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## Literature Cited

- 1.
N. P. Abovskii, “Direct derivation of equations of the net-point method,” in: Space Structures in Krasnoyarsk Krai [in Russian], Izd. PromstroiNIIproekt, Krasnoyarsk (1965).

- 2.
M. R. Irons, “Engineering applications of numerical integration in stiffness methods,” Raketnaya Tekhnika i Kosmonavtika, No. 11 (1966).

- 3.
M. R. Irons, “Comments on the article ‘Stiffness matrices in the form of a sector’” Raketnaya Tekhnika i Kosmonavtika, No. 3 (1970).

- 4.
M. R. Irons and J. Barlow, “Comments on the article ‘Matrices for the direct stiffness method,’” Raketnaya Tekhnika i Kosmonavtika, No. 2 (1964).

- 5.
M. R. Irons and K. J. Draper, “Inconsistency of nodal ties in calculating the bending of plants by the stiffness method,” Raketnaya Tekhnika i Kosmonavtika, No. 5 (1965).

- 6.
F. A. Akyuz and S. Utky, “Automatic renumeration of nodes for minimizing the width of the band in stiffness matrices,” Raketnaya Tekhnika i Kosmonavtika, No. 4 (1968).

- 7.
A. V. Aleksandrov, “Slope-deflection method for calculating slab-beam structures,” Trudy Mosk. Inst. Inzh. Transporta, No. 174 (1963).

- 8.
A. V. Aleksandrov, “Discrete model for calculating orthotropic plates and shells,” Trudy Mosk. Inst. Inzh. Transporta, No. 364 (1971).

- 9.
A. V. Aleksandrov and N. N. Shaposhnikov, “Use of a discrete model in calculating plates with the use of automatic digital computers,” Trudy Mosk. Inst. Inzh. Transporta, No. 194 (1966).

- 10.
J. Argyris, “Energy theorems and calculation of structures,” in: Modern Methods of Calculation of Complex Statically Indeterminate Systems [in Russian], Sudpromgiz, Leningrad (1961).

- 11.
J. Argyris, “Matrix analysis of small and large displacements in three-dimensional elastic media,” Raketnaya Tekhnika i Kosmonavtika, No. 1 (1965).

- 12.
J. Argyris, Current Achievements in Methods of Calculating Structures with the Use of Matrices [Russian translation], IL, Moscow (1968).

- 13.
H. Ir. Armen, G. Isakson, and A. Pifko, “Methods of discrete elements for plastic calculation of structures subjected to cyclic loading,” in: Collection of Translations “Mekhanika,” No. 1 (1971).

- 14.
G. Best. “Formulas for certain types of stiffness elements of structural members,” Raketnaya Tekhnika i Kosmonavtika, No. 1 (1963).

- 15.
G. Best, “General formula for the stiffness matrix of structural members,” Raketnaya Tekhnika i Kosmonavtika, No. 8 (1963).

- 16.
F. K. Bogner, R. L. Fox, and L. A. Schmit, “Calculation of a cylindrical shell by the discrete element method,” Raketnaya Tekhnika i Kosmonavtika, No. 4 (1967).

- 17.
A. N. Bondarenko, “Construction of the stiffness matrix of the finite element of an oblique shell,” Trudy Khabarosk. Inst. Inzh. Zhel.-Dor. Transporta, No. 41 (1970).

- 18.
A. N. Bondarenko, “Construction of the stiffness matrix of an oblique nonsloping finite element of a shell.” Trudy Mosk. Inst. Inzh. Transporta, No. 391 (1971).

- 19.
Z. I. Burman and M. T. Timofeev, “Problems of the methods of computer implementation of problems of a solid deformable body by the finite element method written in matrix form and the creation of adequate automatic programming systems for it,” in: Numerical Methods in Technical and Economic Problems [in Russian], Izd. Kazansk. Univ. (1971).

- 20.
D. V. Vainberg, V. M. Gerashchenko, I. Z. Roitfarb, and A. L. Sinyavskii, “Derivation of net equations of bending of plates by the variational method,” in: Strength of Materials and Structural Mechanics [in Russian], No. 1, Izd. Budiverl'nik, Kiev (1965).

- 21.
D. V. Vainberg, V. V. Kirichevskii, and A. S. Sakharov, “Equations of the finite element method in base curvilinear coordinates,” in: Strength of Materials and Structural Mechanics [in Russian], No. 16, Izd. Budivel'nik, Kiev (1972).

- 22.
D. V. Vainberg, A. S. Sakharov, and A. I. Gulyar, “Equations of shells of complex structure,” in: Strength of Materials and Structural Mechanics [in Russian], No. 14, Izd. Budivel'nik, Kiev (1971).

- 23.
D. V. Vainberg, A. S. Sakharov, and V. V. Kirichevskii, “Derivation of the stiffness matrix of a discrete element of arbitrary form,” in: Strength of Materials and Structural Mechanics [in Russian], No. 14, Izd. Budivel'nik, Kiev (1971).

