Nonlinear bending analysis of size-dependent FG porous microtubes in thermal environment based on modified couple stress theory

Abstract

This study deals with the nonlinear bending analysis of elastic tubes made of functionally graded (FG) porous material based on modified couple stress theory. Immovable simply supported and clamped boundary conditions are assumed for the FG porous microtubes resting on nonlinear elastic foundation. Transverse pressure load is applied uniformly on the upper surface of the microtube which is exposed to uniform temperature field. Temperature-dependent material properties of the microtube with uniformly distributed porosity are graded across the radius of the cross-section. The higher-order shear deformation theory of circular beams is presented to approximate the displacement field. The von Kármán type of kinematic assumptions is utilized for nonlinear strain-displacement relations. The uncoupled thermoelasticity theory is used to derive the constitutive equations. With the establishment of the virtual displacement principle, nonlinear differential equations governing the equilibrium position of the microtube are extracted. These equilibrium equations are analytically solved by means of the two-step perturbation technique and Galerkin procedure. Parametric investigations are performed to demonstrate the size-dependent nonlinear bending responses of an FG porous microtube on nonlinear elastic foundation in thermal environment.