A low-order locking-free hybrid discontinuous Galerkin element formulation for large deformations
A low-order locking-free hybrid discontinuous Galerkin element formulation for large deformations
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DOI：
10.1016/j.cma.2017.05.018
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发表时间：
2017-08
影响因子：
7.2
通讯作者：
S. Wulfinghoff;H. Bayat;A. Alipour;S. Reese
中科院分区：
文献类型：
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作者：
S. Wulfinghoff;H. Bayat;A. Alipour;S. Reese
本文提出了一种混合型不连续伽辽金（dG）四边形单元公式。与通常的混合公式一样，元素的内部与表示元素边界的骨架分开处理。这些是运动学解耦的，也就是说，位移跳跃可以发生在骨架和元素内部之间。整体自由度（dofs）在骨架上被定义为拐角处的位移，这允许在现有的有限元代码中实现。通常在混合dg公式中，内部的自由度在单元水平上被压缩，导致与连续双线性单元相同的全局自由度数量。而不是使用传统的形状函数在内部，变形梯度F被假定为常数在单元内。此外，F通过弱形式连接到骨架自由度。这导致了一个非常简单的公式和实现。用文献中的几个计算实例对该单元进行了测试。研究了惩罚参数的特殊选择，并对其进行了部分解析推导。结果表明，该构件不存在体积锁紧和剪切锁紧。此外，收敛性与其他已知的无锁有限元公式相似。
In this work, a hybrid discontinuous Galerkin (dG) quadrilateral element formulation is presented. As usual in hybrid formulations, the interior of the elements is treated separately from the skeleton, which represents the element boundaries. These are kinematically decoupled, ie, displacement jumps can occur between the skeleton and the interior of the elements. The global degrees of freedom (dofs) are defined on the skeleton as the displacements at the corners, which allows the implementation into existing finite element codes. As usual in hybrid dG-formulations, the degrees of freedom in the interior are condensed out on the element level, leading to the same number of global degrees of freedom as for continuous bilinear elements. Instead of using conventional shape functions in the interior, the deformation gradient F is assumed constant within the element. Furthermore, F is connected to the skeleton degrees of freedom via the weak form. This leads to a very simple formulation and implementation. The element is tested for several computational examples from the literature. Special choices of the penalty parameter are investigated, which are partially derived analytically. It is found that the element is free of volumetric and shear locking. Moreover, the convergence is similar to that of other well-known locking-free finite element formulations.