Literature Cited
L. Treloir, The Physics of the Elasticity of Caoutchouc [Russian translation], IL, Moscow (1953).
É. É. Lavendel, Stress Analysis of Technical Rubber Products [in Russian], Mashinostroenie, Moscow (1976).
N. S. Gusyatinskaya, The Use of Finely Laminated Rubber-Metal Elements (FRME) in Machine Tools and Other Machines [in Russian], Mashinostronie, Moscow (1975).
S. C. Sharda and N. W. Tschoegl, “Strain energy density function for compressible rubberlike materials,” Trans. Soc. Rheology,20, No. 3, 361–372 (1976).
R. W. Penn, “Volume changes accompanying the extension of rubber,” Trans. Soc. Rheology,14, No. 4, 509–517 (1970).
K. F. Chernykh and I. M. Shubina, “Allowance for the compressibility of rubber,” Mekh. Elastomerov,2, 56–62 (1978).
L. R. Gerrmann, “The variational principle for equations of elasticity of incompressible and nearly incompressible materials,” Raket. Tekh. Kosmon., No. 3, 139–144 (1965).
L. R. Herrmann, “Elasticity equations for incompressible and nearly incompressible materials by a variational theorem,” AIAA J.,3, No. 10, 1896–1900 (1965).
S. W. Key, “A variational principle for an incompressible and nearly incompressible anisotropic elasticity,” Int. J. Solids Struct.,5, 455–461 (1965).
T. Pian and S. Li, “The finite element method for nearly incomressible materials,” Raket. Tekh. Kosmon., No. 6, 147–149 (1976).
T. H. H. Pian, “Derivation of element stiffness matrices by assumed stress distributions,” AIAA J.,2, 1333–1336 (1964).
S. W. Lee, An Assumed Stress Hybrid Finite Element for Three Dimensional Elastic Structural Analysis, M.I.T. ASRL TR 170-3, also AFOSR TR 75-0087. May (1974).
D. S. Malkus, “A finite-element displacement model valid for any value of the compressibility,” Int. J. Solids Struct.,12, 731–738 (1976).
J. C. Nagetegaal, D. M. Parks, and J. R. Rice, “On numerically accurate finite element solutions in the fully plastic range,” Comt. Meth. Appl. Mech. Eng.,4, 153–177 (1974).
J. T. Oden and J. E. Key, “On some generalization of the incremental stiffness relations for finite deformations of compressible and incompressible finite elements,” Nucl. Eng. Design.,15, 121–134 (1971).
P. Tong, “An assumed stress hybrid finite element method for an incompressible and near-incompressible material,” Int. J. Solids Struct.,5, 455–461 (1969).
S. Cescotto and G. Fonder, “A finite element approach for large strain of nearly incompressible rubberlike materials,” Int. J. Solids Struct.,15, No. 8, 589–605 (1979).
V. P. Boldychev, “Improving the effectiveness of the finite element method in the solution of degenerating problems,” Vopr. Dinamiki Prochn., No. 42, 38–48 (1983).
G. M. Golemshtok, “Realization of the finite element method for the stress analysis of structures of incomprssible and nearly incompressible materials,” Prikl. Probl. Prochn. Plastichn., No. 23, 47–56 (1983).
G. B. Kuznetsov and A. A. Rogovoi, “One approach to the stress analysis of elastic structures of incompressible and slightly compressible materials with finite deformations,” in: The State of Stress and the Strength of Structures, Ural'skii Nauchnyi Tsentr, Sverdlovsk (1982), pp. 53–60.
A. S. Durdyev and V. I. Gafinov, “The variational principle of the theory of elasticity for incompressible and nearly incompressible materials,” Izv. Vyssh. Uchebn. Zaved., Mashinostr., No. 8, 13–18 (1980).
M. Tuomala, D. R. J. Owen, and O. C. Zienkiewicz, “A penalty function finite element method in nonlinear elasticity,” in: Numer. Meth. Coupl. Probl.: Proc. Int. Conf. Swansea, 7–11 Sept. 1981, pp. 466–477.
O. C. Zienkiewicz, J. Too, and R. L. Taylor, “Reduced integration technique in general analysis of plates and shells,” Int. J. Numer. Meth. Eng.,3, No. 2, 275–290 (1971).
D. J. Naylor, “Stresses in nearly incompressible materials by finite elements with application to the calculation of excess pore pressure,” Int. J. Numer. Meth. Eng.,8, 443–460 (1974).
J. T. Oden and N. Kikuchi, “Finite-element methods for constrained problems in elasticity,” Int. J. Numer. Meth. Eng.,18, No. 5, 701–725 (1982).
I. Fried, “Numerical integration in the finite element method,” Comput. Struct., No. 4, 921–932 (1974).
T. J. R. Hughes, “Equivalence of finite elements for nearly incompressible elasticity,” J. Appl. Mech.,44, 181–183 (1977).
A. E. Beikin and V. L. Biderman, “The effect of slight compressibility of rubber on the operation of a low cylindrical rubber-metal shock absorber,” Raschety Prochn., No. 16, 5–24 (1975).
V. F. Gontsa, “The effect of slight compressibility on the solution of problems of the theory of elasticity on incompressible materials,” Voprosy Dinamiki i Prochn., No. 20, 181–193 (1970).
S. I. Dymnikov, I. R. Meiers, and A. G. Erdmanis, “Elastic potentials for slightly compressible elastomer materials,” Voprosy Dinamiki Prochn., No. 40, 98–108 (1982).
É. É. Lavendel, “Evaluation of the effect of compressibility in the calculation of the rigidity of technical rubber products,” Voprosy Dinamiki i Prochn., No. 27, 109–112 (1973).
D. S. Malkus, “Finite elements with penalties in nonlinear elasticity,” Int. J. Numer. Meth. Eng.,16, Special Issue, 121–136 (1980).
P. Tallec, “Contact between largely deformed incompressible superelastic solids and rigid bodies,” in: Numer. Meth. Coupl. Probl.: Proc. Int. Conf. Swasea, 7–11 Sept. 1981, pp. 478–489.
A. S. Sakharov, “Moment schema of finite elements (MSFE) with a fiew to rigid displacements,” Soprotivlenie Materialov i Teoriya Sooruchenii, No. 24, 147–156 (1974).
A. S. Sakharov, V. N. Kislookii, V. V. Kirichevskii, et al., The Finite Element Method in Solid Mechanics [in Russian], Vyshcha Shkola, Kiev (1982).
N. A. Kil'chevskii, Fundamentals of the Analytical Mechanics of Shells [in Russian], Izd. Akad. Nauk Ukr. SSR, Kiev (1963).
V. V. Kirichevskii, “The system KODETOM for investigating highly elastic massive structures on the basis of the finite-element method,” in: Complex Computerized Stress Analysis of Buildings and Structures [in Russian], Kievskii Inzhenerno-Stroitel'skii Institut, Kiev (1978), pp. 142–148.
Additional information
Voroshilograd Agricultural Institute. Translated from Problemy Prochnosti, No. 11, pp. 105–110, November, 1986.
Rights and permissions
About this article
Cite this article
Kirichevskii, V.V. Generalization of the moment schema of finite elements for investigating structures of slightly compressible elastomers. Strength Mater 18, 1553–1559 (1986). https://doi.org/10.1007/BF01524272
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01524272