This book treats computational modeling of structures in which strong nonlinearities are present. It is therefore a work in mechanics and engineering, although the discussion centers on methods that are considered parts of applied mathematics. The task is to simulate numerically the behavior of a structure under various imposed excitations, forces, and displacements, and then to determine the resulting damage to the structure, and ultimately to optimize it so as to minimize the damage, subject to various constraints. The method used is iterative: at each stage an approximation to the displacements, strains, and stresses throughout the structure is computated and over all times in the interval of interest. This method leads to a general approach for understanding structural models and the necessary approximations.

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