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Abstract

A simple numerical solution strategy for predicting the transient response of slender ductile beams, exhibiting geometric and/or material non-linear behaviour, is presented in this study. In the theoretical development of the problem the governing non-linear equation of motion, in variational form, for the bending and stretching of a Bernoulli-Euler beam is established. The numerical solution procedure is then initiated by employing the assumed displacement version of the Finite Element Method with 1-dimensional 6-DOF beam elements. Elastic-plastic strain-hardening of the beam material is conveniently accounted for by means of the "mechanical sublayer model". Visco-plastic material behaviour is included in the analysis through a simple strain-rate dependent constitutive relationship. The equations of motion for the spatially discretized beam are integrated time-wise by means of the central difference method. A variety of examples are then solved and the results compared with solutions from other sources. In general, the numerical solution strategy yields an efficient and accurate modelling of the non-linear transient response of slender ductile beams.