Explicit formulation of Kuhn-Tucker necessary conditions in structural optimization

Gutkowski, W.; Bauer, J.; Iwanow, Z.

doi:10.1016/0045-7949(90)90104-a

Cited by 14 publications

(5 citation statements)

References 4 publications

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“…• An earlier finding by Gutkowski et al (1990), stating that the optimal weight is also given by the sum of products of Lagrange multipliers and limiting displacement values, was confirmed in the context of trusses.…”

Section: Discussionmentioning

confidence: 79%

Some unexpected properties of exact least-weight plane truss layouts with displacement constraints for several alternate loads

Rozvany¹,

Birker²,

Lewiński³

1994

Structural Optimization

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A b s t r a c tBasic geometrical properties of optimal plane truss layouts for multiple displacement constraints and several load conditions are derived. These include the feature that at any point, optimal bars may run in at most two directions and that even for two nonsymmetric alternative loads at the same point the optimal two-bar layout is always symmetrical for a vertical support. The above general findings are illustrated with examples, in which the results are derived by several independent methods, including a proof of global optimality of the layout.

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Section: Discussionmentioning

confidence: 79%

Some unexpected properties of exact least-weight plane truss layouts with displacement constraints for several alternate loads

Rozvany¹,

Birker²,

Lewiński³

1994

Structural Optimization

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“…A new iterative algorithm based on a Rosen projection gradient method [15] is proposed and applied for the above-mentioned problem's solution.…”

Section: Introductionmentioning

confidence: 99%

Optimal shakedown design of metal structures under stiffness and stability constraints

Merkevičiūtė

Atkočiūnas

2006

Journal of Constructional Steel Research

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“…The present paper continues the investigations of mathematical programming method applications for perfectly elastic-plastic structures in the range of the shakedown theory [1][2][3][4][5][6][7][8][9][10][11][12]. The Rozen project gradient method [13] is applied to solve the cyclically loaded non-linear shakedown plate stress and strain evaluation and that of the load optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Shakedown Loading Optimization Under Constrained Residual Displacements—formulation and Solution for Circular Plates

Jarmolajeva

Atkočiūnas

2002

Journal of Civil Engineering and Management

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The adapted plate load optimization problem is formulated applying the non-linear mathematical programming methods. The load variation bounds satisfying the optimality criterion in concert with the strength and stiffness requirements are to be identified. The stiffness constraints are realized via residual displacements. The dual mathematical programming problems cannot be applied directly when determining actual stress and strain fields of plate: the strained state depends upon the loading history. Thus the load optimization problem at shakedown is to be stated as a couple of problems solved in parallel: the shakedown state analysis problem and the verification of residual deflections bounds. The Rozen project gradient method is applied to solve the cyclically loaded non-linear shakedown plate stress and strain evaluation and that of the load optimization problems. The mechanical interpretation of Rozen optimality criterions allows to simplify the shakedown plate optimization mathematical model and solution algorithm formulations.

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Explicit formulation of Kuhn-Tucker necessary conditions in structural optimization

Cited by 14 publications

References 4 publications

Some unexpected properties of exact least-weight plane truss layouts with displacement constraints for several alternate loads

Some unexpected properties of exact least-weight plane truss layouts with displacement constraints for several alternate loads

Optimal shakedown design of metal structures under stiffness and stability constraints

Shakedown Loading Optimization Under Constrained Residual Displacements—formulation and Solution for Circular Plates

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