Geometrically Nonlinear Stability Analysis of Shells Using Generalized Conforming Shallow Shell Element

A generalized conforming finite element theory was presented to satisfy the C¹continuity condition for plate and shell element. The effectiveness of the theory in the linear analysis has been proved. This paper discusses the membrane locking phenomenon of shallow shell element based on the satisfaction of the requirement of rigid body motion, and a technique is developed to eliminate the membrane locking phenomenon. Accordingly a geometrically nonlinear generalized conforming rectangular shallow shell element with tangential degrees of freedom of midpoints of sides is formulated. Nonlinear numerical analysis of shell stability shows that the element exhibits high precision and fast convergence characteristics.