Geometrically nonlinear mode approximations for impulsively loaded homogeneous viscous beams and frames

Abstract Homogeneous viscous relations are used to model rigid-visco plastic materials under impulsive loading conditions, and offer computational advantages because of their homogeneity and the absence of a rigid phase. This paper extends earlier work on the analysis of geometrically linear problems to the practically more realistic case of structures undergoing large displacements. The well established instantaneous mode approximation technique is used, together with the implementation of a new algorithm for the determination of the instantaneous mode shape. The method has particular advantages, because the determination of the mode shape is essentially a geometrically linear problem, all the non-linearity appearing in the constant average acceleration forward integration technique. Illustrations of the calculations which are possible by this method are presented.

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