| A geometrically nonlinear finite element formulation for an 18-node degenerated solid element was developed for analyzing large deformations of thin shell structures. The element, degenerated from a 27-node solid element from the Lagrange family, contains only translational degrees-of-freedom and thus it can be used to analyze not only thin shell structures but also beam and non-thin-wall structures. Reduced integration is employed to relax locking which is a deficiency in finite elements based upon the Reissner-Mindlin theory. A stabilization procedure using an assumed strain field was developed to alleviate spurious energy modes resulting from the use of reduced integration. Compared with the stabilization procedure formulated based upon the Hellinger-Reissner principle, the proposed stabilization procedure in conjunction with the principle of virtual work yielded a more efficient finite element formulation. Both the Newton-Raphson method with a line search procedure and the Modified Constant-Arc-Length method were formulated to solve for nodal displacements. The formulations were implemented in a FORTRAN computer code and were verified numerically by several structural benchmark problems. |
