Based on the consistent symrnetrizable equilibrated （CSE） corotational formulation, a linear triangular flat thin shell element with 3 nodes and 18~ of freedom, constructed by combination of the optimal membrane element and discrete Kirchhoff trian- gle （DKT） bending plate element, was extended to the geometric nonlinear analysis of thin shells with large rotation and small strain. Through derivation of the consistent tangent stiffness matrix and internal force vector, the corotational nonlinear finite element equations were established. The nonlinear equations were solved by using the Newton-Raphson iteration algorithm combined with an automatic load controlled technology. Three typical case studies, i.e., the slit annular thin plate, top opened hemispherical shell and cylindrical shell, validated the accuracy of the formulation established in this paper.
On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rota- tion and small strain established before and from the generalized-a time integration algorithm, the energy conserving and de- caying 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 conserv- ing 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-a algorithms to indicate that the algorithm in this paper could accurately solve nonlinear dynamic respons- es of thin shells with large displacements and large rotations.
