# Solution of problems in the theory of shells by numerical-analysis methods

Article

Received:

## Preview

Unable to display preview. Download preview PDF.

## Literature Cited

- 1.A. A. Abramov, “Transfer of boundary conditions for systems of ordinary differential equations (variant of the factorization method),” Zh. Vychisl. Mat., No. 3, No. 3, 542–545 (1961).Google Scholar
- 2.Ya. M. Grigorenko (editor), Algorithms and Programs for Solving Problems in the Mechanics of a Deformable Solid [in Russian], Naukova Dumka, Kiev (1976).Google Scholar
- 3.A. V. Aleksandrov, B. Ya. Lashchenikov, N. N. Shaposhnikov, and V. A. Smirnov, Methods of Calculating Rod Systems, Plates, and Shells by the Use of Computers [in Russian], Stroiizdat, Moscow (1976), Part 2.Google Scholar
- 4.N. A. Aluymyaé, “A variational formula for the investigation of thin-walled elastic shells in the post-critical stage,” Prikl. Mat. Mekh.,14, No. 2, 197–202 (1950).Google Scholar
- 5.S. A. Ambartsumyan, Theory of Anisotropic Shells [in Russian], Nauka, Moscow (1961).Google Scholar
- 6.R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems [Russian translation], Mir, Moscow (1968).Google Scholar
- 7.O. M. Belotserkovskii and P. I. Chushkin, “A numerical method for integral relations,” Zh. Vychisl. Mat. Fiz., No., No. 5, 731–739 (1962).Google Scholar
- 8.I. S. Berezin and N. P. Zhidkov, Methods of Calculation [in Russian], Fizmatgiz, Moscow (1962), Vol. 2.Google Scholar
- 9.V. L. Biderman, “Use of the method of factorization for the numerical solution of problems in structural mechanics,” Inzh. Zh. Mekh. Tverd. Tela, No. 5, 62–66 (1967).Google Scholar
- 10.V. L. Biderman, “Some computational methods for solving problems in structural mechanics which have been reduced to ordinary differential equations,” Raschety Prochnost', No. 17, 8–36 (1976).Google Scholar
- 11.V. L. Biderman, Mechanics of Thin-Walled Structures [in Russian], Mashinostroenie, Moscow (1977).Google Scholar
- 12.I. A. Birger, Some Mathematical Methods for the Solution of Engineering Problems [in Russian], Oborongiz, Moscow (1956).Google Scholar
- 13.I. A. Birger, Circular Plates and Shells of Revolution [in Russian], Oborongiz, Moscow (1968).Google Scholar
- 14.Yu. A. Birkgran and A. S. Vol'mir, “Investigation of large deflections of a rectangular plate by means of digital computers,” Izv. Akad. Nauk SSSR, Mekhanika i Mashinostroenie, No. 2, 100–106 (1959).Google Scholar
- 15.V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilayer Structures [in Russian], Mashinostroenie, Moscow (1980).Google Scholar
- 16.V. N. Bulgakov, Statics of Toroidal Shells [in Russian], Izd. Akad. Nauk Ukr. SSR (1962).Google Scholar
- 17.N. V. Valishvili, Computer Methods for Calculating Shells of Revolution [in Russian], Mashinostroenie, Moscow (1976).Google Scholar
- 18.V. S. Vladimirov, “An approximate solution of a boundary-value problem for a secondorder differential equation,” Prikl. Mat. Mekh.,19, No. 3, 315–324 (1955).Google Scholar
- 19.V. Z. Vlasov, General Theory of Shells and Its Applications in Technology. Selected Studies [in Russian], Izd. Akad. Nauk SSSR, Moscow (1962), Vol. 1.Google Scholar
- 20.A. S. Vol'mir, Flexible Plates and Shells [in Russian], Gostekhizdat, Moscow (1956).Google Scholar
