Mindlin-Reissner plate formulation with enhanced kinematics: Theoretical framework and numerical applications

Abstract

This paper presents a kinematic enhanced plate model formulated within the Mindlin-Reissner theory. The main purpose of the model is to simulate the behavior of a structure up to membrane or bending failure. The shear strain is taken into account and the numerical shear locking problem is regularized by the Assumed Transverse Shear strain Field method. Two kinematic enhancements are applied at the level of the displacement fields by introducing two strong discontinuity fields. The first one is associated with the membrane displacement field and allows to describe the membrane failure and the second one is introduced in the rotation field to describe the bending failure. The Embedded Finite Element Method is used to incorporate the two kinematic discontinuities within a plate finite element, which allows to determine these new variables at the local level by the static condensation technique and to keep the architecture of the computational software unchanged. The kinematic and equilibrium operators associated with the enhancement variables are determined by fulfilling specific conditions. Case-studies are considered to asses the relevancy of the behavior of the enhanced membrane component as well as the behavior of the enhanced bending component. A mesh sensitivity analysis is also carried out. Finally, the Willam’s test is performed for both components to verify the numerical robustness of the model and to analyze the apparent anisotropy associated with the development of discontinuities within the element. The present results allow to demonstrate the robustness of the numerical framework reported in this paper.