The influence of the frame stiffness on the deformation of a cylindrical shell

The load acting on a shell through its frame is distributed circumferentially over the shell surface. The stress-strain state of this shell depends on the frame stiffness. To assess the strength of the stiffened shell, it is necessary to develop a mathematical model of joint deformation of the shell and frame and solve this problem numerically. In this paper, the frame is represented by an elastic circle with appropriate stiffness characteristics, which lies in the middle surface of the shell. The mathematical model of deformation of the frame includes the set of equilibrium equations for a circular element and geometrical and physical relationships. In fact, it is a system of four linear ordinary differential equations solvable for the displacement components of a frame point and the angle of twi s t . The proposed mathematical model made it possible to estimate available models used for the analysis of design solutions. The calculations in a wide range of parameters of shells and frames showed that simplified mathematical models of a frame do not provide an adequate accuracy of the resul t s , which i s unacceptable for evaluating strength of shells stiffened by frames.

References

[1] Vlasov V.Z. Obshchaia teoriia obolochek i ee prilozhenie v tekhnike [General theory of shells and its application in engineering]. Moscow, Gostekhizdat publ., 1949, 784 p.

[2] Vlasov V.Z. Izbrannye trudy [Selected Works]. Moscow, AN SSSR publ., 1962, vol. 1. 528 p.

[3] Vinogradov Iu. I. , Kl iuev Iu. I. Tonkos tennye osesimmetrichnye konstruktsii iz kompozitsionnykh materialov (metod resheniia zadach statiki i dinamiki) [Thin-walled axisymmetric structures made of composite materials (method of solving problems of stat ics and dynamics)] . Mekhanika kompozitsionnykh materialov i konstruktsii [Journal on Composite Mechanics and Design]. Institute of Applied Mechanics of Russian Academy of Sciences publ., 1984, vol. 4, no. 1, pp. 57—72.

[4] Vinogradov Yu., Bakulin V. Numerical method investigation of shells under the impact of concentrated load. Matematicke metody v technickych vedach mathematical in engineering. Karlovy Vary, Czechoslovak Scince and Technikal Socity Charles University Prague — Faculty of Mathematies and Phaysics Slovak society for Mechanics subsidiary of Slovak Academy of Sciences, Central Research Institute SKODA Concern, Concern Enterprise Pzen, 1986, vol. 1, pp. 411—412.

[5] Vinogradov Iu.I. Metody vychislenii i postroenie algoritmov resheniia kraevykh zadach stroitel’noi mekhaniki [Calculation methods and the construction of algorithms for solving boundary value problems of structural mechanics]. Report of the Academy of Sciences of the USSR publ., 1988, vol. 298, no. 2, pp. 308—313.

[6] Varvak P.M., Riabov A.F. Spravochnik po teorii uprugosti [Handbook of the theory of elasticity]. Kiev, Budevel’nik publ., 1971. 419 p.