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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。
Vector finite element method is a kind of analysis method based on point value description and vector mechanics theory, which can effectively simulate the large displacement and large rotation of the structure. The basic formulas of vectorial finite element of triangular membrane element are deduced. The pure deformation displacement of element node and the method of solving internal force of element node in deformed coordinate system are elaborated in detail. On this basis, the calculation program of membrane element is compiled, and the correctness of the theoretical derivation and the reliability of the programmed program are verified through a case study. The finite element method is further introduced into the fold analysis of the membrane structure. The principal stress-principal strain criterion and the method of modifying the constitutive matrix method are used to deal with the wrinkle problem of the membrane structure. The mechanical behavior and wrinkle development of a typical membrane structure under the out- The results show that this method can effectively overcome the singularity and iteration of the element stiffness matrix existing in the traditional finite element method in the analysis of membrane structure wrinkles. Not easy to convergence and other issues.