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.

Keywords:

• Functionally graded materials
• Arctangent shear deformation theory
• moving kriging interpolation
• meshfree methods

Acknowledgments

The authors would like to thank the three anonymous reviewers for their insightful suggestions and careful reading of the manuscript. This research was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.01-2018.319.

Conflict of interest

The authors declare that there is no conflict of interest.

Additional information

Funding

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.01-2018.319.