High-Precision Isogeometric Static Bending Analysis of Functionally Graded Plates Using a New Quasi-3D Spectral Displacement Formulation

Abstract

A new quasi-three-dimensional (3D) shear deformation theory, called the spectral displacement formulation (SDF), is proposed for high-precision static bending analyses of functionally graded plates. The main idea is to expand unknown displacement fields into Chebyshev series of a unique form in the thickness direction; the truncation numbers are set to be adjustable to meet various application requirements. Specifically, 3D elasticity solutions and traction-free boundary conditions can be approached by increasing the number of Chebyshev bases. The SDF is also an extension of the classical plate theory and naturally avoids the shear locking problem, making it versatile for functionally graded material (FGM) plates of arbitrary thicknesses. The C1 continuity requirement for the discretization of the generalized displacements is conveniently fulfilled by the nonuniform rational B-splines (NURBS)-based isogeometric method. Numerical examples demonstrate the excellent performance of the proposed method for the displacement and stress analyses of functionally graded plates. The high precision and versatility of the present method have manifested its great potential applications in strain-based or stress-based reliability analysis, optimization design, fatigue analysis, and fracture analysis of FGM plates, and other related fields.

Isogeometric Analysis for Free Vibration of Functionally Graded Plates Using a New Quasi-3D Spectral Displacement Formulation

“…This paper presents a novel quasi-3D theory called the spectral deformation formulation (SDF) [49,50], where the unknown displacement field is expanded as a unique form using the Chebyshev series. Similar to CUF, this theory exhibits hierarchical refinement capability, enabling a perfect match with the 3D elasticity solution.…”

“…Additionally, the SDF is an extension of CPT, thus naturally avoiding the shear-locking problem. Consequently, this theory is applicable to both thin and thick plates while maintaining high accuracy [50]. This study analyzes the free vibration of FGM plates by incorporating this theory with IGA methods.…”