塑性全量理论的变分不等式模式及其无迭代解

变分不等式是解决一类带单侧约束的定常力学问题的有效数学工具.本文就弹塑性全量理论构造了等价的变分不等式模式,解除了弹塑性问题本构约束的不等式关系,比一般能量形式的描述更为简洁.它便于计算,具有可靠的数学依据,可以用二次规划法求解.计算时无需分级加载迭代,一步即可得收敛解.

The Variational Inequality Formulation for the Deformation Theory in Plasticity and Its Non-Iterative Solution

In this paper, the deformation theory in plasticity is formulated in the veri-ational inequality, which can relax the constraint conditions of the constitutive equations. The new form makjs the calculation more convenient than general energy forms and have reliable mathematical basis. Thus the plasticity theory may bs solved by means of the quadratic programming instead of the iterative methods, and the solutions can be made in one stsp without any diversion of the load.