The supercritical fluid flow jetted out from a nozzle was divided into two stages, free jetting and passing through the porous media, in a supercritical spray dyeing process. According to the nature of the flow, the free jetting model and passing through porous media model were established separately. Based on the established models, the characteristics of supercritical fluid flow field in the supercritical fluid spray dyeing process were investigated firstly in this paper. Distributions of the temperature and pressure and their influencing factors in the flow field, which are the determinants of the spray dyeing process, were obtained and analyzed. Besides, the mass flow and covering diameter sprayed by supercritical fluid were studied. The simulating analysis may provide a theoretical basis and guidance for the actual process of supercritical fluid spray dyeing.

According to the constitutive relation of linear thermovisoelasticity, with the help of Laplace transformation method and the introduction of structure functions and thermal functions, the mathematical model and its corresponding variational principle for thermoviscoelastic FGM beams are set up on the basis of the assumption that plane section remains plane and normal to the beam axis. Using Laplace transformation method, the deflection and the stress distribution are discussed.

The material properties of FGM beams are assumed to vary continuously through the thickness according to power law distribution. Based on the assumption that plane section remains plane and normal to the beam axis, the differential equations of motion were established for free vibration of FGM elastic beams under thermal loads and mechanical loads on the premise of the middle plane strain caused by heterogeneity of the materials. Natural frequency and dominant mode shape of FGM beams with four kinds of boundary conditions were obtained.

The governing equation of elastic FGM thin plates was obtained by degenerating the governing equation of viscoelastic FGM thin plates. A Levy solution of a simply supported FGM rectangular plate was gotten. Based on the Levy solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the static responses of the functionally graded materials thin plate is investigated.

The governing equation of elastic FGM thin plates was obtained by degenerating the governing equation of viscoelastic FGM thin plates. A Levy solution of a simply supported FGM rectangular plate was gotten. Based on the Levy solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the static responses of the functionally graded materials thin plate is investigated.