Geometrically exact shell with drilling rotations formulated on the special Euclidean group SE(3)

Abstract

AbstractBased 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.