Winkler弹性介质中多孔功能梯度材料截锥壳的弯曲

Bending of Porous Functionally Graded Truncated Conical Shells in Winkler Elastic Medium

摘要:

弹性介质中板壳结构的力学特性研究，大都假设结构体在变形过程中始终与介质紧密接触。为研究可脱离的Winkler弹性介质中含孔隙功能梯度材料截锥壳在环向荷载作用下的弯曲问题，以陶瓷材料质量分数、体积指数和孔隙率为控制参数，根据混合律计算含均匀孔隙功能梯度材料的物性参数。基于Donnell经典薄壳理论和Hamilton原理，建立Winkler弹性介质和环向荷载共同作用下截锥壳的平衡方程和变形协调方程。考虑锥壳两端简支边界条件，采用Galerkin积分法求解得到截锥壳弯曲挠度的解析解。研究在弹性介质与壳体接触和脱离两种情况下，孔隙率、功能梯度材料组成和截锥壳尺寸等因素对壳体挠度值的影响。结果表明，截锥壳挠度值随着孔隙率、体积指数、壳体长径比、径厚比和半锥角的增大而增大，随着陶瓷质量分数的增大而减小。截锥壳与Winkler弹性介质接触时的挠度值比脱离时小，这是因弹性介质对壳体有一定的反作用力。在截锥壳母线方向上，其中部的挠度值较大，而由中部到两端的挠度值逐渐减小；在截锥壳环向方向上，其挠度值呈现周期变化。分析多孔FGM截锥壳在弹性介质和环向荷载作用下的弯曲问题，为FGM截锥壳在工程领域中的应用提供了理论基础。

Abstract:

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.