基于向量式有限元的三角形薄壳单元研究

Triangular thin-shell element based on vector form intrinsic finite element

基于向量式有限元基本理论,通过三角形常应变CST薄膜单元和三角形离散基尔霍夫DKT薄板单元的线性叠加组合,推导三角形薄壳单元的基本理论计算式。通过逆向运动获得单元节点纯变形位移,进而由变形坐标系求解单元节点内力。通过不同变形坐标系与整体坐标系之间的反复转换,解决膜元部分和板元部分的质点位移和内力、单元应变和应力在时间步末的叠加和下一时间步初的分离这一关键问题,同时对单元节点内力计算提出先沿厚度采用Neuton-Cotes积分,再采用Hammer积分方案进行平面内积分。在此基础上编制薄壳单元的计算分析程序,算例分析表明,所编制的向量式有限元薄壳单元程序可以较好地完成薄壳结构的静力、动力分析和考虑大变形大转动的屈曲分析,验证理论推导和所编制程序的有效性和正确性。

Based on the basic theory of the vector form intrinsic finite element （VFIFE） , the basic theoretical formulas of the triangular thin-shell element are derived by the linear combination of the triangle CST thin-membrane element and the triangle DKT thin-plate element. The basic idea of the derivation procedure is to get the pure nodal deformations through reverse movement first, and then get the internal nodal forces through deformation coordinate system. Through repeated transformations between the different deformation coordinate systems and the global coordinate system, the key problems for membrane element part and plate element part are well solved, including the combination of displacements and internal forces of particles and stresses and strains of elements at the end of one time- step, and the separation of them at the initial of the next time-step. The feasible integration scheme for the calculation of nodal internal forces is also presented. On this basis, a developed. Results from numerical examples show that, computer program of VFIFE triangular thin-shell element is static analysis, dynamic analysis and buckling analysis considering large deformation and large rotation can all be well performed for thin-shell structures by the developed program, verifying the validity and the correctness of the theoretical derivation and the computer program.