- 21.I. I. Vorovich and V. F. Zipalova, “On the solution of nonlinear boundary-value problems in the theory of elasticity by the method of passage to a Cauchy problem,” Prikl. Mat. Mekh.,29, No. 2, 121–128 (1965).Google Scholar
- 22.I. I. Vorovich and N. I. Minakova, “Stability of a nonshallow spherical cupola,” ibid.,32, No. 2, 332–338 (1968).Google Scholar
- 23.I. I. Vorovich and N. I. Minakova, “Investigation of the stability of a nonshallow spherical cupola in high approximations,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 121–128 (1969).Google Scholar
- 24.I. I. Vorovich and N. I. Minakova, “The problem of stability and numerical methods in the theory of spherical shells,” in: Achievements of Science and Technology. Mechanics of Deformable Solids [in Russian], VINITI Akad. Nauk SSSR (1973), Vol. 7, pp. 5–86.Google Scholar
- 25.A. G. Gabril'yants and V. I. Feodos'ev, “Axially symmetric forms of equilibrium of an elastic spherical shells acted upon by a uniformly distributed pressure,” Prikl. Mat. Mekh.,25, No. 6, 1091–1101 (1961).Google Scholar
- 26.V. V. Gaidaichuk, E. A. Gotsulyak, and V. I. Gulyaev, “Branching of the solutions of the nonlinear equations of toroidal shells acted upon by an external pressure,” Prikl. Mekh.,14, No. 9, 38–45 (1978).Google Scholar
- 27.K. Z. Galimov, “Application of the variational principle of possible changes in the stressed state in the nonlinear theory of shallow shells,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 1, 3–11 (1958).Google Scholar
- 28.I. M. Gel'fand and O. V. Lokutsievskii, “The ‘factorization’ method for solving difference equations,” in: S. K. Godunov and V. S. Ryaben'kii, Introduction to the Theory of Difference Schemes [in Russian], Fizmatgiz, Moscow (1962), pp. 283–309.Google Scholar
- 29.A. O. Gel'fond, The Calculus of Finite Differences [in Russian], Fizmatgiz, Moscow (1959).Google Scholar
- 30.S. K. Godunov, “The numerical solution of boundary-value problems for systems of linear ordinary differential equations,” Usp. Mat. Nauk,16, No. 3, 171–174 (1961).Google Scholar
- 31.S. K. Godunov, and V. S. Ryaben'kii, Introduction to the Theory of Difference Schemes [in Russian], Fizmatgiz, Moscow (1962).Google Scholar
- 32.A. L. Gol'denveizer, Theory of Elastic Thin Shells [in Russian], Gostekhizdat, Moscow (1953).Google Scholar
- 33.E. A. Gotsulyak, V. N. Ermishev, and N. T. Zhadrasinov, “Convergence of the method of curvilinear networks in shell-theory problems,” Soprot. Mater. Theor. Sooruzh., No. 39, 80–84 (1981).Google Scholar
- 34.E. A. Gotsulyak and K. Pemsing, “Taking account of rigid displacements in the solution of problems in shell-theory by the method of finite differences,” in: Numerical Methods for the Solution of Problems in Structural Mechanics [in Russian], Kiev (1978), pp. 93–98.Google Scholar
- 35.É. I. Grigolyuk and V. I. Mamai, “Methods of reducing a nonlinear boundary-value problem to a Cauchy problem,” in: Applied Problems in Strength and Plasticity. Methods for the Solution of Problems in Elasticity and Plasticity [in Russian], Izd. Gor'k. Un-ta, Gorky (1979), pp. 3–49.Google Scholar
- 36.É. I. Grigolyuk, V. I. Mamai, and A. N. Frolov, “Investigation of the stability of nonshallow spherical shells in the case of finite displacements on the basis of various equations in the theory of shells,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 154–165 (1972).Google Scholar
