Modeling Deficiencies in the Eight-Node Mindlin Plate Finite Element Physically Explained

Abstract

Modeling errors that prevent the eight-node Mindlin plate finite element to behave correctly, namely shear locking and spurious zero-energy modes, can be explained using strain gradient notation. This notation is physically interpretable, and it allows for the sources of shear locking and spurious zero-energy modes to be clearly identified a priori. This means that spurious terms in shear strain polynomials are precisely identified as parasitic shear terms. Once this is done, such spurious terms are simply removed to correct the element model, resulting in a shear locking-free element. In order to avoid introducing spurious zero-energy modes, the analyst must recognize and retain the compatibility modes in the shear strain polynomials. As the study shows, compatibility modes can easily be confused with parasitic shear terms. Numerical displacement and stress solutions from models containing parasitic shear terms revisit important locking effects. Further, solutions obtained using corrected models are qualitatively correct and have higher rates of convergence.