弹塑性损伤分析的参变量变分原理

参变量变分原理采用了现代控制理论的极值变分思想,将本构关系化为状态方程控制着泛函的变分,是一种有效的求解非线性问题的方法,本文在弹塑性损伤基本方程基础上构造了弹塑性损伤分析的势能泛函,对损伤演化方程和加载函数近拟处理,导出了状态方程,指出求解弹塑性损伤问题归结为求解在状态方程控制下的势能泛函数极值问题,由此建立了弹塑性损伤分析的参变量变分原理;变分原理物理意义明确,并给出了参变量变分原理实施的有限元列式,易于计算机编程实现,文中对一算例进行了数值计算,计算结果表明该方法是求解弹塑性耦合损伤问题的有效方法。

Parametric Variational Principle for Coupled Elasto-Plasticity Damage Problem Analysis

The parametric variational principle adopts the maximum variational idea in the modern control theory and uses state equations deduced from the constitutive laws to control the functional variation, which is an effective solution to the nonlinear equations. Based on the fundamental equations of elasto-plasticity coupled damage, the article constructs the potential functional of elasto-plasticity and deduces the state equations with some approximation of damage evolution equation and load functions. It is verified that the solution of elasto-plasticity damage problem can be deduced to solve problem of the potential energy function minimum under the restriction of state equations. Thus the parametric variational principle for coupled damage is brought forth. The variational principle has the virtue of definite physical meaning and the finite element equations are presented in the article to facilitate the application of parametric variatioal principle, which is easy to program on computer.Using the method mentioned in the article, a numerical calculation is carried out and the calculation result shows that the method is efficient for solving ealsto-plasticity damage problems.