- 37.E. I. Grigolyuk, and V. I. Shalashilin, “Some forms of the method of parametric continuation in nonlinear problems in the theory of elasticity,” Zh. Prikl. Mekh. Tekh. Fiz., No. 5, 158–162 (1980).Google Scholar
- 38.Ya. M. Grigorenko, “Computer solution of problems concerning the stressed state of conical shells of variable rigidity,” in: Computers in Structural Mechanics: Proceedings of the First All-Union Conference on the Use of Computers in Structural Mechanics, Leningrad, 1963 [in Russian], Gosstroiizdat, Moscow-Leningrad (1966), pp. 535–543.Google Scholar
- 39.Ya. M. Grigorenko, “The use of numerical methods for calculating machine elements,” Dinam. Prochn. Mashin., No. 5, 11–17 (1967).Google Scholar
- 40.Ya. M. Grigorenko, Isotropic and Anisotropic Laminated Shells of Revolution of Variable Rigidity [in Russian], Naukova Dumka, Kiev (1973).Google Scholar
- 41.Y. M. Grigorenko, E. I. Bespalova, A. T. Vasilenko, et al., Numerical Solution of Boundary-Value Problems in the Statics of Orthotropic Laminated Shells of Revolution by Means of M-220 Computers [in Russian], Naukova Dumka, Kiev (1971).Google Scholar
- 42.Ya. M. Grigorenko and A. T. Vasilenko, “Numerical solution by computers of boundaryvalue problems concerning the stressed state of shells of revolution,” in: Abstracts of Reports of the Fifth All-Union Conference on the Theory of Plates and Shells [in Russian], Nauka, Moscow (1965), pp. 18–19.Google Scholar
- 43.Ya. M. Grigorenko and A. T. Vasilenko, Theory of Shells of Variable Rigidity [in Russian], Naukova Dumka, Kiev (1981). (Methods of Calculating Shells Vol. 4).Google Scholar
- 44.Ya. M. Grigorenko, A. T. Vasilenko, E. I. Bespalova, et al., Numerical Solution of Boundary-Value Problems in the Statics of Orthotropic Shells with Variable Parameters [in Russian], Naukova Dumka, Kiev (1975).Google Scholar
- 45.Ya. M. Grigorenko, N. D. Draigor, and A. I. Shinkar', “On the solution of problems concerning the stressed state of multilayer orthotropic cylindrical shells with variable rigidity in two directions,” Soprot. Mater. Teor, Sooruzh., No. 30, 3–10 (1977).Google Scholar
- 46.Ya. M. Grigorenko, A. B. Kitaigorodskii, V. V. Semenov, et al., Calculation of Orthotropic Laminated Shells of Revolution with Variable Parameters on ES Computers [in Russian], Naukova Dumka, Kiev (1980).Google Scholar
- 47.Ya. M. Girgorenko and N. N. Kryukov, “Numerical solution of nonlinear boundary-value problems in the theory of flexible circular plates,” Vychisl. Prikl. Mat., No. 41, 46–52 (1980).Google Scholar
- 48.Ya. M. Grigorenko and N. N. Kryukov, “An approach to the numerical solution of boundaryvalue problems in the statics of flexible shells,” Dokl. Akad. Nauk. Ukr. SSR, Ser A, No. 4 21–24 (1982).Google Scholar
- 49.Ya. M. Grigorenko, N. N. Kryukov, and T. G. Akhalaya, “Nonlinear deformation of circular plates of variable thickness,” ibid.,, No. 8, 622–625 (1979).Google Scholar
- 50.Ya. M. Grigorenko, N. N. Kryukov, and V. S. Demyanchuk, “Deformation of flexible shells of revolution with variable rigidity,” ibid., No. 4 42–46 (1983).Google Scholar
- 51.Ya. M. Grigorenko, N. N. Kryukov, and Kh. Saparov, “Not-axially-symmetric deformation of flexible conical shells of variable thickness,” Prikl. Mekh.,9, No. 5, 29–35 (1983).Google Scholar
