Bending of Porous Functionally Graded Truncated Conical Shells in Winkler Elastic Medium
Most of the studies on the mechanical properties of plate and shell structures in elastic media assume that the structure is always in close contact with the medium during the deformation process.In order to study the bending problem of truncated conical shells with functionally graded materials containing pores in separable Winkler elastic medium under circumferential load,the mass fraction,volume index and porosity of ceramic materials are taken as control parameters,and the physical parameter model of functionally graded materials containing uniform pores is calculated according to the mixing law.Based on Donnell's classical thin shell theory and Hamilton principle,the equilibrium equation and deformation coordination equation of truncated conical shells under the combined action of Winkler elastic medium and circumferential load are established.Considering the simply supported boundary conditions at both ends of the conical shell,the analytical solution of the bending deflection of the conical shell is obtained by Galerkin integral method.Considering the contact and detachment of the elastic medium and the shell,the effects of porosity,functionally graded material composition and truncated cone shell size on the deflection value of the shell are discussed.The results show that the deflection value of the truncated cone shell increases with the increase of porosity,volume index,shell aspect ratio,diameter-thickness ratio and half cone angle,but decreases with the increase of ceramic mass fraction.The deflection value of the contact between the Winkler elastic medium and the truncated conical shell is smaller than that when the elastic medium is detached,and the elastic medium has a certain reaction force on the shell.In the direction of the generatrix of the truncated conical shell,the deflection value in the middle is larger,and the deflection value decreases gradually from the middle to both ends.In the circumferential direction of the shell,the deflection value shows a periodic change.The bending problem of porous FGM truncated conical shell under elastic medium and circumferential load is analyzed,which provides a theoretical basis for the application of FGM truncated conical shell in engineering field.
elastic mediumfunctionally graded materialsporestruncated conical shellsbendingDonnell theorygalerkin integral methodstructural stiffness
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