ADVANCED SOLUTION ALGORITHMS IN CONJUNCTION WITH LARGE DEFORMATION CONTACT STRATEGIES

This dissertation develops strategies which permit the automatic load adjustment of the constrained Newton-Raphson approach recently used to extend the range and numerical stability of nonlinear finite element equation solvers. In addition to handling kinematic and materially induced nonlinearity, both pre- and postbuckling behavior can be treated. Moreover, localized constraints applied to the governing field variables are derived and shown to be hierarchical partitions of the displacement function. These local constraints are used to resize, reshape, and orient the global constraint surface thereby allowing automatic deflection incrementation.; In conjunction with the above numerical synthesis, a pantographing self-adaptive gap element contact strategy was developed. Due to the manner of formulation, this scheme can handle: large deformation in the contact zone, contact initiation in structures exhibiting either positive or indefinite stiffness characteristics, kinematic and material nonlinearity. In addition, the scheme includes a modified self-adaptive feature which permits automatic load/time stepping in the vicinity of contact. Hence, contact in the pre- and postbuckling range can be treated.; To demonstrate the above schemes, the numerical strategies and contact element have been implemented into the ADINA finite element program. Included in this work are the results of numerous benchmarks which verify the ability of this research to handle many forms of nonlinearity. Furthermore, a comparison against experiment is provided for the contact algorithm.