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ANCF curvature continuity: application to soft and fluid materials
Nonlinear Dynamics ( IF 5.6 ) Pub Date : 2020-03-21 , DOI: 10.1007/s11071-020-05550-5
Ahmed A. Shabana , Dayu Zhang

Abstract

The continuity of the position-vector gradients at the nodal points of a finite element mesh does not always ensure the continuity of the gradients at the element interfaces. Discontinuity of the gradients at the interface not only adversely affects the quality of the simulation results, but can also lead to computer models that do not properly represent realistic physical system behaviors, particularly in the case of soft and fluid material applications. In this study, the absolute nodal coordinate formulation (ANCF) finite elements are used to define general curvature-continuity conditions that allow for eliminating or minimizing the discontinuity of the position gradients at the element interface. For the ANCF solid element, with four-node surfaces, it is shown that continuity of the gradients tangent to an arbitrary point on a surface is ensured as the result of the continuity of the gradients at the nodal points. The general ANCF continuity conditions are applicable to both reference-configuration straight and curved geometries. These conditions are formulated without the need for using the computer-aided-design knot vector and knot multiplicity, which do not account properly for the concept of system degrees of freedom. The ANCF curvature-continuity conditions are written in terms of constant geometric coefficients obtained using the matrix of position-vector gradients that defines the reference-configuration geometry. The formulation of these conditions is demonstrated using the ANCF fully parameterized three-dimensional solid and tetrahedral elements, which employ a complete set of position gradients as nodal coordinates. Numerical results are presented in order to examine the effect of applying the curvature-continuity conditions on achieving a higher degree of smoothness at the element interfaces in the case of soft and fluid materials.



中文翻译:

ANCF曲率连续性:应用于柔软和流体材料

摘要

有限元网格的节点处位置矢量梯度的连续性并不总是确保元素界面处的梯度连续性。界面处梯度的不连续性不仅会不利地影响仿真结果的质量,而且还会导致计算机模型无法正确地代表现实的物理系统行为,尤其是在软性和流体材料应用中。在这项研究中,使用绝对节点坐标公式(ANCF)有限元来定义一般曲率连续性消除或最小化元素界面位置梯度不连续性的条件。对于具有四节点表面的ANCF实体元素,显示了与节点上任意点相切的梯度的连续性,这是由于节点处的梯度连续性所致。一般的ANCF连续性条件适用于参考配置的直线和曲线几何。无需使用计算机辅助设计的结矢量和结多重性就可以制定这些条件,而结点矢量和结多重性不能正确解释系统自由度的概念。根据使用定义参考配置几何形状的位置矢量梯度矩阵获得的恒定几何系数来编写ANCF曲率连续性条件。使用ANCF完全参数化的三维实体和四面体元素演示了这些条件的制定,这些元素采用了完整的位置梯度集作为节点坐标。给出了数值结果,以检验在软和流体材料的情况下,应用曲率连续性条件对在单元界面处实现更高程度的平滑度的影响。

更新日期:2020-03-22
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