Large deformation analysis of rubber based on a reproducing kernel particle method
Large deformation analysis of rubber based on a reproducing kernel particle method
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DOI：
10.1007/s004660050170
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发表时间：
1997-02-01
影响因子：
4.1
通讯作者：
Wu, CT
中科院分区：
文献类型：
--
作者：
Chen, JS;Pan, C;Wu, CT
针对橡胶材料的大变形问题，提出了一种非线性再生核质点法（RKPM）。在这种方法中，全球节点的形状功能的基础上RKPM派生的Galerkin近似的变分方程制定的边界值超弹性问题的离散方程。讨论了RKPM离散超弹性问题解的存在性。提出了施加本质边界条件的拉格朗日乘子法和直接变换法。讨论了物质核函数和空间核函数的特点。在目前的工作中，使用的材料核函数，确保再生核的稳定性下大变形。通过数值算例研究了RKPM形函数的特性，验证了该方法在大变形分析中的有效性。由于目前的方法采用C-m的整体形状函数，该方法表现出上级性能的常规有限元方法在处理大的材料变形。
A nonlinear formulation of the Reproducing Kernel Particle Method (RKPM) is presented for the large deformation analysis of rubber materials which are considered to be hyperelastic and nearly incompressible. In this approach, the global nodal shape functions derived on the basis of RKPM are employed in the Galerkin approximation of the variational equation to formulate the discrete equations of a boundary-value hyperelasticity problem. Existence of a solution in RKPM discretized hyperelasticity problem is discussed. A Lagrange multiplier method and a direct transformation method are presented to impose essential boundary conditions. The characteristics of material and spatial kernel functions are discussed. In the present work, the use of a material kernel function assures reproducing kernel stability under large deformation. Several of numerical examples are presented to study the characteristics of RKPM shape functions and to demonstrate the effectiveness of this method in large deformation analysis. Since the current approach employs C-m global shape functions, the method demonstrates a superior performance to the conventional finite element methods in dealing with large material distortions.