Static behavior of FG sandwich beams under various boundary conditions using trigonometric series solutions and refined hyperbolic theory

Abstract

A refined hyperbolic shear deformation theory is presented to analyze the mechanical behavior of isotropic and sandwich functionally graded material (FGM) beams under various boundary conditions. The material properties are considered to be isotropic at each point and change across the thickness direction. The volume fraction gradation follows a power law distribution with respect to the FGM core or skins of the beam. The solution is attained by minimizing the total potential energy. This recent theory is a new type of third-order shear deformation theory that includes undetermined integral variables. The recent theory describes the variation of transverse shear strains throughout the thickness of a beam. It shows how these strains satisfy the zero traction boundary conditions on the top and bottom surfaces, all without the need for shear correction factors. An analytical solution based on trigonometric series is developed to solve the problem while satisfying various boundary conditions. Comparative studies are conducted to validate the accuracy and efficiency of this method. The current model can accurately predict the static responses of functionally graded isotropic and sandwich beams with arbitrary boundary conditions.