Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method

Abstract

In the present investigation, geometrically nonlinear response of a shallow curved tube subjected to thermal loading is analyzed. The tube is made of a functionally graded material (FGM), where properties are distributed across the tube radius. Thermomechancal properties of the constituents are assumed to be temperature dependent. The simple case of uniform temperature rise loading is considered. A higher order displacement field is considered for the tube which satisfies the conditions of zero tangential tractions on the inner and outer surfaces of the tube. With the aid of von Kármán strain-displacement relations, linear thermoelastic constitutive law, and Hamilton's principle the governing equations of the tube are obtained. These equations are reduced to new two coupled equations for the case of axially immovable tubes. These new equations are solved using the two step perturbation technique for pinned and clamped tubes. Closed form expressions are provided to estimate the deflections in the FGM temperature dependent curved tubes under uniform thermal load. The effect of boundary conditions, temperature dependency of material properties, and geometrical properties are discussed via numerical examples.