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Extra-dof-free generalized finite element method for non-linear analysis[J].计算力学学报,2021,38(1):60~65

Extra-dof-free generalized finite element method for non-linear analysis
Extra-dof-free generalized finite element method for non-linear analysis

DOI：10.7511/jslx20200413001

 作者 单位 马今伟 大连理工大学 工业装备结构分析国家重点实验室, 大连 116024 段庆林 大连理工大学 工业装备结构分析国家重点实验室, 大连 116024 陈嵩涛 大连理工大学 工业装备结构分析国家重点实验室, 大连 116024

将无额外自由度的广义有限元法由线弹性分析扩展到弹塑性大变形分析。局部强化函数的构建依赖于已有节点，不引入额外自由度，避免了线性相关性问题。在更新拉格朗日框架下，通过控制方程弱形式的线性化推导得到了节点内力的率形式，并分为材料和几何两部分。考虑超弹性和亚弹-塑性两种材料模型，采用Newton-Raphson迭代求解，给出了相关的一致切线刚度阵。三个典型算例的数值结果表明，本文发展的非线性无额外自由度广义有限元方法不仅能够准确求解超弹性和弹塑性大变形问题，同时相比于传统的线性有限元方法具有更高的精度。本文工作进一步拓宽了无额外自由度广义有限元方法的应用领域。

In this paper,the extra-dof-free generalized finite element method (GFEM) is extended from linear elastic analysis to nonlinear elastoplastic large deformation analysis.The local enrichment functions rely on existing nodes without introducing extra degrees of freedom (dof) and hence the issue of linear dependence is removed.In the framework of the updated Lagrangian method,the rate form of the nodal internal force is obtained by the linearization of the weak form of the governing equation and it is divided into material and geometrical parts.Hyperelastic and hypo-elastoplastic material models are considered.The Newton-Raphson iteration is employed and the related consistent tangent stiffness matrix is provided.Three benchmark examples are analysed.Numerical results show that the developed nonlinear extra-dof-free GFEM is able to accurately solve hyperelastic and hypo-elastoplastic large deformation problems and it has higher accuracy than the traditional linear finite element method.This work broadens the range of the application fields of the extra-dof-free GFEM.