- 52.Ya. M. Grigorenko and A. P. Mukoed, Solution of Problems in the Theory of Shells Using Domputers [in Russian], Vishcha Shkola, Kiev (1979).Google Scholar
- 53.Ya. M. Grigorenko and A. P. Mukoed, Solution of Nonlinear Problems in Theory of Shells Using Computers [in Russian], Vishcha Shkola, Kiev (1983).Google Scholar
- 54.Ya. M. Grigorenko and A. M. Timonin, “Solution of not-axially-symmetric nonlinear problems in the statics of shells of revolution with low shear rigidity,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 10, 30–34 (1981).Google Scholar
- 55.Ya. M. Grigorenko and A. M. Timonin, “Numerical solution of not-axially-symmetric problems in the nonlinear theory of laminated shells of revolution,” Prikl. Mekh.,18, No. 5, 43–48 (1982).Google Scholar
- 56.A. N. Guz', I. S. Chernyshenko, V. N. Chekhov, et al., Theory of Thin Shells Weakened by Holes [in Russian], Naukova Dumka, Kiev (1980). (Methods of Calculating Shells; Vol. 1).Google Scholar
- 57.V. I. Gulyaev, “The effect of the shape of a spiral shell on its stressed state,” Soprot. Mater. Teor. Sooruzh., No. 16, 6–10 (1972).Google Scholar
- 58.V. I. Gulyaev, Numerical Analysis of the Deformation of Shells in the Nonclassical and Classical Formulations. Author's abstract of a dissertation for the degree of Doctor of Physical and Mathematical Sciences, Kiev (1978).Google Scholar
- 59.V. I. Gulyaev, V. A. Bazhenov, and E. A. Gotsulyak, Stability of Nonlinear Mechanical Systems [in Russian], Vishcha Shkola, L'vov (1982).Google Scholar
- 60.D. F. Davidenko, “A new method for the numerical solution of systems of nonlinear equations,” Dokl. Akad. Nauk SSSR,88, No. 4, 601–602 (1953).Google Scholar
- 61.A. A. Dorodnitsyn, “A method of solving the equation of a laminar boundary layer,” Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 111–118 (1960).Google Scholar
- 62.A. A. Dorodnitsyn, “A method of solving the equations of a boundary layer,” in: Some Problems of Mathematics and Mechanics [in Russian], Izd. Sib. Otd. Akad, Nauk SSSR, Novosibirsk (1961) pp. 77–83.Google Scholar
- 63.G. N. Dubner, “Use of the method of orthogonal factorization in problems of structural mechanics,” Izv. Vyssh. Uchebn. Zaved., Mashinostroenie, No. 11, 8–14 (1968).Google Scholar
- 64.O. Zienkiewicz and I. K. Cheung, Finite-Element Method in Engineering Science, McGraw-Hill.Google Scholar
- 65.N. P. Znamenskii, “Use of integral equations for calculating conical and cylindrical shells of variable rigidity,” Prikl. Probl. Prochnosti Plastichnosti, No. 8 27–32 (1978).Google Scholar
- 66.V. V. Kabanov and L. P. Zheleznov, “Nonlinear deformation of circular-cylinder shells under not-axially-symmetric pressure,” in: Calculation of Structural Elements of Aircraft [in Russian], Mashinostroenie, Moscow (1982), pp. 83–85.Google Scholar
- 67.V. V. Kabanov and V. D. Mikhailov, “Limiting state and stability of a cylindrical shell under not-axially-symmetric pressure,” in: Calculation of Structural Elements of Aircraft [in Russian], Mashinostroenie,. Moscow (1982), pp. 64–70.Google Scholar
- 68.S. A. Kabrits and V. F. Terent'ev, “Numerical construction of load-displacement diagrams in one-dimensional nonlinear problems in the theory of rods and shells,”, in: Current Problems of Nonlinear Mechanics of Continuous Media. Problems in Mechanics and Control Processes [in Russian], No. 1 (1977_, pp. 155–171.Google Scholar