- 24.
D. V. Vainberg, A. S. Sakharov, and V. V. Kirichevskii, “Investigation of complex space structures by the discrete element method in the case of large displacements,” in: Strength of Materials and Structural Mechanics [in Russian], No. 15, Izd. Budivel'nik, Kiev (1971).

- 25.
D. V. Vainberg, A. S. Sakharov, and A. L. Sinyavskii, “Numerical solution of linear and geometrically nonlinear problems for ribbed shells and plates,” in: Calculation of Space Structures [in Russian], No. 13, Gosstroiizdat, Moscow (1969).

- 26.
P. M. Varvak and V. M. Moyanskii, “Bending of a fixed square slotted plate,” Trudy Kuibyshevskogo Inzh.-Stroit. Inst. (1971).

- 27.
P. M. Varvak and V. M. Moyanskii, “Bending of a square slotted plate,” Trudy Tyumensk. Industr. Inst. (1971).

- 28.
Yu. K. Vilipyl'd, “Derivation of equations of the finite element method by a variant of the discrete variational method,” Trudy Tallinsk. Politekhn. Inst., Seriya A, No. 278 (1968).

- 29.
I. K. Vilipyl'd, “Calculation of ribbed plates by the finite element method,” Trudy Tallinsk. Politekhn. Inst., Seriya A, No. 297 (1970).

- 30.
W. Visser, “Improved variant of a discrete element of a mixed type of plate in bending,” Raketnaya Tekhnika in Kosmonavtika, No. 9 (1969).

- 31.
V. Z. Vlasov, Structural Mechanics of Thin-Walled Space Systems [in Russian], Gosstroiizdat, Moscow (1949).

- 32.
V. Z. Vlasov, Selected Works [in Russian], Vol. 1–3, Izd. AN SSSR Moscow (1963).

- 33.
P. P. Voroshko and O. S. Sakharov, “Investigation of various equations of elasticity theory and their calculation on a computer,” in: Strength of Materials and Structural Mechanics [in Ukrainian], No. 4, Izd. Buidivel'nik, Kiev (1966).

- 34.
R. H. Gallagher, “Methods of obtaining stiffness matrices of elements,” Raketnaya Tekhnika i Kosmonavtika, No. 6 (1963).

- 35.
R. H. Gallagher and J. Padlog, “Investigation of the stability of structures on the basis of an analysis of discrete elements,” Raketnaya Tekhnika in Kosmonavtika, No. 6 (1963).

- 36.
V. M. Gerashchenko, V. N. Kislookii, A. S. Sakharov, and A. L. Sinyavskii, “Calculation of plants of the steam turbine blade shroud type,” in: Strength of Materials and Structural Mechanics [in Russian], No. 8, Izd. Budivel'nik, Kiev (1968).

- 37.
V. M. Gerashchenko and S. N. Lyubchenko, “Formulation of various equations of the plane problem of elasticity by means of the variational method,” in: Strength of Materials and Structural Mechanics [in Ukrainian], No. 1, Izd. Budivel'nik, Kiev (1965).

- 38.
L. R. Hermann and D. M. Campbell, “Discrete element method for thin shells,” Raketnaya Tekhnika i Kosmonavtika, No. 10 (1968).

- 39.
I. I. Gol'denblat, Nonlinear Problems of Elasticity Theory [in Russian], Izd. Nauka, Moscow (1969).

- 40.
A. S. Gorodetskii, “Calculation of thin-walled reinforced-concrete structure in the nonelastic stage,” Trudy NIISK, No. 6, Izd. Budivel'nik, Kiev (1965).

- 41.
A. S. Gorodetskii, “Calculation of three-dimensional thin-walled structures by the finite element method,” Trudy KievZNIIÉP, No. 2 (1971).

- 42.
A. S. Gorodetskii, “Calculation of combined systems by the finite element method,” in: Strength of Materials and Structural Mechanics [in Russian], No. 16 Izd. Budivel'nik, Kiev (1972).

- 43.
A. S. Gorodetskii and G. B. Gil'man, “Bar design models of thin-walled reinforced-concrete structures,” Stroitel'stvo i Arkhitektura, No. 10 (1964).

- 44.
P. E. Grafton and D. R. Strome, “Calculation of axisymmetric shells by the method of direct determination of stiffnesses,” Raketnaya Tekhnika i Kosmonavtika, No. 10 (1963).

- 45.
B. E. Greene, R. E. Jones, and D. R. Strome, “Generalized variational principles in the finite element method,” Raketnaya Tekhnika i Kosmonavtika, No. 7 (1969).

- 46.
A. I. Gulyar, “Calculation of physically nonlinear axisymmetric shells with an arbitrary meridian in the case of large displacements,” in: Strength of Materials and Structural Mechanics [in Russian], No. 16, Izd. Budivel'nik, Kiev (1972).

