基于梯度塑性理论的动力软化问题分析

对于动力应变软化问题，采用梯度塑性模型进行分析，该模型能够有效地克服软化材料在有限元分析中的网格依赖性问题。对于动力非线性软化方程的求解则利用于基于参变量变分原理的参数二次规划方法。对于结构动力方程时域上的求解则采用传统的Newmark方法。本文的算法与传统方法相比在求解基于梯度塑性模型的非线性动力软化问题时保证了已有参数二次规划算法的优良特性，有实现简单与稳定性好等优点。给出的数值算例证实了本文的理论工作与所研制程序的正确性。

Analysis of Dynamic Softening Problem with Gradient Dependent Model

The gradient dependent model is proposed to overcome the result mesh sensitivity problem in the finite element analysis of dynamic strain softening problems. The parametric variational principle and parametric quadratic programming method are adopted for the solution of the governing equations of the nonlinear dynamic softening problems. To solve the problem in time domain, Newmark integration method is used as the implementation algorithm. It can be observed that, compared with the traditional method, the new algorithm presented here has some advantages for the implementation of gradient dependent model such as being easy to implement and stable convergent property during integration process. Numerical examples are shown to demonstrate the validity and efficiency of the theory and algorithm presented in the paper.