English
Русский 37-44 p.
The completeness of the truss design calculation is its configuration and dimensions when specifying the type of loading, material characteristics and directive dimensions. The problem of equilibrium stability with an unknown location of compressed rods hindered the optimization of the topology and geometry of the truss. The proposed variational method of truss synthesis is based on the principle of possible operation and generalization of the variational principles of Lagrange and Castigliano by expanding the functional space of geometric parameters. The solution of a physically linear isoperimetric problem for a given volume of the truss material allowed to establish its quasi-equal stress, which became the design criterion for the formulation of the geometry optimization problem. Its condition is the stationarity of the functional with respect to variable geometric parameters for a given flexibility of compressed rods. The iterative procedure, caused by a change in the initially accepted signs of longitudinal forces, is based both on their direct adjustment and on the change in the flexibility of individual rods. The global minimum of potential strain energy of the optimal truss is accompanied by a global minimum of material consumption. The proposed software allows to conduct automated design calculation of the truss. An example of designing a mechanical truss is considered.
1. Bol'shaya Sovetskaya EHnciklopediya / Pod red. A.M. Prohorova. 3-e izd. v 30 t. 27. M: Sovetskaya EHnciklopediya, 1977. 624 p. (rus.)
2. YUr'ev A.G. Estestvennyj faktor optimizacii topologii konstrukcij. Vestnik BGTU im. V.G. SHuhova. 2013. 5. P. 46 – 48. (rus.)
3. Roux W. Gesammelte Abhandlungen über Entwickelungsmechanik der Organismen. Bd 1-2. Leipzig, 1895.
4. Mazhid K.I. Optimal'noe proektirovanie konstrukcij. M.: Vysshaya shkola, 1979. 238 p. (rus.)
5. Levy M. La statique graphique et ses applications aux constructions, 1873.
6. Maxwell J.C. On the calculation of the equilibrium and stiffness of frames. The Scientific Papers of James Clerk Maxwell. 1890. 2. P. 175 – 177.
7. Michell A.G.M. The limits of economy of materials in framestructures. Philosophical Magazine and Journal of Science. 1904. 8 (47).
8. Pippard A.I.S. On a method for the direct design of framed structures having redundant bracing. Tech. Rep. Aero. Res. Comn. London, for Year 1922-1923.
9. YUr'ev A.G. Stroitel'naya mekhanika: sintez konstrukcij. M.: Izd. MISI 1982. 100 p. (rus.)
10. YUr'ev A.G. Variacionnye principy stroitel'noj mekhaniki. Belgorod: Izd-vo BelGTASM. 2002. 90 p. (rus.)
11. Degtyar' A.N., Seryh I.R., Panchenko L.A., CHernysheva E.V. Ostatochnyj resurs konstrukcij zdanij i sooruzhenij. Vestnik BGTU im. V. G. SHuhova. 2017. 10. P. 94 – 97. (rus.)
12. Matematicheskaya ehnciklopediya. Pod red. I.M. Vinogradova. V 5t. 2. M: Sovetskaya EHnciklopediya, 1979. 1104 p. (rus.)
13. Spravochnik stroitelya. Pod red. L.R. Mailyana. V 2 t. 1. Rostov-na-Donu: Izd. Rostovskogo universiteta, 1996. 576 p. (rus.)
14. Dorn W.S., Gomory R.E., Greenberg H.J. Automatic design of optimal structures. Journal de Mecanique, 1964. 3 (1).
15. Ata EHl'-Karim Soliman. Prodol'nyj izgib betonnyh kolonn, ogranichennyh trubami iz polimerov, armirovannyh voloknami. Vestnik BGTU im. V.G. SHuhova. 2009. 1. P. 4 – 5. (rus.)
2. YUr'ev A.G. Estestvennyj faktor optimizacii topologii konstrukcij. Vestnik BGTU im. V.G. SHuhova. 2013. 5. P. 46 – 48. (rus.)
3. Roux W. Gesammelte Abhandlungen über Entwickelungsmechanik der Organismen. Bd 1-2. Leipzig, 1895.
4. Mazhid K.I. Optimal'noe proektirovanie konstrukcij. M.: Vysshaya shkola, 1979. 238 p. (rus.)
5. Levy M. La statique graphique et ses applications aux constructions, 1873.
6. Maxwell J.C. On the calculation of the equilibrium and stiffness of frames. The Scientific Papers of James Clerk Maxwell. 1890. 2. P. 175 – 177.
7. Michell A.G.M. The limits of economy of materials in framestructures. Philosophical Magazine and Journal of Science. 1904. 8 (47).
8. Pippard A.I.S. On a method for the direct design of framed structures having redundant bracing. Tech. Rep. Aero. Res. Comn. London, for Year 1922-1923.
9. YUr'ev A.G. Stroitel'naya mekhanika: sintez konstrukcij. M.: Izd. MISI 1982. 100 p. (rus.)
10. YUr'ev A.G. Variacionnye principy stroitel'noj mekhaniki. Belgorod: Izd-vo BelGTASM. 2002. 90 p. (rus.)
11. Degtyar' A.N., Seryh I.R., Panchenko L.A., CHernysheva E.V. Ostatochnyj resurs konstrukcij zdanij i sooruzhenij. Vestnik BGTU im. V. G. SHuhova. 2017. 10. P. 94 – 97. (rus.)
12. Matematicheskaya ehnciklopediya. Pod red. I.M. Vinogradova. V 5t. 2. M: Sovetskaya EHnciklopediya, 1979. 1104 p. (rus.)
13. Spravochnik stroitelya. Pod red. L.R. Mailyana. V 2 t. 1. Rostov-na-Donu: Izd. Rostovskogo universiteta, 1996. 576 p. (rus.)
14. Dorn W.S., Gomory R.E., Greenberg H.J. Automatic design of optimal structures. Journal de Mecanique, 1964. 3 (1).
15. Ata EHl'-Karim Soliman. Prodol'nyj izgib betonnyh kolonn, ogranichennyh trubami iz polimerov, armirovannyh voloknami. Vestnik BGTU im. V.G. SHuhova. 2009. 1. P. 4 – 5. (rus.)
Yuryev A.G., Zinkova V.A., Ata El-Karim Soliman Truss design calculation. Construction Materials and Products. 2019. 2 (1). P. 37 – 44. https://doi.org/10.34031/2618-7183-2019-2-1-37-44