Adaptive finite-element methods for shells. Final report, 1 September 1985-31 December 1987

An adaptive finite-element procedure is developed for the transient analysis of nonlinear shells. The scheme is an h-method that employs fission and fusion. Criteria based on incremental work and deviation of the bilinear finite-element approximation to the shell from a Kirchhoff-Love surface are used as criteria for adaptivity. The example problems show that the adaptive schemes are capable of achieving substantial improvements in accuracy for a given computational effort. They include both material and geometric nonlinearities and local and global buckling. In order to formulate an r-adaptive method, the conservation laws, the constitutive equations, and the equation of state for path-dependent materials are formulated for an arbitrary Lagrangian-Eulerian description. Both geometrical and material nonlinearities are included in this setting.