A FINITE ELEMENT METHOD FOR STRESS ANALYSIS OR ELASTOPLASTIC BODY WITH POLYGONAL LINE STRAIN——HARDENING

In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.     

用Duhamel定理计算等效热荷载

本文对有限元法中的结点等效热荷载的计算提出新的计算方法。应用热应力计算中的Duhamel定理,将单元内的温度及其变化率作为假想的体力及面力来计算其等效热荷载,从而算得其应力。将此应力与温度引起的假想的流体静压相加即得真实的热应力。本文的方法较常用的初应变法具有简化计算程序,减少计算时间及提高计算精度等优点。本文列出三种单元等效热荷载的算式。在文内的一个算例显现出这个方法的某些优点。 对于稳定温度场的弹性体热应力问题,用有限元法计算时常将热膨胀转化为结点的等效热荷载。计算结点的等效热荷载是用初应变法。单元的结点等效热荷载列阵{R}为     

A FINITE ELEMENT METHOD FOR STRESS ANALYSIS OR ELASTOPLASTIC BODY WITH POLYGONAL LINE STRAIN——HARDENING

In this paper, the stress-strain curve of material is fitted bg polygonalline composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of everg loading increment follows the yon Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are givento the high-order element applicatioη departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.     

折线强化弹塑性应力分析的有限元法

本文对材料的应力应变曲线用三段直线的折线拟合,按照弹塑性的简单加载理论,对以增量理论得出的完整应力应变关系进行简化,导出按位移求解的有限元的增量方程.其中弹塑性刚度矩阵可以从弹性刚度矩阵补充后得出,从而节省计算时间.根据von Mises屈服准则确定各次荷载的增量,引入迭代法进行求解,省去对弹塑性刚度矩阵的重复地三角分解,进一步减少计算时间.本文对于应用高次单元、偏离简单加载的荷载、卸载计算、曲线拟合以及荷载的估算问题,均作了说明.