变刚度混合型有限元

介绍了一般弹性体变比例混合能量型变分原理.该变分原理的特点是其泛函中包含一个被称为分裂因子的参数,通过改变分裂因子的值可以调整泛函中位能和余能的比例,以该泛函为基础建立了变刚度混合型有限元模型.研究了选择分裂因子的方法,讨论了降低刚度矩阵的条件数、改善解的精度以及克服病态问题的方法.最后,从理论上分析了其能够克服各类有限元病态问题的机理.

Stiffness changeable mix-energy finite element method

A new kind of variational principle which proportion of potential and complementary energy changeable in solid mechanics is introduced. Its distinctive feature is that the functional contains one arbitrary additional parameter, called splitting factor, the proportion of potential and complementary energy in the functional can be changed by the splitting factor. Finite element method, which is based on the new principles, is established. It is called stiffness changeable FEM, its stiffness can be adjusted by properly selecting the splitting factors. The methods to choose the splitting factors, reduce the condition number of stiffness matrix, improve the precision of solutions and conquer ill-conditioned problem are also discussed. Why the new method can transform the ill-conditioned problems into well-conditioned is analyzed finally.