Computational Treatment of Transient Problems in Nonlinear Structural Mechanics
Nonlinear transient problems are often encountered in structural dynamics. While vibration induced problems are usually linear or at most weakly nonlinear and can, therefore, be suitably solved in the frequency domain by applicatition of mode superposition techniques, many mainly accidental loading cases lead to important nonlinear phenomena and may involve wave propagation aspects. Both internal and external phenomena are to be considered: missile impact on industrial plants, shocks induced by fluids or gases during explosions or due to component failure in power plants for instance, crashes of cars or shipping casks, etc. Slower events such as seismic effects usually.reduce the actual problem to a modal analysis although such statements are to be taken with some care. In any case the present lecture notes do not consider inertial problems but rather concentrate on phenomena with relatively short time scales (say of the order of milliseconds for the structures of common interest) which typically exhibit, at least in their initial phase, strong nonlinear effects. These problems require direct time integration techniques and the solution is thus incrementally constructed in the time domain via a step-by-step procedure.
KeywordsYield Surface Cauchy Stress Time Integration Scheme Central Difference Scheme Essential Boundary Condition
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