Exact optimal structural layouts for non-self-adjoint problems

Rozvany, G. I. N.; Sigmund, Ole; Lewiński, Tomasz; Gerdes, D.; Birker, T.

doi:10.1007/bf01743359

Cited by 13 publications

(15 citation statements)

References 8 publications

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“…The second explanation is similar to one proposed by Sigmund (Rozvany, Sigmund et al 1993). First we take only the displacement constraint into consideration.…”

Section: Type "A" Solution (Fig 4a)mentioning

confidence: 61%

Generalized Michell structures — exact least-weight truss layouts for combined stress and displacement constraints: Part I — General theory for plane trusses

Rozvany¹,

Birker²

1995

Structural Optimization

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In Part I of this study, earlier results are briefly reviewed and then general optimality criteria derived for exact leastweight plane truss layouts with combined stress and displacement constraints. Whilst these are necessary conditions for a local minimum with respect to any topology, Part II discusses analytical solutions within a given two-bar topology for a vertical support and a point load. The latter results are used for verifying the general theory in Part I.

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“…The second explanation is similar to one proposed by Sigmund (Rozvany, Sigmund et al 1993). First we take only the displacement constraint into consideration.…”

Section: Type "A" Solution (Fig 4a)mentioning

confidence: 61%

Generalized Michell structures — exact least-weight truss layouts for combined stress and displacement constraints: Part I — General theory for plane trusses

Rozvany¹,

Birker²

1995

Structural Optimization

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“…Rozvany, Sigmund et al 1993), a stationary solution may not represent the global optimum, but a local minimum or even a local maximum. Moreover, if too few displacement contraints are specified (Rozvany, Sigmund et al 1993;Rozvany and Kitsch 1994), the problem may be ill-posed and the optimal solution non-stationary (with a zero weight). However, the problem is always convex and can be made self-adjoint in the case of so-called proportional displacement constraints which are discussed in the next section.…”

Section: Z(l_ Z 2)mentioning

confidence: 98%

“…(53) where c 1 and c 2 are positive constants (Rozvany, Sigmund et al 1993). * The above strain fields are valid for 450 (fll,fl2) ~ 90° in Fig.…”

Section: Proof Of Global Optimalitymentioning

confidence: 99%

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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“…Generalized Michell structures for a single load condition were considered by Rozvany et al (1993bRozvany et al ( , 1994 for several displacement constraints, and by Rozvany and Birker (1995) for combined stress and displacement constraints.…”

Section: Important Notementioning

confidence: 99%

Fundamentals of exact multi-load topology optimization – stress-based least-volume trusses (generalized Michell structures) – Part I: Plastic design

Rozvany

Sokół

Pomezanski

2014

Struct Multidisc Optim

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In this two-part paper, Michell's century-old stress-based single-load truss topology optimization paper is extended to multiple load conditions. In Part I, so-called 'optimal plastic design' of multi-load trusses is reviewed, which is based on ultimate (limit or collapse) load principles and requires only statical admissibility of the solution. However, its connections to 'optimal elastic design' will be explained, and these will be used in Part II for the full extension of Michell's theory to elastic multi-load problems, which will fill a significant gap in our knowledge.

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Exact optimal structural layouts for non-self-adjoint problems

Abstract: Using optimality criteria for trusses with displacement constraints, a truss layout is optimized for a point load and a given displacement in different directions, with a view to demonstrating some unexpected features of non-self-adjoint problems.

Cited by 13 publications

References 8 publications

Generalized Michell structures — exact least-weight truss layouts for combined stress and displacement constraints: Part I — General theory for plane trusses

Generalized Michell structures — exact least-weight truss layouts for combined stress and displacement constraints: Part I — General theory for plane trusses

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

Fundamentals of exact multi-load topology optimization – stress-based least-volume trusses (generalized Michell structures) – Part I: Plastic design

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