Vibração livre e flambagem de placas de Mindlin via elementos finitos strain gradient

Abstract

The finite element method (FEM) is an approximate method for the solution of continuum problems. Among the finite element formulation techniques, there is strain gradient notation. Created in the eighties, strain gradient notation is a physically interpretable which allows for the detailed a-priori analysis of the finite element model. The polynomial expansions are inspected and spurious terms responsible for modeling errors (shear locking) are identified in the shear strains polynomial expansions. The element is corrected by simply removing the spurious terms from the shear strains expansions. Other techniques also do the correction of shear locking. For instance, the isoparametric formulation applies selective reduced-order integration. However, this correction is a-posteriori the computational implementation, and it does not eliminate necessarily the errors completely. This research presents a plate finite element based on the strain notation approach for free vibration and buckling analyses of Mindlin plates. Comparisons are performed between the results provided by strain gradient notation with parasitic shear (SGCP), isoparametric formulation with selective reducedorder integration (ISO) and strain gradient notation without parasitic shear (SG). The three different approaches are compared in examples that are available in the literature (REF), allowing for the evaluation of percent errors and convergence of the models as the meshes are refined. Results show deleterious effects caused by shear locking in free-vibration and buckling analyzes. Especially when analyzing thin plates, SG presents, in general, results closer to REF compared to ISO, always producing numerically lower values. This is explained by the fact that the strain gradient element is completely locking-free. It is possible to conclude that the finite element model based on gradient strain notation presents itself as a valid alternative for calculation of free vibrations and buckling of Mindlin plates.