Schemas explicites d' ordre eleve pour les problemes non lineaires de mecanique des structures
Keywords:
non-linear problems, explicit schemes, Runge-Kutta method, instabilities, prescribed displacement analysisAbstract
This paper presents some numerical schemes for non-linear structural mechanic problems. The proposed algorithms are non-iterative and are associated with technics for time step size and error control. We treat the discrete equilibrium relation as a system of ordinary differential equations. This system is then solved with a fourth order Runge-Kutta method. In order to use these algorithms for numerical simulation of sheet forming processes where instabilities occur we have developed a prescribed displacement technique analysis. The results obtained on bulge test and thermoforming examples show a great computational cost economy in comparison with the iterative Newton-Raphson method.
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