Stifness operator for boundary problems of structural analysis and several new variational formulations

• Autorzy: Zolotov A. B. , Sidorov V. N. , Akimov P. A. , Mozgaleva M. L.
• Języki publikacji: EN

Abstrakty

EN

So-called "stiffness operator" for boundary problems of structural analysis is introduced in the distinctive paper. There is a direct analogy between this stiffness operator and corresponding stiffness matrix of the considering structure in terms of finite element method. Namely we can consider stiffness operator as a limiting (continual) generalization of stiffness matrix. The explicit formulation of stiffness operator is presented. Several new variational formulations are discussed as well.

Słowa kluczowe

EN

stiffness operator; boundary problems; structural analysis; variational formulations

• Wydawca: Wydawnictwo Politechniki Świętokrzyskiej
• Czasopismo: Structure and Environment
• Rocznik: 2010
• Tom: Vol. 2, no. 2
• Strony: 9--13
• Opis fizyczny: Bibliogr. 17 poz., wzory

Twórcy

autor

Zolotov A. B.

autor

Sidorov V. N.

autor

Akimov P. A.

autor

Mozgaleva M. L.

• Moscow State University of Civil Engineering, 26, Yaroslavskoe Shosse, 129337, Moscow, Russia,

Bibliografia

• [1] Akimov P.A., Zolotov A.B.: Discrete-continual Finite Element Method of Analysis for Three-dimensional Curvilinear Structures with Unilateral Constraints. International Journal for Computational Civil and Structural Engineering. Volume 1, Number 5, Begell House Inc. Publishers & ASV Publishing House, 2003, pp. 10-26.
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• [3] Jemielita G.: Bending of Plates Loaded along a Curve. Bulletin De L’Academie Polonoise Des Sciences. Serie des sciences techniques. Volume XX, No. 10, 1972, pp. 385-391.
• [4] Kanwal R.P.: Generalized Functions: Theory and Applications. Birkhäuser Boston, 476 pages.
• [5] Shilov G.E.: Mathematical Analysis. Second Special Course. Moscow, „Nauka”, 1965, 327 pages (in Russian).
• [6] Zienkiewicz O.C., Taylor R.L.: The Finite Element Method Set, Sixth Edition. Butterworth-Heinemann, 2005, 1872 pages.
• [7] Zolotov A.B., Akimov P.A.: Semianalytical Finite Element Method for Two-dimensional and Threedimensional Problems of Structural Analysis. Proceedings of the International Symposium LSCE 2002 organized by Polish Chapter of IASS, Warsaw, Poland, 2002, p. 431-440.
• [8] Zolotov A.B., Akimov P.A.: Practical Methods of Structural Analysis. Numerically-Analytical Methods. Moscow, ASV Publishing House, 2006, 200 pages (in Russian).
• [9] Zolotov A.B., Akimov P.A.: Some Semianalytical Methods of Analysis of Boundary problems of Structural Mechanics. Moscow, ASV Publishing House, 2004, 200 pages (in Russian).
• [10] Zolotov A.B., Akimov P.A., Sidorov V.N.: Correct Discrete-Continual Finite Element Method for Three-Dimensional Problems of Structural Analysis. // Journal of Beijing University of Civil Engineering and Architecture. Vol. 25, No. 2, Jun. 2009.
• [11] Zolotov A.B., Akimov P.A., Sidorov V.N.: Stiffness Operator and Several New Variational Formulations of Problems of Structural Analysis. XVI Slovak - Polish - Russian Seminar „Theoretical Foundation of Civil Engineering”. Proceedings. Zilina, Slovak Republic, 11.06.2007 - 15.06.2007, pp. 65-70 (in Russian).
• [12] Zolotov A.B., Akimov P.A., Sidorov V.N.: Stiffness Operator as a Continual Analogue of Stiffness Matrix for Boundary Problems of Structural Analysis and Several New Variational Formulations. International Journal for Computational Civil and Structural Engineering. Volume 1, Issue 3, Begell House Inc. Publishers & ASV Publishing House, 2007, pp. 77-82.
• [13] Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L.: Discrete-continual Methods of Structural Analysis. Moscow, „Arkhitectura - S”, 2010, 336 pages (in Russian).
• [14] Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L.: Discrete-continual Finite Element Method. Applications in Construction. Moscow, ASV Publishing House, 2010, 336 pages (in Russian).
• [15] Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L.: Mathematical Method in Structural Mechanics. Moscow, ASV Publishing House, 2008, 336 pages (in Russian).
• [16] Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L.: Numerical and Analytical Methods of Structural Analysis. Moscow, ASV Publishing House, 2009, 336 pages (in Russian).
• [17] Zolotov A.B., Larionov A.V., Mozgaleva M.L., Mskhalaya Zh.I.: Formulation and Approximation of Boundary Problems with the Use of Method of Extended Domain. Moscow, MSUCE, 1992, 86 pages (in Russian).