Geometrically nonlinear coupled analysis of thin-walled $$\hbox {Al/Al}_{2}\hbox {O}_{3}$$ Al/Al 2 O 3 FG sandwich box beams with single and double cells

Abstract

In this study, a geometrically nonlinear coupled analysis of thin-walled $$\hbox {Al/Al}_{{2}}\hbox {O}_{{3}}$$ functionally graded (FG) sandwich box beams with single and double-cell sections is presented. The material properties such as Young’s modulus and Poisson’s ratio are continuously graded through the thickness of wall. The geometric nonlinearity is considered in the von Karman sense, and the analysis model includes the effects of elastic coupling and restrained warping. The nonlinear governing equations are derived and solved by the Newton–Raphson method. The displacement-based one-dimensional finite element model using the Hermite cubic interpolation polynomials is employed with the scope to discretize the nonlinear governing equations. Numerical results are obtained for $$\hbox {Al/Al}_{{2}}\hbox {O}_{{3}}$$ FG sandwich box beams with single- and double-cell sections. Three types of material distributions are considered to investigate the effects of geometric nonlinearity, gradient index, thickness ratio of ceramic, material ratio, span-to-height ratio, and boundary conditions on the nonlinear coupled responses of $$\hbox {Al/Al}_{{2}}\hbox {O}_{{3}}$$ FG sandwich box beams. Numerical results show that above-mentioned effects play an important role on the nonlinear behavior of FG sandwich box beams.