Discrete Dynamic Models for Elasto-Inelastic Beams

Three discrete physical models, obtained by lumping the flexibility and the mass of the continuous system, or both, are used to compute the dynamic response of beams. The beams may have general elasto-inelastic bending moment curvature relations such as the linearly elastic, elasto (perfectly) plastic, and strainhardening relations. The method of solution, based on simple physical concepts, follows from considerations of geometry of deformation, material properties, kinetics, and a numerical integration procedure in the time dimension. The relative merits of the models are discussed from the standpoint of accuracy, arranging equations, programming, and computer time. Rather extensive results were obtained for the response of a simply supported beam. The data shows that all models yield the same apparent limit deflection. Presented also are several other numerical examples to compare with certain numerical results available in the literature; comparisons generally indicate good agreement.