An ES-MITC3+ plate element for static, free vibration, and buckling analyses of porous plates based on a higher-order shear deformation theory

Abstract

In this paper, a new three-node triangular plate element is proposed to analyze porous plates based on the higher-order shear deformation theory (HSDT). This approach eliminates the need for shear correction factors to adjust transverse shear behaviors by incorporating higher-order terms into the displacement fields. A bubble node located at the centroid of the element enhances displacement approximations with a cubic shape function. The in-plane strain fields are improved by averaging over the domains of elements sharing common edges, following the edge-based smoothed (ES) strain method. The surface integration of the in-plane stiffness matrices transforms to line integration on the boundaries of the smoothing domain based on the divergence theorem. The transverse shear strain fields are separately interpolated based on the MITC3+ shear-locking removal technique. The robustness of the presented element, namely ES-MITC3+ element, is investigated through static, free vibration, and buckling analyses of several benchmark porous plates with various shapes, distributions of porosity, ratios of length to thickness, porosity coefficients, and boundary conditions. Compared to other references, the proposed element has shown excellent performance in the static analysis and has proven suitable for the free vibration and buckling analyses of porous plates. As the porosity coefficient rises, the deflections of porous plates increase, while their natural frequencies and critical buckling loads diminish due to a decrease in their rigidity.