非线性复合材料的一种杂交应力有限单元方法

Hybrid Stress Finite Element Method for Nonlinear Composite Materials

建立了非线性复合材料模型的杂交应力有限元方法,并在材料主坐标系下提出直接方法计算单元非线性应力场,然后由此计算单元切线刚度矩阵和剩余载荷并转换到整体坐标系下,利用Newton-Raphson方法进行结构的位移迭代。在Hahn-Tsai非线性复合材料杂交元分析中,由位移和应力方程所导出求解单元非线性应力场的简单迭代法是条件收敛的,对较大载荷当迭代位移增加到一定程度以后无法得到应力收敛解。但是,利用本文提出的直接法由于完全避免了非线性应力场迭代,不仅很好地解决了这一问题,而且极大地提高了计算效率。数值算例说明该方法是确实有效的。

The hybrid stress finite element for nonlinear composite material is established,and the straightforward approach to calculate the nonlinear stress field of element is presented for the local material coordinates system,the corresponding tangent stiffness matrixes and residual equivalent nodal force of element are updated,which then are transformed into the global coordinate system to iterate the displacement of the structure with Newton-Raphson method.The proposed straightforward approach solves the difficulty of divergent stress field under large iterated displacement due to the absence of stress iteration.And the efficiency of the hybrid finite element method without stress iteration is verified.