- 47.
R. E. Jones, “Generalization of the direct stiffness method of analysis of structures,” Raketnaya Tekhnika i Kosmonavtika, No. 5 (1964).

- 48.
R. E. Jones and D. R. Strome, “Calculation of shells of revolution by the direct stiffness method by means of curvilinear elements,” Raketnaya Tekhnika i Kosmonavtika, No. 9 (1966).

- 49.
M. W. Jonson and R. W. MacLay, “Convergence of the finite element method in elasticity theory,” tProceedings ASME, “Prikl. Mekhan.,

__90__, No. 2 (1968). - 50.
M. I. Dlugach, “Development of a model of the net-point method,” Prikl. Mekhan.,

__2__, No. 3 (1956). - 51.
M. I. Dlugach, Net-Point Method in the Mixed Plane Problem of Elasticity Theory [in Russian], Izd. Naukova Dumka, Kiev (1964).

- 52.
L. G. Dmitriev, “Possible bar design models of some discrete systems,” in: Transactions of the All-Union Conference on the Use of Digital Computers in Structural Mechanics [in Russian], Sudpromgiz (1963).

- 53.
L. G. Dmitriev and P. M. Sosis, Programming the Calculation of Space Structures [in Russian], Gosstroiizdat, Kiev (1963).

- 54.
O. C. Zienkiewicz, “Finite element method: from intuition to generality,” in: Collection of Translations “Mekhanika” [in Russian], No. 6 (1970).

- 55.
O. C. Zienkiewicz and Y. K. Cheung, Finite Element Method in Problems of Structural and Continuum Mechanics [Russian translation], GONTI, Moscow (1971).

- 56.
E. N. Il'chenko and A. S. Sakharov, “Solution of large systems of equations in calculating plates and shells,” in: Strength of Materials and Structural Mechanics [in Russian], No. 16, Izd. Budivel'nik, Kiev (1972).

- 57.
A. A. Il'yushin, Plasticity [in Russian], GITTL, Moscow-Leningrad (1948).

- 58.
G. R. Cowper, E. Kosko, G. M. Lindberg, and M. D. Olson, “Use of high-precision triangular elements of deflectable plates in static and dynamic problems,” Raketnaya Tekhnika i Kosmonavtika, No. 10 (1969).

- 59.
A. L. Kvitka and P. P. Voroshko, “Finite element method as applied to the axisymmetric problem of elasticity theory,” Probl. Prochnosti, No. 11 (1970).

- 60.
V. I. Kel'in and M. F. Fedosov, “Solution of three-dimensional problems of elasticity theory in arbitrary curvilinear coordinates on the basis of a discrete design model,“ Trudy Kievsk. Inst. Inzh. Grazhd. Aviatsii, No. 3 (1969).

- 61.
V. N. Kislookii, “Vibrations of shells and plates,” in: Strength of Materials and Structural Mechanics [in Russian], No. 8, Izd. Budivel'nik, Kiev (1969).

- 62.
V. N. Kislookii and T. L. Reva, “Algorithmization of investigations of vibrations and stability of plates,” in: Numerical Methods of Calculating Space Structures [in Russian], Izd. Kievsk. Inzh.-Stroit. Inst. (1969).

- 63.
V. N. Kislookii and A. S. Sakharov, “Large deflections and stability of shells of complex form,” in: Strength of Materials and Structural Mechanics [in Russian], No. 16, Izd. Budivel'nik, Kiev (1972).

- 64.
R. W. Clough, “Finite element method in solving the two-dimensional problem of elasticity theory,” in: Computer-Aided Calculation of Structural Members [in Russian], Gosstroiizdat, Moscow (1967).

- 65.
V. G. Korneev, “Comparison of the finite element method with the variate difference method of solving problems of elasticity theory,” Izv. VNIIGidrotekhnika, 83 (1967).

- 66.
V. G. Korneev, “Finite element method for solving problems of elastic equilibrium,” in: Structural Mechanics of Structures [in Russian], Izd. LPI, Leningrad (1971).

- 67.
V. M. Korobkov and V. N. Slivker, “Computer-aided solution of the two-dimensional problem of elasticity theory for rectangular regions,” in: Computational and Organizational Techniques (Construction and Architecture), No. 4, Izd. Literatury po Stroitel'stvu (1968).

- 68.
J. L. Krahula and G. F. Lauterbach, “Solution of the St. Venant problem by the finite element method,” Radetnaya Tekhnika i Kosmonavtika, No. 12 (1969).

- 69.
J. L. Krahula and J. F. Polhemus, “Use of Fourier series in the discrete element method,” Raketnaya Tekhnika i Kosmonavtika, No. 4 (1968).

- 70.
R. D. Cook and J. K. Al-Abdulla, “Some ‘hybrid’ plane quadrangular finite elements,” Raketnaya Tekhnika i Kosmonavtika, No. 11 (1969).

