A Refined Solution to the System of Differential Equations in the Problem of Bending in Thin-Shell Waveguide Structures

We suggest a particular analytical solution to a system of linear partial differential equations for computing the stress state parameters of thin-walled straight sections belonging to waveguides found in waveguide switch systems of communication spacecraft. We take into account the basic requirements for structural, functional and performance parameters of waveguides subjected to bending, using the concepts of the plate and shell theory employing the semi-inverse Saint-Venant method for displacements and stresses that makes it possible to find the stress-strain state at any point in the structure. We derive equations determining refined normal stress values in a waveguide subjected to bending and deduce the presence of local tangent stress regions in the zones where the plates forming its cross-section join

References

[1] Feodos'ev V.I. Soprotivlenie materialov [Materials strength]. Moscow, Bauman MSTU Publ., 1999. 592 p.

[2] Feodosev V.I. Izbrannye zadachi i voprosy po soprotivleniyu materialov [Select problems and questions on materials strength]. Moscow, Nauka Publ., 1967. 376 p.

[3] Agamirov L.V. Soprotivlenie materialov [Materials strength]. Moscow, Astrel Publ., 2003. 256 p.

[4] Vlasov V.Z. Izbrannye Trudy. T. 2: Tonkostennye uprugie sterzhni. Printsipy postroeniya obshchey tekhnicheskoy teorii obolochek [Select as. Vol. 2. Thin-walled elastic rods. Constructing principles of general technical theory of shells]. Moscow, AN SSSR Publ., 1963. 507 p.

[5] Rzhanitsyn A.R. Stroitelnaya mekhanika [Structural mechanics]. Moscow, Vysshaya Shkola Publ., 1982. 400 p.

[6] Bychkov D.V. Stroitelnaya mekhanika sterzhnevykh tonkostennykh konstruktsiy [Structural mechanics of thin-walled rod constructions]. Moscow, Gosstroyizdat Publ., 1962. 387 p.

[7] Silchenko P.N., Kudryavtsev I.V., Mikhnev M.M., Nagovitsin V.N. Method of stressdeformation distribution computation for waveguide spacecraft systems. Zhurnal SFU. Tekhnika i tekhnologii [Journal of SibFU. Engineering and Technologies], 2012, no. 2, pp. 150–161 (in Russ.).

[8] Sil’chenko P.N., Kudryavtsev I.V., Mikhnev M.M. Differential equation system for spacecraft waveguide cell. Mezhd. konf. po diff. uravneniyam i dinamicheskim sistemam [Int. conf. on differential equations and dynamic systems. Suzdal’, July 2–7, 2010]. Pp. 172–174 (in Russ.).

[9] Sil’chenko P.N., Kudryavtsev I.V., Mikhnev M.M., Khalimanovich V.I., Nagovitsin V.N. Dynamic state analysis of waveguide distribution systems from vibration loads effects while launching spacecraft into the orbit. Zhurnal SFU. Tekhnika i tekhnologii [Journal of SibFU. Engineering and Technologies], 2012, no. 2, pp. 205–219 (in Russ.).

[10] Sil’chenko P.N., Mikhnev M.M., Ankudinov A.V., Kudryavtsev I.V. Ensuring the strength and accuracy of large-size waveguide distribution systems of communication satellites. Journal of Machinery Manufacture and Reliability, 2012, vol. 41, no. 1, pp. 91–95. DOI: 10.3103/S1052618811060173

[11] Timoshenko S., Woinowsky-Krieger S. Theory of plates and shells. McGraw Hill, 1959. 591 p. (Russ. ed.: Plastinki i obolochki. Moscow, Editorial URSS Publ., 2009. 640 p.).

[12] Novozhilov V.V., Chernykh K.F., Mikhaylovskiy E.I. Lineynaya teoriya tonkikh obolochek [First-order theory of thin shells]. Sankt-Petersburg, SPbGU Publ., 2010. 380 p.

[13] Kecman D. Bending collapse of rectangular and square section tubes. Int. J. Mech. Sci., 1983, vol. 25, no. 9-10, pp. 623–636. DOI: 10.1016/0020-7403(83)90072-3 Available at: http://www.sciencedirect.com/science/article/pii/0020740383900723

[14] Aleksandrov A.V. Osnovy teorii uprugosti i plastichnosti [Fundamentals of elasticity and plasticity theory]. Moscow, Vysshaya Shkola Publ., 1990. 400 p.

[15] Sil'chenko P.N., Kudryavtsev I.V., Mikhnev M.M., Gotselyuk O.B. Some approaches to obtaining a solution of the system of differential equations for an element of the waveguide system of a spacecraft. Vestnik NIYaU MIFI, 2015, vol. 4, no. 1, pp. 19–24 (in Russ.).

[16] Sil’chenko P.N., Kudryavtsev I.V., Mikhnev M.M., Gotselyuk O.B. Comparative evaluation of differential equation solutions in the problem of waveguide straight sections bend in communication spacecraft. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mech. Eng.], 2017, no. 1, pp. 4–23 (in Russ.). DOI: 10.18698/0236-3941-2017-1-4-23