塑性全量理论中的控制变量变分原理

The Controled Variational Principles in Deformation Theory of Plasticity

控制变量变分原理也称参变量变分原理,其主要特点是在能量泛函中引入了不直接参加变分的控制变量,并要求极值过程始终受状态方程的控制。文[10-16]建立了弹塑性增量理论下的若干控制变量变分原理,使得增量问题有限元解不必迭代且精确度高。本文针对简单加载全量理论问题,建立了相应的控制变量变分原理,使得这一类工程上应用较多的弹塑性理论可以用解参数二次规划的方法求解,不再依靠传统迭代途经。全量问题可用解增量问题的程序统一解算,前者只相当于在后者的本构材料库的程序接口里增添新的材料性质而巳。

The controled variational principle is also called the parametric variational principle characterized by control variables in the energy functional and a set of constitutive state linear-complementary equations ( CSLCE ). The control variables control but not particirate in the variational procedure toward extremum along with the CSLCE. The principles given by ref.[10-16] in flow theory of plasticity indicated that their numerical approximation by FEM need not any iteration and converges at great accuracy. In this paper, four minimum and two generalized energy principles are described for the deformation theory of plasticity under simple loading condition so that the most common used plasticity theory in engineering may be solved through simultaneously linear equations or quadratic programming instead of iterative methods. Consequently, the software, programmed for flow theory[17] can also calculate the deformation theory problems as long as new material properties being added into the data base interface designed in the software.