Nonlinear stability of moderately thick functionally graded sandwich shells with double curvature in thermal environment

Abstract Theoretical closed-form solutions and numerical results for nonlinear stability of the moderately thick functionally graded sandwich shells subjected to thermomechanical loadings are presented in this study. Two proposed material distribution models supported by elastic foundations are examined. The nonlinear strain field is deduced from the first-order shear deformation theory taking the stretching, bending and shear effects into consideration. The Bubnov–Galerkin procedure and harmonic balance principle are utilized to bring about the explicit algebraic expression for the shell static behaviors from governing equations derived from Hamilton's principle. Mechanical buckling loads and critical thermal rises for the shells in spherical, cylindrical, and hyperbolic paraboloid forms are obtained. The effect of geometry, elastic foundations, volume fraction index, material distribution models, buckling modes, and imperfections on the shell stability behaviors are considered in parametric studies. The yielding plateau in the thermal analysis of the spherical shells in case of temperature dependent characteristics is recognized for the first time. Verification studies are also conducted.