一种高效率弹塑性有限元分析新方法——增量杂交/混合修正弦线模量法

A High Efficient Algorithm For Elasto-Plastic Finite Element Analysis: Increment Hybrid/Mixed Method of Modtfing Secant Modulus

本文在文献[1]给出的放松应力增量平衡约束的修正余能广义变分原理基础上,提出一种高效率的弹塑性有限元分析的新方法——增量杂交/混合修正弦线模量法。该法保持了文[1]方法的全部优点,而在迭代过程中,依据材料的单向拉伸应力—应变关系,不断改变过渡区和塑性区单元柔度矩阵和塑性矩阵中的弹性模量;并在体积压缩模量不变假设下,相应地改变过渡区单元矩阵中的泊松系数。从而大大降低了迭代收敛次数和单刚计算量,提高了多类变量弹塑性有限元分析的计算效率和收敛精度。

Based on the modified complementary energy principle [1], which relaxed the equilibrium limitation of stress increment, a high efficient algorithm, increment Hybrid/mixed method of modifing secant modulus for elasto-plastic finite element analysis has been proposed in this paper. This algorithm keeps all the advantages of Hybrid/mixed FEM. During iteration, the algorithm continuously modifies the elastic modulus for the flexibility matrix and plastic matrix both in transitional region and in plastic region according to the stress-strain relation of materials used. On assumption that the volumetrical compression modulus keeeps constant, the Poisson's ratio can be modified continuously as well, so that the number of iteration and computing time can be dramatically reduced. Therefore, the computing efficiency and convergent accuracy for elasto-plastic finite element analysis can be greatly increased.