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1.弹塑性有限元分析的基本公式根据von Mises 屈服准则和Prandtl-Reuss塑性流动律,可以导出弹塑性阶段的应力增量-全应变增量之间的本构关系:{dσ}=[D_(eP)]{dε} (1)其中{dσ}为应力增量列阵,{dε}为应变增量列阵,[D_(eP)]为弹塑性系数矩阵,它的表达式为:其中(?)为有效应力,[D_e]为弹性系数矩阵,H=(?)/((?)~p)为有效应力和有效塑性应变曲线的斜率.增量形式的平衡方程为:[K]{△u}={△P} (3)其中[K]为总体刚度矩阵,{△u}为位移增量列阵,{△P}为外载荷增量列阵.2.几种解法方程(3)是非线性的.对于一般问题,精确求解比较困难.目前,一般都用近似法来求解.下面介绍几种解法.
1. The basic formula of elastic-plastic finite element analysis According to the von Mises yield criterion and the Prandtl-Reuss plastic flow law, the constitutive relationship between the stress increment-total strain increment of the elastoplastic stage can be derived: {dσ}=[D_ (eP)]{dε} (1) where {dσ} is an incremental stress array, {dε} is a strain-incremental array, and [D_(eP)] is an elastoplastic coefficient matrix. Its expression is: (?) is the effective stress, [D_e] is the elastic coefficient matrix, H=(?)/((?)~p) is the slope of the effective stress and the effective plastic strain curve. The equilibrium equation in the incremental form is: [K] {△u}={△P} (3) where [K] is the overall stiffness matrix, {Δu} is the displacement increment matrix, and {△P} is the external load increment matrix. 2. Several solution equations (3) is non-linear. For the general problem, exact solution is more difficult. At present, the approximate method is generally used to solve. The following describes several solutions.