- 69.B. Ya. Kantor, Nonlinear Problems in the Theory of Inhomogeneous Shallow Shells [in Russian], Naukova Dumka, Kiev (1971).Google Scholar
- 70.B. Ya. Kantor and S. I. Katorzhnoi, Variational-Segmental Method in the Nonlinear Theory of Shells [in Russian], Naukova Dumka, Kiev (1982).Google Scholar
- 71.B. Ya. Kantor, V. M. Mitkevich, and E. S. Shishkina, “Calculation of thin-walled structures of revolution by the finite-element method,” Int. Probl. Mashinostroeniya Akad. Nauk Ukr. SSR, Kharkov (1976).Google Scholar
- 72.L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis [in Russian], Fizmatgiz, Moscow-Leningrad (1962).Google Scholar
- 73.A. V. Karmishin, V. A. Lyaskovets, V. I. Myachenkov, and A. N. Frolov, Statics and Dynamics of Thin-Walled Shell-Type Structures [in Russian], Mashinostroenie, Moscow (1975).Google Scholar
- 74.N. A. Kil'chevskii, G. A. Izdebskaya, and L. M. Kiselevskaya, Lectures on the Analytical Mechanics of Shells [in Russian], Vishcha Shkola, Kiev (1974).Google Scholar
- 75.A. D. Kovalenko, Ya. M. Grigorenko, and L. A. Il'in, Theory of Thin Conical Shells and Its Application in Machine Design, [in Russian], Izd. Akad. Nauk Ukr. SSR (1963).Google Scholar
- 76.N. V. Kolkunov, Fundamentals of the Calculation of Elastic Shells [in Russian], Vishcha Shkola (1972).Google Scholar
- 77.L. Collatz, Functional Analysis and Numerical Mathematics, Academic Press (1966).Google Scholar
- 78.V. G. Korneev, “Comparison of the finite-element method with the variational-difference method of solving problems in the theory of elasticity,” Izv. VNII Gidrotekhniki, No. 83, 286–307 (1967).Google Scholar
- 79.M. S. Kornishin, Nonlinear Problems in the Theory of Plates and Shells and Methods of Solving Them [in Russian], Nauka, Moscow (1964).Google Scholar
- 80.M. S. Kornishin and F. S. Isanbaeva, Flexible Plates and Panels [in Russian], Nauka, Moscow (1968).Google Scholar
- 81.A. V. Korovaitsev, “Numerical solution of nonlinear equations of axially symmetric shells of revolution,” Izv. Vyssh. Uchebn. Zaved., Mashinostroenie, No. 2, 13–17 (1978).Google Scholar
- 82.A. V. Korovaitsev, “Calculation of axially symmetric forms of equilibrium of an elastic spherical shell,” ibid., No. 3, 5–8 (1978).Google Scholar
- 83.V. A. Krys'ko, Nonlinear Statics and Dynamics of Inhomogeneous Shells [in Russian], Izd, Saratov. Un-ta, Saratov (1976).Google Scholar
- 84.A. L. Lur'e, Statics of Thin-Walled Elastic Shells [in Russian], Gostekhizdat, Moscow-Leningrad (1947).Google Scholar
- 85.G. I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Novosibirsk (1973).Google Scholar
- 86.I. E. Mileikovskii and V. D. Raizer, “Development of applied methods in problems in the static design of thin-walled spatial systems (shells and folds),” in: Proceedings of the the Seventh All-Union Conference on the Theory of Shells and Plates [in Russian], Nauka, Moscow (1970), pp. 820–830.Google Scholar
- 87.P. I. Monastyryi, “An analog of A. A. Abramov's method,” Zh. Vychisl, Mat. Mat. Fiz., 5, No. 2, 342–347 (1965).Google Scholar
- 88.V. I. Myachenkov and I. V. Grigor'ev, Calculation of Composite Shell-Type Structures by Computers: A Handbook [in Russian], Mashinostroenie, Moscow (1981).Google Scholar
- 89.A. A. Nazarov, Fundamentals of the Theory and Methods of Calculating Shallow Shells [in Russian], Izd. Lit. Str-vu, Leningrad-Moscow (1966).Google Scholar
