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

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