几何非线性分析的高效高阶无网格法

Efficient high order meshfree method for geometrically non-linear analysis

准确高效地处理几何非线性对于材料破坏等大变形过程的数值分析至关重要。考虑到无网格法具有易于形成高阶近似函数等诸多优点,本文发展了几何非线性分析的高阶无网格法。采用上一载荷步收敛的构形作为计算的参考构形,位移本质边界条件由罚函数法施加。为提高计算效率,将针对线性问题发展的二阶一致三点积分格式QC3(Quadratically Consistent 3-point integration scheme)拓展到考虑构形变化的几何非线性分析,大幅度减少了所需的积分点数目。数值结果表明,本文发展的高阶无网格法能够准确有效地处理几何非线性问题,而且在计算效率、精度以及应力场光滑性等方面均表现出显著优势。

An accurate and efficient treatment of geometrical non-linearity is crucial to the numerical analysis of a large deformation process such as material failure.In view of the merits of meshfree methods such as their convenience to construct high order approximation functions,this paper presents the high order meshfree method for geometrically nonlinear analysis.The configuration converged in the last loading step is employed as the reference configuration.The essential boundary condition in displacement is enforced by the penalty method.To improve the computational efficiency,the quadratically consistent 3-point(QC3)integration scheme which is originally developed for linear problems is extended to geometrically non-linear analysis where the change in configuration must be considered.As a consequence,the number of quadrature points required for domain integration is dramatically reduced.Numerical results show that the proposed high order meshfree method is able to deal with geometrically non-linear problems accurately and exhibits remarkable superiorities in computational efficiency,accuracy and smoothness of the resulting stress fields.