- 71.
R. Courant, C. Fredricks, and G. Levy, “Difference equations of mathematical physics,” Ukr. Mat. Zh. No. 8 (1940).

- 72.
J. Khanna, “Criterion of selection of stiffness matrices,” Raketnaya Tekhnika i Kosmonavtika, No. 10 (1965).

- 73.
J. Khanna and R. F. Hooley, “Comparison and evaluation of stiffness matrices,” Raketnaya Tekhnika i Kosmonavtika, No. 12 (1966).

- 74.
M. A. Levin, Relation Between Discrete Bar and Continuous Systems in Structural Mechanics and Its Application to the Calculation of Plates, Author's Abstract of Candidate's Dissertation, Minsk (1965).

- 75.
A. W. Leissa, W. E. Clausen, L. E. Hulbert, and A. T. Hopper, “Comparison of approximate methods of solving problems on bending of plates,” Raketnaya Tekhnika in Kosmonavtika, No. 5 (1969).

- 76.
H. P. Lae, “Generalized stiffness matrix for an element of a curved beam,” Raketnaya Tekhnika i Kosmonavtika, No. 10 (1969).

- 77.
S. W. McCormick, “Solution of the two-dimensional problem of elasticity theory,” in: Computer-Aided Calculation of Structural Members [in Russian], gosstroiizdat, Moscow (1967).

- 78.
A. M. Maslennikov, “Approximate calculation of wall-beam type structures by the slope-deflection method,” in: Reports of the 21st Scientific Conference, Structural Mechanics [in Russian], Izd. Leningr. Inzh.-Stroit. Inst. (1963).

- 79.
A. M. Maslennikov, “Approximate solution of the two-dimensional problem of elasticity theory by the slope-deflection methods,” in: Reports of the Conference on the Use of Digital Computers in Structural Mechanics [in Russian], Sudpromgiz, Leningrad (1966).

- 80.
A. M. Maslennikov, “Calculation of slabs on the basis of a discrete design model,” Izv. Vuzov, Stroitel'stvo i Arkhitektura, No. 6 (1966).

- 81.
A. M. Maslennikov, “Substantiation of a discrete design model,” in: Reports of the 25th Scientific Conference, Structural Mechanics, [in Russian], Izd. Leningr. Inzh.-Stroit. Inst. (1967).

- 82.
R. R. Meyer and M. B. Harmon, “Finite element method for investigating edge-loaded truncated shells of revolution,” Raketnaya Tekhnika i Kosmonavtika, No. 4 (1963).

- 83.
É. Sh. Melamed, “Calculation of shells with an arbitrary middle surface on a rectangular plan by the finite element method,” in: Proceedings of the 25th Conference of the Khabarovsk Institute of Transportation Engineers [in Russian] (1967).

- 84.
É. Sh. Melamed, “Derivation of the stiffness matrix of finite elements for analysis of complex space systems,” Trudy Khabarovsk. Inst. Inzh. Transporta, No. 34 (1968).

- 85.
É. Sh. Melamed, “Analysis of complex space structures by the direct stiffness method,” Trudy Khabarovsk. Inst. Inzh. Transporta, No. 34 (1968).

- 86.
R. J. Melosh, “Bases for derivation of matrices for the direct stiffness method,“ Raketnaya Tekhnika i Kosmonavtika, No. 7 (1963).

- 87.
R. J. Melosh, “Construction of stiffness matrices,” in: Computer-Aided Calculation of Structural Members [Russian translation], IL, Moscow (1967).

- 88.
R. J. Melosh, “Calculation of massive bodies by methods of structural mechanics of bar systems,” in: Computer-Aided Calculation of Structural Members [Russian translation], IL, Moscow (1967).

- 89.
L. P. Mironov, “Calculation of a lattice cylindrical shell as a three-dimensional bar system,” Trudy Mosk. Inst. Inzh. Transporta, No. 274 (1968).

- 90.
S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Izd. Nauka, Moscow (1970).

- 91.
D. W. Murray, “Convergence of the solutions of the finite element method,” Raketnaya Tekhnika i Kosmonavtika, No. 4 (1970).

- 92.
D. W. Murray and E. L. Wilson, “Investigation of the supercritical behavior of thin elastic plates by the finite element method,” Raketnaya Tekhnika i Kosmonavtika, No. 10 (1969).

- 93.
D. R. Navaratna, “Determination of resulting stresses in the case of using the finite element method,” Raketnaya Tekhnika i Kosmonavtika, No. 11 (1966).

- 94.
L. K. Narets, “Calculation of plates by the E-method,” Trudy Tallinsk. Politekhn. Inst., Seriya A, No. 257 (1967).

- 95.
J. T. Oden, “Determination of large strains of elastic membranes by the finite element method,” in: Continuous Shells [in Russian], Vol. 1, Stroiizdat, Moscow (1969).

