In this paper we develop the formulation for large displacement, large rotation, but small strain, for Timoshenko beam. The so-called "finite rotation vector" is used. Rather to use a finite element formulation we solve the exact semi-local differential equations, written in the actual configuration, using a space (finite difference method) and time (Runge Kutta method) integration scheme. This method is retricted to geometrically simple structures but is developed to validate FEM codes. We present a static and dynamic example.
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