- 90.V. V. Novozhilov, Theory of Thin Shells [in Russian], Sudostroenie, Leningrad (1962).Google Scholar
- 91.V. V. Novozhilov, “The accuracy of models used in the mechanics of a deformable solid,” in: Program of the All-Union Scientific and Technical Conference entitled “Problems of Strength and Material Savings in Shell-Type Structures of Future Transport Ships and Floating Installations,” dedicated to the memory of Academician Yu. A. Shimanskii [in Russian], Leningr. Korablestroit. In-t (1982).Google Scholar
- 92.V. V. Novozhilov, “Ways of developing the theory of the deformation of polycrystals. Two articles on mathematical models in the mechanics of continuous media,” Moscow (1983). pp. 29–56. (Preprint Akad. Nauka SSSR, In-t Probl. Mekhaniki; No. 215).Google Scholar
- 93.I. F. Obraztsov, Variational Methods for the Calculation of Thin-Walled Aircraft Structure [in Russian], Mashinostroenie, Moscow (1966).Google Scholar
- 94.I. F. Obraztsov, “Problems in the statics and dynamics of modern engineering structures. State of the art, new problems, and prospects,” Probl. Prochnosti, No. 11, 3–11 (1982).Google Scholar
- 95.I. F. Obraztsov and R. M. Onanov, Structural Mechanics of Thin-Walled Skew Systems [in Russian], Mashinostroenie, Moscow (1973).Google Scholar
- 96.V. N. Paimushin, “On the problem of parametrization of the midele surface of a shell with complicated geometry,” in: Strength and Reliability of Complicated Systems [in Russian], Naukova Dumka, Kiev (1979), pp. 87–94.Google Scholar
- 97.V. N. Paimushin, Boundary-Value Problems in the Mechanics of the Deformation of Shells with Complicated Geometry, Author's abstract of a dissertation for the degree of Doctor of Physical and Mathematical Sciences, Kazan (1980).Google Scholar
- 98.P. F. Papkovich, Structural Mechanics of Ships. Part 2. Complex Flexure and Stability of Rods. Flexure and Stability of Plates [in Russian], Sudpromgiz, Leningrad (1941).Google Scholar
- 99.V. V. Petrov, “Investigation of finite deflections of plates and shallow shells by the method of successive loadings,” in: Theory of Plates and Shells. Proceedings of the Second All-Union Conference [in Russian], Izd. Akad. Nauk Ukr. SSR, Kiev (1962), pp. 328–331.Google Scholar
- 100.A. N. Potrov, The Method of Successive Loadings in the Nonlinear Theory of Plates and Shells [in Russian], Izd. Saratov, Un-ta, Saratov (1975).Google Scholar
- 101.A. N. Podgornyi, G. A. Marchenko, and V. I. Pustynnikov, Principles and Methods of the Applied Theory of Elasticity [in Russian], Vishcha Shkola, Kiev (1981).Google Scholar
- 102.Ya. S. Podstrigach and R. N. Shvets, Thermoelasticity of Thin Shells [in Russian], Naukova Dumka, Kiev (1983).Google Scholar
- 103.V. A. Postnov, S. A. Dmitriev, B. K. Eltyshev, and A. A. Rodionov, The Method of Super-elements in Calculations of Engineering Structures [in Russian], Sudostroenie, Leningrad (1979).Google Scholar
- 104.V. A. Postnov, V. S. Korneev, and N. G. Slezina, “Calculation of thin shells of revolution of arbitrary shape by the finite-element method,” Stroit. Mekh. Korablya, No. 148, 5–18 (1970).Google Scholar
- 105.V. A. Postnov and L. A. Rozin, “The finite-element method in the theory of plates and shells,” in: Proceedings of the Ninth All-Union Conference on the Theory of Shells and Plates [in Russian], Sudostroenie, Leningrad (1975), pp. 292–296.Google Scholar