- 96.
B. O. Almroth and D. Bushnell, “Numerical calculation of various shells of revolution,” Raketnaya Tekhnika i Kosmonavtika, No. 10 (1968).

- 97.
M. D. Olson, “Some solutions for flutter with the use of finite elements,” Raketnaya Tekhnika i Kosmonavtika, No. 4 (1970).

- 98.
J. T. Oden, “Calculation of the stiffness matrix of discrete elements of thin shells of arbitrary form,” Raketnaya Tekhnika i Kosmonavtika, No. 5 (1968).

- 99.
J. H. Percy, T. H. H. Pian, S. Klein, and D. R. Navaratna, “Application of the matrix method to a linear elastic analysis of shells of revolution,” Raketnaya Tekhnika i Kosmonavtika, No. 11 (1965).

- 100.
Yu. P. Petrov, “Discrete method of calculating the strength of shallow doubly-curved shells rectangular in plan,” in: Dynamics and Strength of Machines [in Russian], No. 4, Izd. Khar'kovsk. Univ. (1966).

- 101.
Yu. P. Petrov, in: Strength of Materials and the Theory of Constructions [in Russian], Vol. 10, Izdvo Bydivel'nik (1970).

- 102.
T. H. H. Pian, “Derivation of relations for stiffness matrices based on the selection of the stress distribution law,” Raketnaya Tekhnika i Kosmonavtika, No. 2 (1964).

- 103.
T. H. H. Pian, “Derivation of the stiffness matrices of elements,” Raketnaya Tekhnika i Kosmonavtika, No. 3 (1964).

- 104.
A. Pifko and G. Isakson, “Finite element method for analysis of plastic twisting of plates,” Raketnaya Tekhnika i Kosmonavtika, No. 10 (1969).

- 105.
V. I. Potapenko, “Calculation of systems with yielding connections by the finite element method in a matrix form,” Stroitel'stvo i Arkhitektura Uzbekhistana, No. 5 (1970).

- 106.
C. A. Prato, “Comments on the report' Exact solution of some solutions by the discrete element method,” Raketnaya Tekhnika i Kosmonavtika, No. 6 (1969).

- 107.
I. S. Raju and A. K. Rao, “Stiffness matrices of elements in the form of a sector,” Raketnaya Tekhnika i Kosmonavtika, No. 1 (1969).

- 108.
I. S. Raju and A. K. Rao, “Authors' response to Irons,” Raketnaya Tekhnika i Kosmonavtika, No. 3 (1970).

- 109.
A. F. Smirnov (editor), “Computer-aided calculation of structural members,” in: Collection of Articles [Russian translation], IL, Moscow (1967).

- 110.
A. R. Rzhanitsyn, “Representation of a continuous isotropic elastic body in the form of a hinged bar system” in: Investigation of problems of Structural Mechanics and Plasticity Theory [in Russian], Gosstroiizdat, Moscow (1956).

- 111.
L. Rozin, “A scheme for partitioning equatitioning equations of shell theory,” Inzhenernyi Zhurnal, Mekhanika Tverdogo Tela, No. 2 (1961).

- 112.
L. A. Rozin, “Method of partitioning the shell theory,” Prikl. Mat. i Mekhan.,

__25__, No. 5 (1961). - 113.
L. A. Rozin, “Relation of the finite element method with the Bubnov—Galerkin and Ritz methods,” in: Structural Mechanics of Structures [in Russian], Izd. LPI, Leningrad (1971).

- 114.
E. I. Sankov and A. P. Goryachev, “Solution of two-dimensional nonlinear problems by the finite element method,” Uchnye Zapiski Gor'kovsk. Univ. Mekhanika, No. 108 (1970).

- 115.
A. S. Sakharov, “Equilibrium of guy rope nets,” in: Strength of Materials and Structural Mechanics [in Russian], No. 3, Izd. Budivel'nik, Kiev (1965).

- 116.
A. S. Sakharov, “Investigation of the algorithm for solving net systems of equations of plates and shells,” in: Strength of Materials and Structural Mechanics [in Russian], No. 7, Izd. Budivel'nik, Kiev, (1969).

- 117.
H. Simpson and D. Antebee, “Investigation of complex shells by the finite element method,” in: Continuous Shells [in Russian], Vol. 1, Stroiizdat, Moscow (1969).

- 118.
Yu. E. Skabitskii and M. F. Fedosov, “Determination of the stress tensor of an elastic body by the finite element method,” Trudy Kievsk. Inst. Inzh. Grazhd. Aviatsii, No. 3 (1969).

- 119.
A. F. Smirnov, “Selection of the algorithm for solving a system of crossbeams with a large number of unknowns,” Trudy Mosk. Inst. Inzh. Transporta, No. 155 (1962).

- 120.
A. F. Smirnov, A. V. Aleksandrov, B. Ya. Lyashchennikov, and N. N. Shaposhnikov, Computer-Aided Calculation of Structures [in Russian], Gosstroiizdat, Moscow (1964).

