Shape optimization of elastic bars in torsion

Hou, J. W.; Haug, Edward J.; Benedict, Robert Leon

doi:10.1007/bfb0073068

Cited by 9 publications

(4 citation statements)

References 7 publications

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“…Notice that the constant S is supposed to be given. The necessary optimality condition has the following form (Banichuk, 1975;Hou et al, 1984):…”

Section: Statement Of the Optimization Problemmentioning

confidence: 99%

“…In the latter case, an exact solution of the optimization problem was obtained by Kurshin and Onoprienko (1976) using a complex variable technique. Finite element algorithms adjusted for structural shape optimization of elastic bars in torsion were suggested by Hou et al (1984) and Mejak (2000). Curtis and Walpole (1982) obtained an asymptotic solution of the three-dimensional optimization problem for an axisymmetric hollow shaft with a specified inner variable cross-section in the case of small shaft thickness.…”

Section: Introductionmentioning

confidence: 99%

“…The necessary optimality condition for the optimization problem with a multiply-connected cross-section was derived by Banichuk (1975) and Hou et al (1984). A regular perturbation technique was employed by Banichuk (1976) and Parbery and Karihaloo (1977) to obtain approximate solutions of the shape optimization problems with a doubly-connected cross-section.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic models for optimizing the contour of multiply-connected cross-section of an elastic bar in torsion

Argatov

2010

International Journal of Solids and Structures

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a b s t r a c tAn asymptotic solution is obtained for the problem of maximizing the torsional rigidity of elastic, multiply-connected cylindrical bars for a given area of cross-section. The shapes of the inner contours of the multiply-connected cross-section are specified while the outer contour is determined as a result of the shape optimization. We apply the method of matched asymptotic expansions to construct a first-order asymptotic model. The conditions for unique solvability of the asymptotic model have been established under some restrictions imposed on the location of the inner contours and their polarization matrices. The economy achieved by optimization is estimated.

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“…Notice that the constant S is supposed to be given. The necessary optimality condition has the following form (Banichuk, 1975;Hou et al, 1984):…”

Section: Statement Of the Optimization Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotic models for optimizing the contour of multiply-connected cross-section of an elastic bar in torsion

Argatov

2010

International Journal of Solids and Structures

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“…We note that using the ÿrst Green formula material derivative of the torsional rigidity into direction of the velocity ÿeld V can be expressed [12] aṡ…”

Section: Discretization Of the Problemmentioning

confidence: 99%

Optimization of cross-section of hollow prismatic bars in torsion

Mejak

2000

Commun. Numer. Meth. Engng.

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The problem of optimal shape design of a doubly connected prismatic bar in torsion is formulated and solved numerically by the ÿnite element method. The cost function is torsional rigidity of the domain, constraint is the constant area of the cross-section while shape parameters are co-ordinates of the ÿnite element nodes along the variable boundary. The variable boundary is either the inner or outer boundary of the domain. A dual problem of minimizing the area at the constant torsional rigidity is also considered. The problem is solved directly by optimizing the cost function with respect to the shape parameters. Numerical examples are given for two benchmark problems.

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Boundary Elements in Shape Optimal Design of Structures

Soares

Choi

1986

The Optimum Shape

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Shape optimization of elastic bars in torsion

Cited by 9 publications

References 7 publications

Asymptotic models for optimizing the contour of multiply-connected cross-section of an elastic bar in torsion

Asymptotic models for optimizing the contour of multiply-connected cross-section of an elastic bar in torsion

Optimization of cross-section of hollow prismatic bars in torsion

Boundary Elements in Shape Optimal Design of Structures

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