Geometrically nonlinear analysis of functionally graded shallow curved tubes in thermal environment

Present research aims to analyze the nonlinear bending response of the functionally graded material curved tube subjected to the uniform lateral pressure. The effect of thermal environment is also included. Properties of the arch are distributed through the radial direction using a power law function. Thermomechanical properties of the media are assumed to be temperature dependent. The governing nonlinear equilibrium equations of the arch are obtained by means of the von Kármán assumption and a higher order shear deformation tube theory which satisfies the traction free boundary conditions on the inner and outer surfaces of the tube. The three coupled nonlinear equations of the tube are reduced to new two ones in a dimensionless presentation. These two equations are solved using the two step perturbation technique for pin ended and clamped ended boundary conditions. Closed form and accurate expressions are provided to estimate the deflection of the arch as a function of the thermal and mechanical load parameters. Numerical results are provided to explore the effect of different parameters such as the power law index of the FGM tube, boundary conditions of the tube, thermal environment, and three geometrical parameters.