- 121.
A. P. Filin, editor, Current Methods of Calculating Complex Statistically Indeterminate Systems, Collection of Articles [Russian translation], IL, Moscow (1962).

- 122.
N. A. Solovei, “Determination of geometric characteristics in computer-aided solution of problems of the strength of shells of complex configuration” in: Strength of Materials and Structural Mechanics [in Russian], No. 16, Izd. Budivel'nik, Kiev (1972).

- 123.
P. M. Varvak and A. F. Ryabov, editors, Handbook on Elasticity Theory [in Russian], Izd. Budivel'nik, Kiev (1971).

- 124.
E. L. Stanton and L. A. Schmit, “Calculation of stresses and displacements in elastoplastic plates by the discrete element method,” Raketnaya Tekhnika i Kosmonavtika, No. 7 (1970).

- 125.
J. A. Striklin, D. R. Navaratna, and T. H. H. Pian, Raketnaya Tekhnika i Kosmonavtika, No. 11 (1966).

- 126.
J. A. Striklin, W. E. Haisler, P. T. Tisdale, and R. Gunderson, “Element in the form of an extremely narrowing triangular plate,” Raketnaya Tekhnika i Kosmonavtika, No. 1 (1969).

- 127.
N. S. Ter-Émanuil'yan, Development and use of the finite element matrix method for solving the two-dimensional problem of an isotropic body with consideration of shear creep,” Mekhan. Polim. No. 4 (1970).

- 128.
S. P. Timoshenko, History of Strength of Materials, McGraw-Hill, New York (1953).

- 129.
P. Tong, “Exact solution of some problems by the discrete element method,” Raketnaya Tekhnika i Kosmonavtika, No. 1 (1969).

- 130.
A. G. Ugodchikov and Yu. G. Korotkikh, Some Methods of Solving Physically Nonlinear Problems of Plates and Shells on a Digital Computer [in Russian], Izd. Naukova Dumka, Kiev (1971).

- 131.
A. P. Filin, “Calculation of a shell of arbitrary configuration on the basis of a discrete design model,” in: Transactions of the Conference on Theory of Plates and Shells (kazan, 1960), Kazan (1961).

- 132.
A. P. Filin, “Calculation of three-dimensional bar structures as a system of cross ties and its application to shells with the use of computers, Investigations in Structural Mechanics,” Trudy Mosk Inst. Inzh. Transporta, No. 190 (1962).

- 133.
A. P. Filin, “Discrete design models in structural mechanics,” Izv. AN SSSR, Mekhan. i Mashinostroenie, No. 5 (1964).

- 134.
A. P. Filin, “Approximate solution of the three-dimensional problem of elasticity theory, Investigations in Structural Mechanics, in: Trudy Leningr. Inst. Inzh. Zhel-Dor. Transporta, No. 249, Leningrad—Moscow (1966).

- 135.
A. P. Filin, “Computer-aided calculation of shells on the basis of a discrete design model (finite element method),” in: Continuous Shells [in Russian], Vol. 1, Stroiizdat, Moscow (1969).

- 136.
J. Fried, “Gradient methods of investigating finite element problems of eigenvalues,” Raketnaya Tekhnika i Kosmonavtika, No. 4 (1969).

- 137.
J. Fried, “Investigation of time-dependent phenomena by means of discrete elements,” Raketnaya Tekhnika i Kosmonavtika, No. 6 (1969).

- 138.
J. Fried, “Some aspects of the use of natural coordinates in the discrete element method,” Raketnaya Tekhnika i Kosmonavtika, No. 7 (1969).

- 139.
A. Khrennikov and S. Tetskan, “Calculation of cylindrical shells by the finite element method,” in: Continuous shells [in Russian], Vol. 1, Stroiizdat, Moscow (1969).

- 140.
K. M. Khuberyan, “Calculation of arch dams by the general variational-bar method,” Gidrotekh. Stroitel'., No. 3 (1962).

- 141.
K. M. Khuberyan, “General mixed variational-bar (variational-discrete) method of calculating shells and plates. Some results and prospects of development,” Trudy Tbilisk. NII Sooruzhenii i Gidroénergetiki, No. 1, Tbilisi (1968).

- 142.
I. M. Cherneva, “Discrete method of calculating plates and shells,” Trudy Leningr. Inst. Inzh. Transporta, No. 249 (1966).

- 143.
I. M. Cherneva, “Bar design model of plates and shells and finite element method, Theoretical Investigation in Structural Mechanics, Trudy Leningr. Inst. Inzh. Transporta, No. 248 (1968).

- 144.
V. G. Chudnovskii, Investigation of vibration and stability of plates and laminated systems by the method of partitioning partial differential equations,” in: Calculation of Space Structures [in Russian], No. 2, Gosstroiizdat, Moscow (1967).

- 145.
N. N. Shaposhnikov, “Calculation of bending of plates by the finite element method,” Trudy Mosk. Inst. Inzh. Transporta, No. 260 (1968).

