Energy conserving and decaying algorithms for corotational finite element nonlinear dynamic responses of thin shells

On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rotation and small strain established before and from the generalized-alpha time integration algorithm, the energy conserving and decaying algorithms for corotational formulation nonlinear dynamic response analysis of thin shells are established in this paper. Responses are solved by means of a predictor-corrector procedure. In the case of ignoring the structural damping, the conserving or decaying total energy of structure and the controllable numerical damping for high frequency responses can ensure the numerical stability of the algorithm. The inertial parts are linearly interpolated directly in the fixed global coordinate system by using the element nodal displacement in the global coordinate system for obtaining the constant mass matrix, while the elastic parts adopt the corotational formulation. Hence, the whole formulation obtained in this paper is element independent. Through three typical numerical examples, the performances of the algorithm in this paper were compared with those of the classical Newmak and HHT-alpha algorithms to indicate that the algorithm in this paper could accurately solve nonlinear dynamic responses of thin shells with large displacements and large rotations.