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Nonlinear Computational Structural Mechanics
New Approaches and Non-Incremental Methods of Calculation
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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 of solution and approximation that are classically considered as parts of applied mathematics. The goal 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 the structure to minimize the damage subject to various constraints. Practical applications of the methods include design and optimization of structures and analyses of their reliability. The method used is iterative: at each stage one computes an approximation to the displacements, strains, and stresses everywhere in the structure and for all times in the interval of interest. The method rests on some remarkable properties satisfied by most of the models encountered in structural mechanics, and it leads to a general approach for understanding structural models and the necessary approximations.
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