- 106.V. A. Postnov and I. Ya. Kharkhurism, “Use of the finite-element method in the structural mechanics of ships,” Stroit. Mekh. Korablya, No. 149, 37–43 (1971).Google Scholar
- 107.V. A. Postnov and I. Ya. Kharkhurim, The Finite-Element Method in Ship Design Calculations [in Russian], Sudostroenie, Leningrad (1974).Google Scholar
- 108.V. L. Rvachev, The Theory of R-Functions and Some of Its Applications [in Russian], Naukova Dumka, Kiev (1982).Google Scholar
- 109.L. A. Rozin, Calculation of Hydrotechnical Structures by Computer. The Finite-Element Method [in Russian], Énergiya, Moscow (1971).Google Scholar
- 110.L. A. Rozin and L. A. Gordon, “The finite-element method in the theory of plates and shells,” Izv. VNII Gidrotekhniki, No. 95, 85–97 (1971).Google Scholar
- 111.L. A. Rozin and L. B. Grinze, “Calculation of arbitrary shells of revolution by the method of separation using computers,” Issled. Uprug. Plastich., No. 5, 70–118 (1966).Google Scholar
- 112.Ya. G. Savula, “Use of the semianalytic method of finite elements in calculating shells with a Monge middle surface,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 2, 39–42 (1983).Google Scholar
- 113.Ya. G. Savula, N. P. Fleishman, and G. A. Shinkarenko, “The method of calculating pipes with an arbitrary curvilinear axis,” Soprot. Mater. Teor. Sooruzh., No. 32, 95–98 (1979).Google Scholar
- 114.A. A. Samarskii, Introduction to the Theory of Difference Schemes [in Russian], Nauka, Moscow (1971).Google Scholar
- 115.A. A. Samarskii, “Mathematical simulation and computational experimentation,” Vestn. Akad. Nauk SSSR, No. 5, 38–49 (1979).Google Scholar
- 116.L. V. Svirskii, Methods of the Bubnov-Galerkin Type and of Successive Approximations [in Russian], Nauka, Moscow (1968).Google Scholar
- 117.L. I. Sedov, “Future trends and problems in the mechanics of continuous media,” in: Modern Problems in Theoretical and Applied Mechanics [in Russian], Naukova Dumka, Kiev (1978), pp. 7–24.Google Scholar
- 118.A. L. Sinyavskii, Numerical Investigation of Spatial Systems. Author's abstract of a dissertation for the degree of Doctor of Physical and Mathematical Sciences, Kiev (1974).Google Scholar
- 119.G. Hall and J. Watt (eds.), Modern Numerical Methods for Ordinary Differential Equations [Russian translation], Mir, Moscow (1976).Google Scholar
- 120.S. P. Timoshenko and S. Voinovskii-Kriger, Plates and Shells [in Russian], Fizmatgiz, Moscow (1963).Google Scholar
- 121.A. G. Ugodchikov, Yu. G. Korotkikh, S. A. Kapustin, et al., “Numerical analysis of quasistatic elastoplastic problems in shells and plates,” in: Proceedings of the Ninth All-Union Conference on the Theory of Shells and Plates [in Russian], Sudostroenie, Leningrad (1975), pp. 334–340.Google Scholar
- 122.V. I. Feodos'ev, Elastic Elements of Precision Instrument Making [in Russian], Oborongiz, Moscow (1949).Google Scholar
- 123.V. I. Feodos'ev, “A method for solving problems of stability in deformable systems,” Prikl. Mat. Mekh.,27, No. 2, 265–275 (1963).Google Scholar
- 124.V. I. Feodos'ev, “Use of the step method for analyzing the stability of a compressed rod,” ibid.,27, No. 5, 833–841 (1965).Google Scholar
- 125.V. I. Feodos'ev, Ten Lectures on the Resistance of Materials [in Russian], Nauka, Moscow (1969).Google Scholar
