Optimal design of the beam under Eigen-oscillation frequency constraints
Published: 11.09.2015
Authors: Gurchenkov A.A., German I.M., Romanenkov A.M.
Published in issue: #5(41)/2015
DOI: 10.18698/2308-6033-2015-5-1402
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
The problem considered in the work is relevant to the current situation in the field of elastic body shape optimization. The proposed method of solving the problem is suitable for use in practice. Various conditions of end restraint were studied. For the numerical solving the extreme problem the methods of successive approximations and the gradient projection were used. The problem is solved considering various beam parameter constraint conditions naturally arising in solving such problems. To calculate the optimal shape of the beam deflection by the modern information technology, convenient for the user software was developed, allowing the results of calculations to be clearly demonstrated.
References
[1] Banichuk N.V. Izvestiya AN SSSR. Mekhanika tverdogo tela - Proceedings of the USSR AS. Mechanics of Rigid Body, 1974, no. 4, pp. 44-51.
[2] Bakhvalov N.S., Zhidkov N.P., Kobelkov G.M. Chislennye metody [Numerical Techniques]. Moscow, Binom. Laboratoriya znaniy Publ., 2012.
[3] Samarskiy A.A. Vvedenie v teoriyu raznostnykh skhem [Introduction to the Theory of Difference Schemes]. Moscow, Nauka Publ., 1971.
[4] Vasilyev F.P. Metody optimizatsii. V 2 knigakh [Optimization Techniques. In 2 books.]. Moscow, Moskovskiy Tsentr Nepreryvnogo Matematicheskogo Obrazovaniya Publ., 2011.
[5] Chernousko F.L. Banichuk N.V. Variatsionnye zadachi mekhaniki i upravleniya [Variational Problems in Mechanics and Control]. Moscow, Nauka Publ., 1973.
[6] Tsvey A.Yu. Balki i plity na uprugom osnovanii [Beams and Plates on Elastic Foundation]. Moscow, MADI Publ., 2014, 96 p.
[7] Vasserman N.N., et al. Soprotivlenie materialov [Strength of Materials]. Perm, Perm National Research Polytechnic University Publ., 2011, 365 p.
[8] Makarov E.G. Kursovaya rabota po metodu konechnykh elementov [Term paper on the finite element method]. St. Petersburg, Baltic State Technical University "Voenmeh" Publ., 2011, 49 p.
[9] Sankin Yu.N., Yuganova N.A. Nestatsionarnye kolebaniya sterzhnevykh system pri soudarenii sprepyatstviem [Unsteady Oscillations of Rod Systems in a Collision with an Obstacle]. Ulyanovsk, Ulyanovsk State Technical University Publ., 2010, 174 p.
[10] Isaev V.I. Matematicheskie modeli sterzhney, balok i plit v zadachakh sosredotochennogo udara [Mathematical Models of Rods, Beams and Plates in Problems of the Centric Impact]. Ph.D. Thesis (Phys.-Math.). Moscow, 2007, 155 p.
[11] Atamuratov A.Zh. Molodoy uchenyy - Young Scientist , 2014, no. 1, pp. 13-18.
[12] Andreev V.I., Barmenkova E.V., Matveeva A.V. Vestnik MGSU - Herald of the National Research University, Moscow State University of Civil Engineering, 2014, no. 1, pp. 25-32.
[13] Hjelmstad K.D. Fundamentals of the Structural Mechanics. Springer Science Media, 2005, XIV, 480 p.
[14] Andreev V.I. Optimization of thick-walled shells based on solutions of inverse problems of the elastic theory for inhomogeneous bodies. Computer Aided Optimum Design in Engineering, 2012, pp. 189-202.
[15] Kravanja S., Zlender B. Optimization of the underground gas storage in different rock environments. Computer Aided Optimum Design in Engineering, 2012, pp. 15-26.
[16] Issa H.K. Simplified structural analysis of steel portal frames developed from structural optimization. Computer Aided Optimum Design in Engineering, 2012, pp. 47-58.
[17] Syngellakis S. Longitudinal buckling of slender pressurized tubes. Fluid Structure Interaction XII, 2013, pp. 133-144.
[18] Gurchenkov A.A., Nosov M.V., Tsurkov V.I. Upravlenie vraschauschimisya tverdymi telami s zhidkostyu [Control of Fluid-Containing Rotating Rigid Bodies]. Moscow, Fismatlit Publ., 2011, 202 p.
[19] Gurchenkov A.A., Nosov M.V., Tsurkov V.I. Control of Fluid-Containing Rotating Rigid Bodies. CRC Press, 2013, pp. 147.
[20] Gurchenkov A.A. Izvestiya vuzov. Priborostroenie - Proceedings of Universities. Instrument Engineering, 2001, vol. 44, no. 2, p. 44.
[21] Gurchenkov A.A. Stability of a fluid-filled gyroscope. J. of Engineering Physics and Thermo Physics, 2002, vol. 75, no. 3, pp. 554.
[22] Gurchenkov A.A. Dinamika zavikhrennoy zhidkosti v polosti vraschayuschegosya tela [Dynamics of Swirling Liquid in the Cavity of a Rotating Body]. Moscow, Fismatlit Publ., 2010, 221 p.
[23] Gurchenkov A.A. Doklady RAN - Reports of RAS, 2002, vol. 382, no. 4, p. 476.