弹塑性大变形分析的一致性高阶无单元伽辽金法

Consistent high order element-free Galerkin method for elastoplastic large deformation analysis

采用无单元伽辽金法求解弹塑性大变形问题。充分利用无单元法易于建立高阶近似函数的优点,位移采用二阶移动最小二乘近似。在更新拉格朗日方法的框架下,通过对控制方程弱形式的线性化建立了内力率的表达式,并区分为材料和几何两部分。采用Hughes-Winget算法更新应力,建立了Newton-Raphson迭代求解所需的一致切线刚度阵。刚度阵的数值积分采用近来针对小变形分析建立的二阶一致三点积分格式QC3(Quadratically Consistent 3-point integration scheme)。数值结果证明了本文方法分析弹塑性大变形问题的有效性和优越性。

In this paper,the element-free Galerkin(EFG)method is employed to solve elastoplastic large deformation problems.By taking full advantage of the merit that the EFG method is convenient to construct high order approximation functions,second order moving least-squares approximation of the displacement is employed.In the framework of the updated Lagrangian method,through the linearization of the weak form of the governing equation,the expression of the rate of the internal force is established and it is divided into material part and geometrical part.Hughes-Winget algorithm is employed to update the stress.The consistent tangent stiffness matrix is established,which is required in the Newton-Raphson iteration.The Quadratically Consistent 3-point(QC3)integration scheme,which is recently developed for small deformation analysis,is employed to numerically evaluate the stiffness matrix.Numerical results demonstrate the validity and superiority of the developed method in solving elastoplastic large deformation problems.