- 126.V. I. Feodos'ev, “Axially symmetric elasticity of a spherical shells,” Prikl. Mat. Mekh.,33, No. 2, 280–286 (1969).Google Scholar
- 127.A. N. Frolov and T. I. Khodtseva, “Investigation of the nonlinear behavior of a toroidal shell under external pressure,” in: Proceedings of the Tenth All-Union Conference on the Theory of Shells and Plates [in Russian], Tbilisi (1975), Vol. 1, pp. 698–702.Google Scholar
- 128.R. W. Hamming, Numerical Methods for Scientists and Engineers [Russian translation], Nauka, Moscow (1968).Google Scholar
- 129.V. S. Chernina, Statics of Thin-Walled Shells of Revolution [in Russian], Nauka, Moscow (1968).Google Scholar
- 130.K. F. Chernykh, Linear Theory of Shells [in Russian], Izd. LGU, Leningrad, Part 1 (1962), 374 pp.; Part 2 (1964).Google Scholar
- 131.V. S. Chuvikovskii, O. M. Palii, and V. E. Spiro, Shells in Ship Design [in Russian], Sudostroenie, Leningrad (1966).Google Scholar
- 132.V. I. Shalashilin, “The method of parametric continuation of the solution in a problems concerning large axially symmetric deflections of shells of revolution,” in: Proceedings of the Twelfth All-Union Conference on the Theory of Shells and Plates [in Russian], Izd. Erevan. Un-ta, Erevan (1980), pp. 264–271.Google Scholar
- 133.V. E. Shamanskii, Methods of Numerical Solution of Boundary-Value Problems on Computers [in Russian], Naukova Dumka, Kiev (1966), part 2.Google Scholar
- 134.L. E. El'sgol'ts, The Calculus of Variations [in Russian], Gostekhizdat, Moscow (1958).Google Scholar
- 135.B. Budiansky and P. P. Radkowski, “Numerical analysis of unsymmetrical bending of shells of revolution,” AIAA Journal,1, No. 8, 1833–1842 (1963).Google Scholar
- 136.G. A. Gohen, “Computer analysis of asymmetrical deformation of orthotropic shells of revolution,” AIAA Journal,2, No. 5, 932–934 (1964).Google Scholar
- 137.P. F. Gordan and P. E. Shelley, “Stabilization of unstable two-point boundary-value problems,” AIAA Journal,4, No. 5, 923–924 (1966).Google Scholar
- 138.K. Junghauss, “Berechnung von Rotationsschalen beliebiger Meridianform und veranderlicher Wanddicke,” Maschinenbautechnik,17, 349–354 (1968).Google Scholar
- 139.A. Kalnins, “Analysis of shells of revolution subjected to symmetrical and nonsymmetrical loads,” Trans. ASME, Ser. E,31, No. 3, 467–476 (1964).Google Scholar
- 140.A. Kalnins, “Analysis of curved thin-walled shells of revolution,” AIAA J.,6, No. 4, 584–588 (1968).Google Scholar
- 141.L. Knöfel, Über ein numerisches Verfahren zur Berechnung der Schnittogroben in geschlossenen Kreiszylinderschalen mit linear veränderlicher Wandstärke bei unsymmetricscher Belastung,” Wiss. Z. Techn. Hochsch. Otto von Guericke, Magdeburg,12, No. 2-3, 231–241 (1968).Google Scholar
- 142.P. P. Radkowski, R. M. Davis, and M. P. Boldas, “Numerical analysis of equations of thin shells of revolution,” ARS J., No. 32, 36–41 (1962).Google Scholar
- 143.W. K. Sepetoski, C. E. Pearson, J. W. Dingwell, and A. W. Adkins, “A digital computer program for the general axially symmetric thin shells problem,” Trans. ASME, Ser. E,29, No. 4, 655–661 (1962).Google Scholar
- 144.S. Utku and N. S. Head, “Utilization of digital computers in the analysis of thin shells,” Bul. Reunion Inter. Lab. Essais Rech. Mater. Constr., No. 19, 29–44 (1963).Google Scholar

## Copyright information

© Plenum Publishing Corporation 1985