Nonlinear analysis of shell structures by degenerated isoparametric shell element

Abstract

Two rotation strategies termed the finite rotation method and the mixed rotation method are proposed to describe the rotation of the shell normal and four rotation strategies in the literature are reviewed. The rotation variables of the finite rotation method are chosen to be the incremental rotations with respect to the x 1 and x 2 axes of a moving coordinate system rigidly tied to the shell. Both the rotation increments between two successive increments and the rotation corrections between two successive iterations are used as the incremental rotations. The previous convergent stress is employed to update the geometric stiffness matrix and its performance is compared with that of the standard geometric stiffness matrix update method. The six types of rotation variables are embedded into a shell element whose formulation is based on that of the degenerated isoparametric shell element proposed by Ramm. In order to test and compare the performance of the various rotation strategies, numerous numerical examples are studied. The numerical algorithm used here is an incremental-iterative method based on the Newton-Raphson method combined with the constant arc length method.