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Geometrically exact shell with drilling rotations formulated on the special Euclidean group SE(3)
International Journal for Numerical Methods in Engineering ( IF 2.9 ) Pub Date : 2021-05-25 , DOI: 10.1002/nme.6750 Teng Zhang 1 , Cheng Liu 1 , Huiying Tang 1
International Journal for Numerical Methods in Engineering ( IF 2.9 ) Pub Date : 2021-05-25 , DOI: 10.1002/nme.6750 Teng Zhang 1 , Cheng Liu 1 , Huiying Tang 1
Affiliation
Based on the local frame approach, a new geometrically exact shell with drilling rotations is proposed in the SE(3) framework when dealing with the finite deformation and rotation issues. To eliminate the geometric nonlinearity of rigid-body motion, a drilling rotation formulation is applied to the 5-DoF shell presented in advance. As expected, the shell with drilling rotations completely eliminates the geometric nonlinearity of rigid-body motion, which results in the invariance of the Jacobian matrices of inertial and internal forces under any rigid-body motion, while the shell without drilling rotations does not. Therefore, the updates times of Jacobian matrices decreases sharply and the computational costs can be significantly reduced during dynamic analysis. By removing the rigid-body motion of the reference point, the objectivity of the discretized strain measures is guaranteed by interpolating the relative motion. To maintain second-order convergence, the expressions of the inertial and internal forces are strictly derived by linearizing the discrete weak form of the equilibrium equations. Furthermore, locking alleviation techniques are employed to alleviate shear and membrane locking. For dynamic analysis, the generalized-α method on Lie group is used to solve dynamic equilibrium equations. Finally, numerical examples are presented to illustrate the versatility and robustness of the present formulation.
中文翻译:
在特殊欧几里得群 SE(3) 上制定的具有钻孔旋转的几何精确壳
基于局部框架方法,在SE 中提出了一种具有钻孔旋转的新几何精确壳(3)框架在处理有限变形和旋转问题时。为了消除刚体运动的几何非线性,预先将钻孔旋转公式应用于 5-DoF 壳。正如预期的那样,有钻孔旋转的壳完全消除了刚体运动的几何非线性,这导致在任何刚体运动下惯性力和内力的雅可比矩阵都是不变的,而没有钻孔旋转的壳则没有。因此,在动态分析过程中,雅可比矩阵的更新次数急剧减少,计算成本可以显着降低。通过去除参考点的刚体运动,通过插入相对运动来保证离散应变测量的客观性。为了保持二阶收敛,通过对平衡方程的离散弱形式进行线性化,可以严格推导出惯性力和内力的表达式。此外,采用锁定缓解技术来减轻剪切和膜锁定。对于动力分析,采用李群广义α法求解动力平衡方程。最后,给出了数值例子来说明本公式的通用性和鲁棒性。
更新日期:2021-05-25
中文翻译:
在特殊欧几里得群 SE(3) 上制定的具有钻孔旋转的几何精确壳
基于局部框架方法,在SE 中提出了一种具有钻孔旋转的新几何精确壳(3)框架在处理有限变形和旋转问题时。为了消除刚体运动的几何非线性,预先将钻孔旋转公式应用于 5-DoF 壳。正如预期的那样,有钻孔旋转的壳完全消除了刚体运动的几何非线性,这导致在任何刚体运动下惯性力和内力的雅可比矩阵都是不变的,而没有钻孔旋转的壳则没有。因此,在动态分析过程中,雅可比矩阵的更新次数急剧减少,计算成本可以显着降低。通过去除参考点的刚体运动,通过插入相对运动来保证离散应变测量的客观性。为了保持二阶收敛,通过对平衡方程的离散弱形式进行线性化,可以严格推导出惯性力和内力的表达式。此外,采用锁定缓解技术来减轻剪切和膜锁定。对于动力分析,采用李群广义α法求解动力平衡方程。最后,给出了数值例子来说明本公式的通用性和鲁棒性。