Theory and Finite-Element Formulation for Shell Structures Undergoing Finite Rotations

Abstract For the analysis of shell structures with finite displacements and rotations a consistent shear-deformation theory is derived and discussed under different aspects. Unlike in the earlier formulations, the constraint for the so-called difference vector is replaced by new conditions with which this variable can be determined clearly in all nonlinear range. The paper continues with the finite-element implementation of the theory presented, using a mixed-formulation. The finite-element family developed on the basis of HELLINGER-REISSNER functional consists of quadrilateral shell elements with 4 and 9 nodes. Their efficiency is due to the exact enforcement of the above mentioned constraints at the element level. The ability of the finite elements to predict the displacements and the real force distribution is finally demonstrated by some strongly nonlinear examples.