Hahn-Tsai复合材料的非线性杂交应力有限元方法

The nonlinear hybrid stress finite element method for Hahn-Tsai composite materials

成功建立了Hahn-Tsai复合材料模型的非线性杂交应力有限元方程,采用Newton-Raphson迭代法求解结构的非线性位移方程。在迭代过程中,为了提高计算效率可采用简单迭代法由节点位移求解单元应力场。但是,当载荷增加到一定程度以后,非线性应力场由于循环迭代而无法收敛,显然,一般的加速方法不能解决这种循环迭代的发散问题。因此,本文发展了一种确实有效的非线性应力场迭代新方法,在不增加计算工作量的情况下,不仅极大地提高了收敛速度,而且对于较大载荷也能够很好地收敛,从而解决了大载荷下非线性杂交元方法失败的关键问题。数值算例表明该方法是确实可行的。

The nonlinear hybrid stress finite element method for Hahn-Tsai composite materials is established successfully. The Newton-Raphson iteration technique is employed to solve the displacement nonlinear equations of the structure. To save the computer cost, the element stress field can be computed by the simple iteration method from the nodal displacements. However, the fact is that the simple stress iteration is recurrent so that divergent for the large load. Obviously, the ordinary accelerating techniques cannot overcome this problem of divergence of recurrent iteration. So, a new method of nonlinear stress iteration is derived in this paper. It is useful and the rapidly convergent solution can be obtained without more computer cost. In particular, it also results in the convergent solution for large load. It is the key to the successful nonlinear hybrid finite analysis for the large load. The numerical example shows that the method is effective.