基于向量式有限元的三角形薄壳单元研究

发布时间：2018-08-13 16:27

【摘要】：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。
[Abstract]:Based on the basic theory of vector finite element, the basic theoretical formula of triangular thin shell element is derived by the combination of linear superposition of triangle constant strain CST thin film element and triangular discrete Kirchhoff DKT thin plate element. The pure deformation displacement of the element node is obtained by reverse motion, and then the internal force of the element node is solved by the deformed coordinate system. Through the repeated transformation between the different deformation coordinate system and the whole coordinate system, the key problems such as the mass displacement and internal force of the membrane element and the plate element, the superposition of the element strain and stress at the end of the time step and the separation of the next time step are solved. At the same time, the Neuton-Cotes integral is used to calculate the internal force of the element node, and then the Hammer integral scheme is used to carry out the in-plane integration. On the basis of this, the calculation and analysis program of thin shell element is compiled. The numerical example shows that the program of vector finite element thin shell element can accomplish the static analysis, dynamic analysis and buckling analysis of thin shell structure with large deformation and large rotation. Verify the validity and correctness of the theoretical derivation and the program.
【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) 浙江省重点科技创新团队项目(2010R50034)
【分类号】：TU33

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