Dynamic Snap-Through Instability of Hygro-Thermally Excited Functionally Graded Porous Arches

Abstract

In this paper, the dynamic buckling of functionally graded (FG) porous shallow arches under hygro-thermal loading is studied through a numerical approach. Even and uneven porosity imperfections, hygroscopic stresses generated due to the nonlinear rise in moisture concentration, and the temperature dependence of material properties are all taken into account. The transient heat conduction equation is solved to derive the temperature profile. Hygro-thermo-mechanical properties of the arch are obtained applying the modified Voigt’s rule of mixture. The first-order shear deformation theory, the von-Kármán geometrical nonlinearity assumption, and the hygro-thermal strains are considered concomitantly to derive the equations of motions based on Hamilton’s principle. The generalized differential quadrature method (GDQM) and Newmark-beta integration schemes are also employed in conjunction with an iterative approach to solve the set of nonlinear governing differential equations of motion. The Budiansky–Hutchinson stability criterion is utilized to capture the dynamic buckling temperature of the structure. A parametric study is conducted in order to investigate the effects of porosity distribution, FG index, geometrical parameters, hygroscopic loading, and thermal/mechanical boundary conditions on arch’s dynamic buckling temperature.