An Application of Analytical Multi-Objective Optimization to Truss Structures

Lévi, F.; Gobbi, Massimiliano

doi:10.2514/6.2006-6975

Cited by 7 publications

(7 citation statements)

References 7 publications

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“…and therefore the solution is either an active constraint or the Pareto-optimal set of the unconstrained problem [18]. In fact, if the problem is unconstrained, the L matrix is L = ∇F and the solution is given by det(∇F) = 0 (42)…”

Section: Discussionmentioning

confidence: 99%

Thin-walled tubes under torsion: multi-objective optimal design

2019

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The lightweight design of a thin-walled tube under torsion is addressed in the paper. A multi-objective optimization approach is adopted to minimize the mass while maximizing the structural stiffness of the thin walled tube.Constraints on available room (maximum diameter), safety (admissible stress), elastic stability (buckling), minimum thickness (forced by manufacturing technologies) are included in the problem. The analytical solution of the multi-objective optimization problem is obtained by applying a relaxed formulation of the Fritz John conditions for Pareto-optimality.Relatively simple analytical expressions of the Pareto-optimal set are derived both in the design variables (tube diameter and wall thickness) and objective functions (mass and compliance) domain. Simple practical formulae are provided to the designer for the preliminary design of thin-walled tubes under torsion. Finally, the comparative lightweight design of tubes made from different materials is presented and an application of the derived formulae to a simple engineering problem is discussed.

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Section: Discussionmentioning

confidence: 99%

Thin-walled tubes under torsion: multi-objective optimal design

2019

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“…The condition is also sufficient if the objective functions and the constraints are convex or pseudoconvex 24,25 Equation (30) can be rearranged in a matrix form as 14,26 L…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…and therefore the solution is either an active constraint or the Pareto optimal set of the unconstrained problem. 26 In fact, if the problem is unconstrained, the L matrix is L ¼ rF and the solution is given by…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Bending of lightweight circular tubes

Mastinu

Previati

2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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The concept design (sizing) of thin-walled tubes subject to bending is dealt by resorting to rigorous design principles pertaining to engineering science. Multi-objective optimization is the proper theory that has been exploited. Minimum mass and maximum stiffness (minimum compliance) are the optimization objectives. Safety (admissible stress), stability (buckling), available room (external radius of the tube), and thickness of the tube (arising from technological issues) are introduced as constraints. Linear elastic theory is used. Optimal solutions are given in analytical form for a prompt use by designers. Such optimal solutions refer both to the objectives (mass and compliance) and to the design variables (radius and thickness of the tube). The best attainable lightweight design is discussed as a function of the constraints. In particular, given the upper and lower bounds for radius and thickness respectively, three candidate optimal solutions are addressed in the paper for concept design purposes. The comparative lightweight design of tubes made from different materials is presented. Contrary with respect to the reputation of aluminum for effective lightweight construction, steel can be the best choice, when the available room has to be saturated.

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“…The following theoretical procedure for the analytical derivation of the Pareto-optimal set has been presented in Gobbi et al (2015) and Levi and Gobbi (2006) along with mathematical examples and the analytical solution of the optimal design of a beam of rectangular section subjected to bending. Here, the procedure is summarized.…”

Section: Analytical Derivation Of the Pareto-optimal Setmentioning

confidence: 99%

“…and therefore the solution is either an active constraint or the Pareto optimal set of the unconstrained problem (Levi and Gobbi 2006). In fact, if the problem is unconstrained, the L matrix is L = ∇F and the solution is given by det (∇F) = 0 (3.12)…”

Section: Fritz John Necessary Conditionmentioning

confidence: 99%

Bending of beams of arbitrary cross sections - optimal design by analytical formulae

Gobbi

Ballo

Mastinu

2016

Struct Multidisc Optim

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The paper deals with the conceptual design of a beam under bending. The common problem of designing a beam in a state of pure bending is discussed in the framework of Pareto-optimality theory. The analytical formulation of the Pareto-optimal set is derived by using a procedure based on the reformulation of the Fritz John Pareto-optimality conditions. The shape of the cross section of the beam is defined by a number of design variables pertaining to the optimization process by means of efficiency factors. Such efficiency factors are able to describe the bending properties of any beam cross section and can be used to derive analytical formulae. Design performance is determined by the combination of cross section shape, material and process. Simple expressions for the Pareto-optimal set of a beam of arbitrary cross section shape under bending are derived. This expression can be used at the very early stage of the design to choose a possible cross section shape and material for the beam among optimal solutions

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An Application of Analytical Multi-Objective Optimization to Truss Structures

Cited by 7 publications

References 7 publications

Thin-walled tubes under torsion: multi-objective optimal design

Thin-walled tubes under torsion: multi-objective optimal design

Bending of lightweight circular tubes

Bending of beams of arbitrary cross sections - optimal design by analytical formulae

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