航空学报 > 1985, Vol. 6 Issue (6): 530-537

任意坐标系中的弹塑性矩阵

任孝安   

  1. 中国科学院力学研究所
  • 收稿日期:1984-04-03 修回日期:1900-01-01 出版日期:1985-12-25 发布日期:1985-12-25

ELASTOPLASTIC MATRIX IN NON-ORTHOGONAL CURVILINEAR COORDINATE SYSTEM

Ren Xiaoan   

  1. Institute of Mechanics, Academia Sinica
  • Received:1984-04-03 Revised:1900-01-01 Online:1985-12-25 Published:1985-12-25

摘要: 本文推导了三维问题及平面应力、平面应变、轴对称问题在任意曲线坐标系中的弹塑性矩阵。由此最一般的表达式可以方便地得到任何特定坐标系中的弹塑性矩阵,供各类不同特点问题的有限元计算时使用。 文中推导得到的任意曲线坐标系中的本构方程,也同时为曲线差分法求解弹塑性问题提供了刚度系数显式。

Abstract: The expressions for pijkl of the elastoplastic incremental constitutive equation (Eq. 6) are derived in non-orthogonal curvilinear coordinates (Eqs. 15 and 19). Choice of a proper curvilinear coordinate system sometimes makes the problem easy to treat, especially the boundary conditions to be satisfied easily and exactly. - From these general equations the eiastoplastic matrix for finite element method can be obtained in any specific coordinate system.The adaptability and flexibility of conventional finite difference method are greatly enhanced by using non-orthogonal curvilinear coordinates. The eiastoplastic constitutive equation expressed in curvilinear coordinates also provides explicit stiffness coefficients for solving elastoplas?tic problems with curvilinear finite difference.