张量分量混合插值板单元的构造及应用

Construction and application of plate element using mixed interpolation of tensorial components

阐明了Mindlin板单元及张量分量混合插值4节点板单元(MITC4)的基本原理;利用HyperMesh划分有限元网格,依据Mindlin板单元和MITC4板单元的基本理论,设计了Mindlin板单元与MITC4板单元的有限元程序.对简支矩形板进行静力分析,比较了利用MITC4板单元的计算值与解析解的差异.相比Mindlin板单元,论证了MITC4板单元在剪切自锁、单元几何扭曲及收敛性方面的优势.对存在孔洞的板结构进行静力分析和模态分析,比较ADINA和Matlab的计算结果,研究证明MITC4板单元算法的有效性.

The basic principles of Mindlin plate element and a 4-node plate element using a mixed interpolation of tensorial components(MITC4)were elaborated.The finite element mesh was divided by HyperMesh,and the finite element program was written by Matlab based on the basic theory of Mindlin plate element and MITC4 plate element.The static analysis of simply supported rectangular plates was performed,and the differences between the numerical solution of the MITC4 plate element and analytical solution were compared.In constrast with Mindlin plate elements,the advantages of MITC4 plate element were verified in shear locking,geometric distortion and convergence.The static analysis and modal analysis of the plate structure with holes were carried out in comparison with numerical solution of automatic dynamic incremental nonlinear analysis(ADINA)and Matlab,and research results show the effectiveness of MITC4 plate element.