A novel Chebyshev-based both meshfree method and shear deformation theory for functionally graded triply periodic minimal surface flat plates

Abstract

This study introduces an innovative framework for the free vibration analysis of functionally graded (FG) triply periodic minimal surface (TPMS) plates. By utilizing Chebyshev polynomials, the study integrates a new shear deformation theory with a novel the moving Kriging meshfree method. The Chebyshev shear deformation theory is proposed, inherently satisfying the zero-shear stress condition at the plate’s top and bottom surfaces without additional constraints. Furthermore, a new shape function for the moving Kriging meshfree method is developed by integrating radial basis function with Chebyshev interpolations to significantly enhances the solution accuracy of the TPMS plate. The FG-TPMS plate, characterized by porous structures with Primitive (P), Gyroid (G), and Wrapped Package-Graph (IWP) patterns, features six distinct volume distribution cases. To determine mechanical properties such as elastic modulus, shear modulus and Poisson’s ratio, a fitting technique based on a two-phase piecewise function is employed. The governing equations for the FG-TPMS plate are derived using the virtual work principle and solved with the Chebyshev moving Kriging meshfree method. Numerical results demonstrate the high reliability to produce accurately obtained results.