Optimal shape of a twisted and compressed rod

DOI10.1016/S0997-7538(01)01165-2zbMath0998.74058OpenAlexW2049216155MaRDI QIDQ5949081

Teodor M. Atanacković, Valentin B. Glavardanov

Publication date: 12 November 2001

Published in: European Journal of Mechanics. A. Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0997-7538(01)01165-2

zbMATH Keywords

optimal shapelinearizationeigenvaluesbucklingPontryagin's maximum principlecoupleconcentrated forceminimal volumestability boundarynonlinear second-order equationtwisted compressed rod

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Bifurcation and buckling (74G60) Compliance or weight optimization in solid mechanics (74P05)

Related Items (8)

Does generalized elastica lead to bimodal optimal solutions? ⋮ Optimal design of clamped columns for stability under combined axial compression and torsion ⋮ Optimal design of a torsional shaft system using Pontryagin's maximum principle ⋮ Multi-objective optimal control for eigen-frequencies of a torsional shaft using Pontryagin's maximum principle ⋮ Optimal shape analysis of a column structure under various loading conditions by using differential transform method (DTM) ⋮ Optimal configurations of circular bars under free torsional and longitudinal vibration based on Pontryagin's maximum principle ⋮ Buckling of a twisted and compressed rod supported by Cardan joints ⋮ Optimal shape of an elastic column on elastic foundation

Cites Work

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• Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity
• The shape of the ideal column
• Twisted axially loaded rod with shear and compressibility
• On the optimal shape of a Pflüger column
• Postbuckling of a twisted prismatic rod under terminal thrust
• Strongest Columns and Isoperimetric Inequalities for Eigenvalues
• Problems of Optimal Structural Design
• Nonlinear problems of elasticity

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