Meshfree analysis of functionally graded plates with a novel four-unknown arctangent exponential shear deformation theory

Abstract

A novel refined arctangent exponential shear deformation theory (RAESDT) is presented for analysis the mechanical behavior of both isotropic and sandwich FGM plates. Material properties are set to be isotropic at each point and varied across the thickness direction obeying to a power-law distribution of the volume fraction gradation with respect to FGM core or skins of the plate. Unlike high-order shear deformation plate theories based on five or more variables, the displacement field of the novel RAESDT using arctangent exponential variations in planed displacements were approximated by only four unknowns, satisfying naturally tangential stress-free conditions at the plate surfaces and leading to reduce computational efforts. In accordance with RAESDT and enhanced moving kriging interpolation (EMKI)-based meshfree method with a new quadrature correlation function is introduced for the numerical modeling. Numerical validations with different plate configurations, geometries, length to thickness ratios and boundaries conditions are conducted. The obtained results are compared with the corresponding solutions available in the literature showing the accuracy and efficiency of the present approach.

Free vibration analysis of the structural integrity on the porous functionally graded plates using a novel Quasi-3D hyperbolic high order shear deformation theory

“…Vu et al [34] Hyperbolic high-order shear deformation theory The new shear deformation function is developed based on the following conditions:…”

“…Vu et al [33] developed a new refined quasi-3D hyperbolic shear deformation theory combined with the Navier solution to analyze the compressive buckling of porous FG plates placed on the Winkler-Pasternak foundation. Based on the moving kriging interpolation meshfree method and a novel arctangent exponential shear deformation theory, Vu et al [34] presented a mechanical behavior analysis of sandwich FG plates. They used a displacement field with only four unknowns.…”

“…Vu et al [37] and Tan-Van Vu [38] conducted a mechanical behavior analysis of an FG plate resting on elastic foundations based on a refined quasi-3D logarithmic shear deformation theory and a simple quasi-3D hyperbolic shear deformation theory, respectively. The new refined high-order theories mentioned in the references [33][34][35][36][37][38], which were combined with the meshfree method, showed many advantages, including the mathematical simplicity of their modeling, the lowest computational cost, and the accuracy compared to many high-order shear deformation theories. Due to technical issues, porosities may appear inside the material during FGM manufacturing.…”

Buckling analysis of functionally graded sandwich plates resting on Pasternak foundation using a novel refined quasi-3D third-order shear deformation theory

“…Unfortunately, the correlation parameter had a significant impact on the quality of traditional MKI shape functions, resulting in unstable solutions. Van et al [22,23] has recently attempted to overcome this limitation by improving the quality of the MK shape function through the key improvement in order to get rid of the correlation parameter effect. Utilizing this enhanced MKI-based meshfree method [22], Van et al [24] analyzed the static bending and free vibration problems of functionally graded porous plates laid on elastic foundation based on the refined quasi-3D sinusoidal shear deformation theory.…”

“…In this work, for the first time, the buckling analysis of FGSP resting on the elastic Pasternak foundations by a new refined quasi-3D third-order shear deformation theory (RQ-3DTSDT) integrated with MKI-based meshfree method based on the quadric correlation function [23] is presented.…”