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.
General
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