- 146.
N. N. Shaposhnikov, “Solution of the two-dimensional problem of elasticity theory by a discrete model,” Trudy Mosk. Inst. Inzh. Transporta, No. 274 (1968).

- 147.
N. N. Shaposhnikov, “Passage to the limit for a discrete model of the two-dimensional problem of elasticity theory,” Trudy Mosk. Inst. Inzh. Transporta, No. 374 (1968).

- 148.
N. N. Shaposhnikov, “Calculation of the stability and vibrations of plates by the finite element method,” Investigation in the area of Transport and Structural Mechanics, Trudy. Mosk. Inst. Inzh. Transporta, No. 311 (1970).

- 149.
V. N. Shevchenko and L. G. Dmitriev, “Bending of nonlinear elastic plates, Computers in the investigation and design of construction installations,” Trudy Kiev ZNIIÉP, Izd. Budivel'nik, Kiev (1970).

- 150.
L. A. Schmit, F. K. Bogner, and R. L. Fox, “Calculation of structures in the presence of finite deflection with the use of discrete plate and shell elements,” Raketnaya Tekhnika i Kosmonavtika, No. 5 (1968).

- 151.
W. S. Schnobrich, J. W. Melin, and B. Moraz, “Numerical method of calculating structures partitioned into a system of discrete elements,” in: Continuous Shells [in Russian], Vol. 1, Stroiizdat, Moscow (1969).

- 152.
H. M. Adelman, D. S. Catherines, and W. C. Walton, “Accuracy of calculating stresses by the finite element method,” Raketnaya Tekhnika i Kosmonavtika, No. 3 (1970).

- 153.
F. A. Akyuz and J. E. Merwin, “Solution of nonlinear problems of elastoplasticity by the discrete element method” Raketnaya Tekhnika i Kosmonavtika, No. 10 (1968).

- 154.
J. H. Argyris, Energy Theorems and Structural Analysis, Butterworth, London (1960).

- 155.
J. H. Argyris, “Matrix methods of structural analysis,” Proc. 14th Meeting of AGARD, AGARDo-graph, 72 (1962).

- 156.
J. H. Argyris, S. Kelsey, and H. Kamel, “Matrix method of structural analysis,” AGARDograph, 72, Pergamon Press, Oxford (1963).

- 157.
J. M. Boisseries, “Generation of two-and three-dimensional finite elements,” Intern. Journal for Numerical Methods in Engineering, Vol. 3 (1971).

- 158.
G. Brebbia and J. Connor, “Geometrically nonlinear finite-element analysis,” J. of the Eng. Mech. Div.,

__95__, No. EM2 (1969). - 159.
D. Bushnell, “Computer analysis of shell structures,“ Paper Amer. Soc. Mechn. Eng., N WA PVP-13 (1969).

- 160.
G. Cantin, “Rigid body motions in curved finite elements,” AIAA Journal,

__8__, No. 7 (1970). - 161.
R. Courant, “Variable methods for the solution of problems of equilibrium and vibration,” Bull. Amer. Math. Soc.

__49__, No. 1 (1943). - 162.
S. H. Crandall, Engineering Analysis, McGraw-Hill, N. Y. (1956).

- 163.
P. H. Denke, “The matrix solution of certain problems in structural analysis,” J. Aeronaut, Sci.,

__23__(1956). - 164.
J. Ergatoudis, B. M. Irons, and O. S. Zienkiewicz, “Curved isoparametric quadrilateral elements in finite element analysis,” Intern. J. Solids and Struct.,

__4__, No. 1 (1968). - 165.
J. Ergatoudis, B. M. Irons, and O. C. Zienkiewicz, “Three-dimensional analysis of arch dams and their foundations,” Proc. Symp. on Arch. Dams, Inst. Engrs., London (1968).

- 166.
L. Euler, “De motu vibratorio tympanorum,” Navi Commentarie Acad. Petropolit, No. 10 (1966).

- 167.
H. Fette, “Gekrummte finite Elemente bei Schalengerechnungen,” Z. Angew. Math. und Mech., No. 50 (1970).

- 168.
R. H. Gallagher, “A correlation study of methods of matrix structural analysis,” AGARDograph, 69 (1962).

- 169.
R. H. Gallagher, J. Pablog, and P. P. Bijlaard, “Stress analysis of heated complex shapes,” ARS Journal,

__32__, No. 5 (1962). - 170.
v. Grastan, “Anwendung lines 'elementen-methode'-Programmes zur Lösung von Temperaturvertilungsproblemen,” Nuclear Engineering and Desing, No. 15 (1971).

- 171.
D. S. Griffin and R. B. Kellog, “A numerical solution of axially symmetrical and plane elasticity problems,” Intern. J. Solids and Struct., No. 3 (1967).

- 172.
A. Hrennikoff, “Solution of problems in elasticity by the framework method,” J. Appl. Mech., No. 8, Ser. A (1941).

