NONLINEAR DYNAMICS FOR MIXED SHELLS WITH LARGE ROTATION AND ELASTOPLASTICITY

Abstract

From a more recent and comprehensive perspective, work on the nonlinear dynamic response of plates and shells calls for detailed studies of several important factors. These include the effect of large spatial rotations on the geometric stiffness and inertia operators, the accurate updating procedures for nodal rotations and associated angular velocities and accelerations, as well as material inelasticity (especially for finite strains). Several of these issues are examined here in conjunction with a recently developed mixed finite element formulation for plates and shells. To this end, and restricting the scope to the case of large overall motions but small strains, low-order displacement/strain interpolations are utilized, together with a radial return algorithm (backward-Euler-integration scheme) for plasticity effects. The Newmark implicit scheme has been employed to integrate the semi-discrete equations of motion. A selective set of elastic as well as elasto-plastic problems has been solved to demonstrate the effectiveness and practical utility of the formulation described for plate and shells with arbitrary geometry.