厚壳理论及其在圆柱壳中的应用
Theory of Thick-Walled Shells and Its Application in Cylindrical Shell
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摘要: 本文从Hellinger-Reissner广义变分原理出发,以位移和应力的假设为基础,建立了厚壳理论.文中把壳体的位移展开为其厚度方向的幂级数,对平行和垂直于中面的位移分别保留其级数的前四项和前三项.并假定壳体的法向挤压和横向剪切应力沿壳厚为三次曲线,使其满足上下壳面上的应力条件,利用变分原理推导出分析厚壳所需的物理方程,平衡方程和边界条件.文中对圆柱壳的情况作了实例计算,并作了光弹性实验,结果表明理论和实验符合良好.Abstract: In this paper,a theory of thick-walled shells is established by means of Hellinger-Reissner's variational principle,with displacement and stress assumptions.The displacements are expanded into power series of the thickness coordinate.Only the first four and the first three terms are used for the displacements parallel and normal to the middle surface respectively.The normal extruding and transverse shear stresses are assumed to be cubic polynomials and to satisfy the boundary stress conditions on the outer and inner surfaces of the shell.The governing equations and boundary conditions are derived by means of variational principle.As an example,a thick-walled cylindrical shell is disscussed with the theory proposed.Furthermore,a photoelastic experiment has been carried out,and the results are in fair agreement with the computations.
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[1] Naghdi,P.M.,On the theory of thin elastic shells.Quart.Appl.,Math.,14,4(1957),369-38O. [2] Hildebrand.F.B.,E.Reissncr and G.B.Thomas,Notes on the foundations of the theory of small displacements of orthotropic shell,NACA TN.1833(1949). [3] Niodson,F.L,A consistent refined shell theory,Tech.Univ.Denmark,Report No.104(1976). [4] Vlasov.V.Z.General theory of shells and its application to the engineering(English translation),NASA TT F-99.(1964). [5] Mayes,P.J.D.End stress calculations on elastic cylinders,Int.J.Sol.Struct.,19,10(1983),895-906. [6] Reissner E.,On a variational theorem in elasticity,J.Math.Phy,29(1950),90-95. -
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