基于共旋三角形厚薄通用壳元的几何非线性分析

GEOMETRICALLY NONLINEAR ANALYSIS USING A COROTATIONAL TRIANGULAR THICK AND THIN SHELL ELEMENT

  • 摘要: 基于共旋列式方法发展了一种用于复合材料层合板结构几何非线性分析的简单高效的三结点三角形平板壳元。该壳元由具有面内转动自由度的广义协调膜元GT9与假设剪切应变场和假设单元转角场的广义协调厚薄通用板元TMT组合而成。为避免薄膜闭锁而采用单点积分计算与薄膜应变有关的项, 同时增加一个稳定化矩阵以消除单点积分导致的零能模式。基于层合板一阶剪切变形理论, 给出了考虑层合板具体铺层顺序的修正的横向剪切刚度, 使该壳元可用于中厚层合板结构的分析。由于共旋列式大转动小应变的假设, 共旋列式内核的几何线性的单元刚阵可仅计算一次而保存下来用于整个几何非线性求解的过程以提高计算效率。数值算例表明提出的壳元进行包括复合材料层合板结构的厚薄壳结构的几何非线性分析的精度高且效率高。

     

    Abstract: A simple and efficient 3-node triangular planar shell element for the geometrical nonlinear analysis of laminated composite structures is developed based on corotational formulation (CR). The shell element is constructed by combining the generalized conforming membrane element GT9 with the drilling degree of freedom and the generalized conforming thick/thin plate element TMT with assumed rotation and transverse shear strain fields. In order to avoid membrane locking, one-point reduced integration scheme is employed for calculating the terms related to membrane strains, and a stabilization matrix is added to eliminate zero energy modes. Based on the first-order shear deformation theory (FSDT) for laminated composite plates, the correctional transverse shear stiffness is calculated, considering the real ply stacking sequence of the laminate, such that the shell can be applicable to modeling moderately thick laminated composite structures. The geometrically linear stiffness matrix in the core of CR formula can be calculated only once and can be saved to be used throughout the whole procedure for the nonlinear analysis. Numerical examples show that the present shell element is accurate and efficient for thin and thick shell structures, including laminated composite structures.

     

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