Analysis of buckling by computer algebra. (English) Zbl 0743.73033
Summary: A combined analytical-numerical tool is presented for the evaluation of the buckling force of columns with abrupt changes in geometric and material properties. The iterative initial parameter method is computerized, and the symbolic (REDUCE) program is included. Several examples are solved, and the results are compared with existing data.
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74G60 | Bifurcation and buckling |
| 74-04 | Software, source code, etc. for problems pertaining to mechanics of deformable solids |
| 68W30 | Symbolic computation and algebraic computation |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
Keywords:
one end clamped; other unsupported; system of concentrated axial compressive forces; transcendental equation for critical parameter; FORTRAN program; columns; abrupt changes in geometric and material properties; iterative initial parameter method; symbolic (REDUCE) programSoftware:
REDUCEReferences:
| [1] | S.P. Timoshenko and J.M. Gere, Theory of Elastic Stability, Second Edition (McGraw-Hill Kogakusha, Ltd. Tokyo) 2-3.; S.P. Timoshenko and J.M. Gere, Theory of Elastic Stability, Second Edition (McGraw-Hill Kogakusha, Ltd. Tokyo) 2-3. |
| [2] | Snitko, N. K., Stability of column systems in the elasto-plastic range, ((1968), Izdatel’stvo Literatury po Stroitel’stvu: Izdatel’stvo Literatury po Stroitel’stvu Leningrad), 37-41, (in Russian). |
| [3] | Klein, G. K.; Rekach, V. G.; Rosenblatt, G. I., Rukovodstvo k Prakticheskim Zaniatiam po Kursu Stroitel’noi Mekhaniki, ((1972), Vyshaya Shkola Publishing House: Vyshaya Shkola Publishing House Moscow), 32, (in Russian). |
| [4] | (Palii, O. M.; Chuvikovski, V. S., Handbook of Structural Mechanics of Ships, Vol. 3 (1982), Sudostroenie Publishing House: Sudostroenie Publishing House Leningrad), 207-208, (in Russian). |
| [5] | (Column Research Committee of Japan, Handbook of Structural Stability (1971), Corona Press Ltd: Corona Press Ltd Tokyo) |
| [6] | Snitko, N. K., Deformational calculations and stability of high-rise towers, Izvestyia Vyschikh Uchebnykh Zavedenii, Stroitel’stvo i Architektura, 10, 32-35 (1966), (in Russian). |
| [7] | Snitko, N. K., Stability of compressed and bent columns systems, ((1956), Izdatel’stvo Literatury po Stroitel’stvu i Architeckture: Izdatel’stvo Literatury po Stroitel’stvu i Architeckture Leningrad), 13, (in Russian). |
| [8] | Hearn, A. C., (REDUCE User’s Manual (1987), RAND Corporation: RAND Corporation Santa Monica), Version 3.3 |
| [9] | Beltzer, A., Engineering analysis via symbolic computation, Appl. Mech. Rev., 43, 119-127 (1990) |
| [10] | Noor, A.; Elishakoff, I.; Hulbert, G., (Symbolic Computations and Their Impact on Mechanics, Vol. 25 (1990), ASME: ASME New York), PVP · Zbl 0850.73022 |
| [11] | Elishakoff, I.; Wang, X., General Smith-Herrmann problem with the aid of computerized symbolic algebra, J. Sound Vibration, 117, 537-542 (1987) |
| [12] | Elishakoff, I.; Tang, J., Buckling of polar orthotropic circular plates on elastic foundation by computerized symbolic algebra, Comput. Methods Appl. Mech. Engrg., 68, 229-247 (1988) · Zbl 0626.73039 |
| [13] | (Rao Singampalli, S. S., COSMOS Users Manual (1985), COSMOS Users Group: COSMOS Users Group Santa Monica, California) |
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