基于共转法U.L.列式三节点壳元几何非线性有限元分析

以三维连续介质力学和虚功原理为基础,推导出增量U.L.有限元列式,该列式保留了大位移增量刚度矩阵项,通过对该刚度矩阵进行修正可使之成为对称矩阵.根据该增量U.L.列式,文中采用三边形的形函数推导了三维三节点壳元的切线刚度矩阵,并考虑了横向剪切应力的影响.在求解增量方程时,采用CR(Co-rotational)法,将刚体位移从节点位移增量中扣除,得到节点纯变形增量,利用小应变理论计算单元内力.编制了非线性有限元程序,通过算例进行了几何非线性分析,验证该理论的精确性、高效性和通用性.

Incremental Nonlinear Finite Element Analysis of 3 node Co rotational Shell Element Based on U.L.

According to continuum mechanics and virtual work principle, incremental updated Lagrangian formulation (U.L.) was presented. The large displacement incremental stiffness matrix was considered in U.L., which was rectified to be symmetrical matrix. Based on U.L., three dimensional general-purpose three node triangular shell element was presented when the triangular shape function was employed, transverse shear stress was also considered. During the solution of incremental equilibrium equation, the pure nodal point incremental deformation was obtained when the rigid body rotation was removed from the nodal point incremental displacement by using co-rotational procedure. Furthermore, by utilizing aforementioned theory, the nonlinear finite element program was developed. Several geometrically nonlinear numerical problems were presented to demonstrate the accuracy, effectiveness, and generality of the three dimensional three node shell element.