕捉了从褶皱出现、褶皱大范围扩展直至褶皱最终消失的全过程,证明了该方法在膜结构皱褶分析中可有效克服传统有限元方法存在的单元刚度矩阵奇异、迭代不易收敛等问题。
[Abstract]:The vector finite element method is an analytical method based on the point value description and the theory of vector mechanics, which can effectively simulate the spatial large displacement and large rotation behavior of the structure. The vector finite element formula of triangular membrane element is derived, and the method to obtain the pure deformation displacement of element node by reverse motion and to solve the internal force of element node in deformed coordinate system is described in detail. On this basis, the calculation program of the membrane element is compiled, and the correctness of the theoretical derivation and the reliability of the program are verified by an example. Furthermore, the vector finite element method is introduced into the fold analysis of the membrane structure, and the principal stress-principal strain criterion and modified constitutive matrix method are used to deal with the fold problem of the membrane structure. The mechanical behavior and fold development of a typical membrane structure under the action of out-of-plane load are followed and analyzed. The whole process from the appearance of the fold, the wide spread of the fold to the final disappearance of the fold is successfully captured. It is proved that this method can effectively overcome the problems of the singularity of element stiffness matrix and the difficulty of convergence in the traditional finite element method in the wrinkle analysis of membrane structures.
【作者单位】：浙江大学空间结构研究中心;浙江省建筑设计研究院;
【基金】：国家自然科学基金项目(51378459)
【分类号】：TU383;TU311.4

【共引文献】