Higher-order model for the thermal analysis of laminated composite, sandwich, and functionally graded curved beams

Abstract

In this paper, a polynomial type fifth-order curved beam theory is developed and applied to investigate the bending response of laminated composite, sandwich, and functionally graded beams curved in elevation under the temperature load changing linearly through the thickness. The theory developed herein considered the effects of both transverse shear strain (${\gamma }_{xz}\ne 0$) and transverse normal strain (${\epsilon }_z\ne 0$) along with the curvature effects (1+z/R). Governing equations and boundary conditions of the curved beams are derived with the help of the principle of virtual work. Navier’s method is used to get the analytical solutions of simply supported curved beams under the action of thermal load. The numerical results are obtained for various (h/L) and (R/L) ratios along with the different values of the power-law exponent in the case of functionally graded beams. The numerical results obtained using the present theory for laminated composite, sandwich, and functionally graded straight beams are compared with previously published results and then the formulation and computer codes are extended to derive the numerical results corresponding to curved beams. The authors have presented many useful results in the present paper on curved beams which can be serving as a benchmark for further studies.

Keywords:

• A fifth-order curved beam theory
• curved beams
• functionally graded
• thermal load
• laminated and sandwich
• transverse shear and normal strains