DEEP BEAM ANALYSIS WITH THE USE OF DISCRETE-CONTINUAL FINITE ELEMENT METHOD IN THE PRESENCE OF A VERTICAL CRACK
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Abstract
Deep beam analysis with the use of discrete-continual finite element method in the presence of vertical crack is under consideration in the distinctive paper. The operational formulation within discrete-continual approach is given, examples of analysis are presented. Cases of different lengths of the corresponding vertical crack are analyzed. The presented examples demonstrate the advantages of the discrete-continual finite element method used in comparison with the conventional finite element method (the use of the latter is associated with a significant increase in the number of nodes in the grid domain and, consequently, with an increase in the order of the resolving system of equations).
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References
Akimov P.A. Correct Direct Discrete-Continual Boundary Element Method of Structural Analysis. // Applied Mechanics and Materials Vols. 395-396 (2013), pp. 529-532.
Akimov P.A., Mozgaleva M.L. Method of Extended Domain and General Principles of Mesh Approximation for Boundary Problems of Structural Analysis. // Applied Mechanics and Materials, 2014, Vols. 580-583, pp. 2898-2902.
Akimov P.A., Mozgaleva M.L. Wavelet-based Multilevel Discrete-Continual Finite Element Method for Local Deep Beam Analysis. // Applied Mechanics and Materials Vols. 405-408 (2013), pp. 3165-3168.
Akimov P.A., Mozgaleva M.L., Mojtaba Aslami, Negrozov O.A. About Verification of Discrete-Continual Finite Element Method of Structural Analysis. Part 1: Two-Dimensional Problems // Procedia Engineering, Vol. 91 (2014), pp. 2-7.
Akimov P.A., Mozgaleva M.L., Mojtaba Aslami, Negrozov O.A. Wavelet-Based Discrete-Continual Finite Element Method of Local Structural Analysis for Two-Dimensional Problems // Procedia Engineering, Vol. 91 (2014), pp.8-13.
Akimov P.A., Mozgaleva M.L., Negrozov O.A. About Verification of Discrete-Continual Finite Element Method for Two-Dimensional Problems of Structural Analysis. Part 1: Deep Beam with Constant Physical and Geometrical Parameters Along Basic Direction. // Advanced Materials Research, Vols. 1025-1026 (2014), pp. 89-94.
Akimov P.A., Mozgaleva M.L., Negrozov O.A. About Verification of Discrete-Continual Finite Element Methodfor Two-Dimensional Problems of Structural Analysis. Part 2: Deep Beam with Piecewise Constant Physical and Geometrical Parameters Along Basic Direction. // Advanced Materials Research, Vols. 1025-1026 (2014), pp. 95-103.
Akimov P.A., Sidorov V.N. Correct Method of Analytical Solution of Multipoint Boundary Problems of Structural Analysis for Systems of Ordinary Differential Equations with Piecewise Constant Coefficients. // Advanced Materials Research Vols. 250-253, 2011, pp. 3652-3655.
Mozgaleva M.L., Akimov P.A. Solution of the Problem of Two-Dimensional Theory of Elasticity with the Use of Discrete-Continual Finite Element Method in the Presence of a Crack. // International Journal for Computational Civil and Structural Engineering, 2024, Volume 20, Issue 2, pp. 192-198.
Zienkiewicz O.C., Morgan K. Finite Elements and Approximation. Dover Publications, 2006, 352 pages.
Zienkiewicz O.C., Taylor R.L., Zhu J.Z. The Finite Element Method: Its Basis and Fundamentals. Butterworth-Heinemann, Sixth edition, 2005, 752 pages.
Zienkiewicz O.C., Taylor R.L. The Finite Element Method for Solid and Structural Mechanics. Volume 2. Butterworth-Heinemann, Sixth Edition, 2005, 736 pages.
Zolotov A.B., Akimov P.A. Semianalytical Finite Element Method for Two-dimensional and Three-dimensional Problems of Structural Analysis. // Proceedings of the International Symposium LSCE 2002 organized by Polish Chapter of IASS, Warsaw, Poland, 2002, pp. 431-440.
Lur'e A.I. Teorija uprugosti [Theory of Elasticity]. Moscow, Nauka, 1970, 939 pages (in Russian).
Parton V.Z., Perlin P.I. Metody matematicheskoj teorii uprugosti [Methods of Mathematical Theory of Elasticity]. Moscow, Nauka, 1981, 688 pages (in Russian).