- 173.
J. C. Jofrtet and G. M. Neice, “Finite element analysis of reinforced concrete slabs,” J. of the Struct. Div.,

__97__, No. ST3 (1971). - 174.
P. Lannay, “The thermoelastic computer code “TITUS,” Prepr. 1st. Intern. Conf. Struct. Mech. React. S-L.S. a. M5-4/1-M5-4.

- 175.
S. Levy, “Structural analysis and influence coefficient for delta wings,” J. Aernonaut. Sci., No. 20 (1953).

- 176.
P. V. Marcal, “Effect of initial displacement on the problem of large deflection and stability,” Techn. Rep. ARPA, 54 Brown Univ. (1967).

- 177.
C. Mareczek and D. Scharpf, “Three dimensional analysis of a pretwisted impellerblade by means of ASKA,” Research Report, No. 9, Pratt and Whitney, I. S. D., Univ. of Stuttgart (1968).

- 178.
H. C. Martin, “Plane elasticity problems and the direct stiffness method,” Trends in Engineering,

__13__(1961). - 179.
D. McHenry, “A lattice analogy for the solution of plane stress problems,“ J. Inst. Civil. Eng., No. 21 (1943).

- 180.
R. W. McLay, “Completeness and convergence properties of finite element displacement functions — a general treatment,” AIAA Journal (1967).

- 181.
R. J. Melosh, “Basis for derivation of matrices for the direct stiffness method,” AIAA Journal (1963).

- 182.
W. Mizumachi, “Application of the finite element method to three-dimensional stress and vibration analysis of BWR primary plant systems,” Prepr. 1st. Intern. Conf. Struct. Mech. React. Technol., Berlin, Vol. 5, M6-7/1-M6-7/17 (1971).

- 183.
K. H. Murray, “Comments on the convergence of finite element solutions,” AIAA Journal,

__8__, No. 4 (1970). - 184.
N. M. Newmark, “Numerical methods of analysis in bars, plates and elastic bodies, Numerical methods of analysis in engineering, edited by L. E. Grinter, MacMillan (1949).

- 185.
E. R. Oliveira, “Theoretical foundations of the finite element method,” Intern. J. Solids and Struct.,

__4__, No. 10 (1968). - 186.
B. W. Pappenfuss, “Lateral plate deflection by stiffness matrix methods, M. S. Thesis, Dept. of Civil Eng., Univ. of Washington, Seattle, Wash (1959).

- 187.
K. Parikh and C. H. Norris, “Analysis of Shells using a framework analogy, Paper Presented at the World Conf. on Shell Structures, San Francisco, National Academy of Sci., No. 2 (1960).

- 188.
J. S. Prezemieniecki, “Triangular plate element in the matrix force method of structural analysis,” AIAA Jornal

__8__, No. 8 (1963). - 189.
L. A. Schmit and G. R. Monforton, “Finite deflection discrete element analysis of sandwich plates and cylindrical shells with laminated forces,” AIAA Journal,

__8__, No. 8 (1970). - 190.
R. T. Severn and D. R. Taylor, “The finite element method for flexure of slabs when stress distributions are assumed,” Proc. Inst. Civ. Engrs., 34 (1966).

- 191.
E. L. Stanton and L. A. Schmit, “A discrete element stress and displacement analysis of elastoplastic plates,” AIAA Journal, No. 7 (1970).

- 192.
M. J. Turner, R. W. Clough, H. C. Martin and L. J. Topp, “Stiffness and deflection analysis of complex structures,” J. Aeronaut. Sci.

__23__, No. 9 (1956). - 193.
O. C. Zienkiewicz and Y. K. Cheung, “Finite elements in the solution of field problems,” Engineering,

__220__(1965). - 194.
O. C. Zienkiewicz and Y. K. Cheung, The Finite Element Method in Structural and Continuum Mechanics, London (1967).

- 195.
O. C. Zienkiewicz, B. W. Irons, J. Ergatoudis, S Ahmad, and F. C. Scott, “Isoparametric and associated element families for two-and three-dimensional analysis,” Chap. 13 of Finite Element Method in Stress Analysis, Edited by I. Holand and K. Bell, Trondheim, Norway (1969).

- 196.
O. C. Zienkiewicz, C. Taylor, and A. Gallico, “Three dimensional finite element analysis of the Tachien arc dam,” Water Power, No. 5-6 (1970).

## Additional information

Kiev Civil Engineering Institute. Translated from Prikladnaya Mekhanika, Vol. 8, No. 8, pp. 3–28, August, 1972.

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Vainberg, D.V., Gorodetskii, A.S., Kirichevskii, V.V. *et al.* Finite element method in mechanics of deformable bodies.
*Soviet Applied Mechanics* **8, **819–840 (1972). https://doi.org/10.1007/BF00886062

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### Keywords

- Finite Element Method
- Deformable Body