论文标题
简单且坚固的无元素彩色方法，具有有限变形弹性的插值形状函数
Simple and robust element-free Galerkin method with interpolating shape functions for finite deformation elasticity
论文作者
论文摘要
在本文中，我们提出了一种属于无元素Galerkin（EFG）方法家族的无网格方法。提出的无网格方法的区别特征是它允许准确地强制实施必需边界条件。该方法将总拉格朗日公式与明确的时间集成在一起，以促进涉及大变形和非线性材料的应用中的代码简单性和可靠的计算。我们使用正规重量函数，该函数紧密近似于Kronecker Delta，以生成插值形状函数。边界上规定的位移的施加变得像有限元（Fe）方法一样简单。使用3D数值示例（包括其初始高度的70％）和大脑压痕（包括大脑的凹痕），证明了所提出方法的有效性和准确性。
In this paper, we present a meshless method belonging to the family of element-free Galerkin (EFG) methods. The distinguishing feature of the presented meshless method is that it allows accurate enforcement of essential boundary conditions. The method uses total Lagrangian formulation with explicit time integration to facilitate code simplicity and robust computations in applications that involve large deformations and non-linear materials. We use a regularized weight function, which closely approximates the Kronecker delta, to generate interpolating shape functions. The imposition of the prescribed displacements on the boundary becomes as straightforward as in the finite element (FE) method. The effectiveness and accuracy of the proposed method is demonstrated using 3D numerical examples that include cylinder indentation by 70% of its initial height, and indentation of the brain.
