On the optimal shape of a compressed column subjected to restrictions on the cross-sectional area

Novakovic, Branislava N.; Atanacković, Teodor M.

doi:10.1007/s00158-010-0609-4

Cited by 9 publications

(7 citation statements)

References 19 publications

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“…For example, based on the Rayleigh quotient principle, Cheng and Zhong (1983) developed the sensitivity analysis and method of solution for optimal design of clamped-clamped columns under axial compressive forces, and Zhong and Cheng (1986) further proposed a Sequential Quadratic Programming approach for solution of the optimization problems. As recent papers on bimodal optimum design of columns, one may cite Novakovic and Atanackovic (2011) and Olhoff and Seyranian (2008), where the columns in the latter paper rest on a linearly elastic (Winkler) foundation. A notable paper (Bochenek, 1999) on bimodal optimum design of thermal buckling and post buckling behavior of elastic columns is closely related to the present study.…”

Section: Introductionmentioning

confidence: 99%

Optimum design of thermally loaded beam-columns for maximum vibration frequency or buckling temperature

Cheng

Yu²,

Olhoff

2015

International Journal of Solids and Structures

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Fundamental natural frequency of vibrations Critical thermal buckling temperature a b s t r a c tWith the cross-sectional area function as the design variable, we seek the optimum design of clamped-clamped, thin, linearly elastic beam-columns under thermal load that maximizes the buckling temperature or the fundamental natural frequency of transverse vibrations. The beam-columns have given length, geometrically similar cross-sections of variable size and a given volume of material. A lower and/or upper bound constraint may be prescribed for the cross-sectional area of the beam-columns. To account for possible bimodality of the optimum designs, both the unimodal and bimodal optimality criterion approaches are applied. For a lower bound smaller than a specific value, bimodal optimum designs are obtained for problems of maximum buckling temperature. When maximizing the thermal fundamental natural frequency, optimum designs may be uni-or bimodal depending on the values of the given thermal load and the lower bound on the cross-sectional area. The geometrically unconstrained optimum design for maximum fundamental natural frequency obtained by Olhoff (1976) without consideration of thermal load, is shown to be at the same time an optimum design that maximizes the fundamental natural frequency at any temperature rise, but it is found to be associated with zero buckling load. Moreover, the optimum design maximizing the critical buckling temperature is very similar to that maximizing the mechanical buckling load obtained by Olhoff and Rasmussen (1977). This interesting analogy is explained by studying optimum design for minimum axial compressive force.

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Section: Introductionmentioning

confidence: 99%

Optimum design of thermally loaded beam-columns for maximum vibration frequency or buckling temperature

Cheng

Yu²,

Olhoff

2015

International Journal of Solids and Structures

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“…Optimization problems of engineering structures, from the static viewpoint, are mainly associated with the problem of optimization of the columns against buckling. Thus, for example, [1,2] employed buckling optimization approach based on the Hencky bar-chain model of beams, while [3][4][5][6][7] considered a series of optimization problems of the shape of columns against buckling by using Pontryagin's maximum principle. In [8] thin elastic structures under the presence of unilateral constraints were considered by using Pontryagin's maximum principle.…”

Section: Introductionmentioning

confidence: 99%

“…The present paper considers the latter cause of vibrations coupling for the case of simply supported beam with the inclined right end. Moreover, the approach from [3][4][5][6][7] based on using Pontryagin's maximum principle is extended to the problem of mass minimization of the mentioned simply supported beam with coupled bending and axial vibrations at prescribed fundamental frequency. Here, it should be particularly emphasized that in [3][4][5][6][7] the phenomenon of the self-adjoint system in the problems of determining the optimum beam shapes has been noticed for the first time in the literature.…”

Section: Introductionmentioning

confidence: 99%

Mass minimization of an Euler-Bernoulli beam with coupled bending and axial vibrations at prescribed fundamental frequency

Obradović

Šalinić

Grbović

2021

Engineering Structures

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“…The optimal shape of an elastic column with clamped ends positioned on elastic foundation of Winkler type was determined in [14]. The optimal shape of a column on elastic foundation subjected to restrictions on minimum and maximum cross-sectional area was treated in [15]. It is shown that in this case the optimization can be both bimodal and unimodal.…”

Section: Introductionmentioning

confidence: 99%

Optimal shape of a column with clamped-elastically supported ends positioned on elastic foundation

Novakovic

2015

Theor appl mech (Belgr)

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We determine optimal shape of an elastic column positioned on elastic foundation of Winkler type. The Euler-Bernoulli model of beam is considered. The column is loaded by a compressive force and has one clamped end and the other elastically supported end. In deriving the optimality conditions, the Pontryagin?s principle was used. The optimality conditions for the case of bimodal optimization are derived. Optimal cross-sectional area is obtained from the solution of a non-linear boundary value problem. A first integral (Hamiltonian) is used to monitor accuracy of integration. This system is solved by using standard Math CAD procedure. New numerical results are obtained. [Projekat Ministarstva nauke Republike Srbije, br. 174005]

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On the optimal shape of a compressed column subjected to restrictions on the cross-sectional area

Cited by 9 publications

References 19 publications

Optimum design of thermally loaded beam-columns for maximum vibration frequency or buckling temperature

Optimum design of thermally loaded beam-columns for maximum vibration frequency or buckling temperature

Mass minimization of an Euler-Bernoulli beam with coupled bending and axial vibrations at prescribed fundamental frequency

Optimal shape of a column with clamped-elastically supported ends positioned on elastic foundation

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