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UBC Theses and Dissertations

Finite deflection dynamic analysis of rigid-plastic beams Vaziri, Reza


An analytical procedure, which retains the influence of finite deflections, is developed herein for the dynamic behaviour of rectangular shaped rigid-plastic beams. In the general formulation of the problem deformation is assumed to proceed under two distinct mechanisms depending on the extent to which the value of the peak pressure exceeds the static collapse pressure of the beam. These mechanisms are described by kinernatically admissible velocity fields that satisfy the appropriate continuity conditions. The governing equations of motion are derived from a variational statement consisting of the principle of virtual work and D'Alembert's principle. The conventional parabolic yield surface (which describes the coupling action between axial forces and bending moments at yield) and its associated flow rule are adopted to describe the plastic behaviour of the beam material. The kinematic small but finite deflection analysis, in which the membrane forces and bending moments interact, generally leads to basic equations which are of nonlinear character. These resulting equations are solved analytically and closed form expressions are developed for the prediction of maximum permanent deformation of the beam. A dynamic membrane analysis is carried out in those cases when the input energy is sufficiently high that the beam undergoes moderately large deformation (i.e. deflections of the order of beam thickness). Finally the dependence of the permanent deflection on the applied pressure and impulse is obtained for a family of rectangular pulses. This relationship is represented by an isoresponse curve in a form convenient for direct engineering use.

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