A novel upper bound finite-element for the limit analysis of plates and shells
Résumé
Shear-locking is a classical issue in displacement-based finite-element approaches for thick plates and shells. It is even more important when considering kinematic limit analysis approaches which attempt at producing an upper bound estimate of the structure collapse load. Previous locking-free finite-element discretizations for thick plates either rely on mixed approaches or approximate strain compatibility relations which inevitably loose the upper bound status of the solution or on discontinuous interpolations which are difficult to implement and have a much higher computational cost. In this contribution, we investigate the use of a simple element with a continuous quadratic displacement and a piecewise linear rotation with continuity at the element mid-edges only. We show that this element can either produce strict upper-bound estimates taking into account the contribution of rotation jumps or a pseudo-upper bound when neglecting this contribution. Although the upper bound status is lost a priori in this case, numerical evidence indicate that limit loads usually converge from above and have a very good accuracy. Finally, we also use this element for shell problems and discuss in particular the formulation of strength criteria for thick shells. Illustrative applications show that the proposed element is free from any shear locking and produces very accurate limit load estimates for plate as well as shell problems.
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