Michell cantilevers constructed within trapezoidal domains—Part III: force fields

Graczykowski, Cezary; Lewiński, Tomasz

doi:10.1007/s00158-005-0601-6

Cited by 18 publications

(10 citation statements)

References 5 publications

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“…Complementary to region T 4 , there will need to be two additional regions T 5 and T 5 , sim- (Pichugin et al 2012) ilar to, but not identical to the fields constructed by Chan (1967) (H. S. Y. Chan's solutions assume that the vertical boundaries of the domain are fixed, whereas in our case one must enforce the conditions for reflective symmetry). One can then construct further extensions of the field above, by adding further fully strained regions akin to the approach taken for Michell cantilevers by Lewiński et al (1994), Graczykowski and Lewiński (2006a), Graczykowski and Lewiński (2006b), and Graczykowski and Lewiński (2007).…”

Section: Global Optimalitymentioning

confidence: 99%

Optimum structure for a uniform load over multiple spans

Pichugin

Tyas

Gilbert

et al. 2015

Struct Multidisc Optim

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This paper presents a new half-plane Michell structure that transmits a uniformly distributed load of infinite horizontal extent to a series of equally-spaced pinned supports. A full kinematic description of the structure is obtained for the case when the maximum allowable tensile stress is greater than or equal to the allowable compressive stress. Although formal proof of optimality of the solution presented is not yet available, the proposed analytical solution is supported by substantial numerical evidence, involving the solution of problems with in excess of 10 billion potential members. Furthermore, numerical soluThis is an extended version of a paper prepared by tions for various combinations of unequal allowable stresses suggest the existence of a family of related, simple, and practically relevant structures, which range in form from a Hemp-type arch with vertical hangers to a structure which strongly resembles a cable-stayed bridge.

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Section: Global Optimalitymentioning

confidence: 99%

Optimum structure for a uniform load over multiple spans

Pichugin

Tyas

Gilbert

et al. 2015

Struct Multidisc Optim

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“…Having found these axial forces (which are constant along the boundary lines DB, DC) one can solve the equilibrium problem of the interior of the domain ABDC, i.e. find the internal forces in the meaning of Hemp (1973) by following the method developed in Graczykowski and Lewiński (2007a). These internal forces are defined by…”

Section: Geometry Of the Domain Rbdcnarmentioning

confidence: 99%

On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight

Sokół

Lewiński

2010

Struct Multidisc Optim

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Two problems of minimum weight design of plane trusses are dealt with. The first problem concerns construction of the lightest fully stressed truss subject to three self-equilibrated forces applied at three given points. This problem has been solved analytically by H.S.Y. Chan in 1966. This analytical solution is re-derived in the present paper. It compares favourably with new numerical solutions found here by the method developed recently by the first author. The solution to the three forces problem paves the way to half-analytical as well as numerical solutions to the problem of minimum weight design of plane symmetric frameworks transmitting two symmetrically located vertical forces to two fixed supports lying along the line linking the points of application of the forces.

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“…The desired final material distribution contains two distinct regions of fully dense material (ρ = 1) and regions that have zero relative density (ρ min <<1) with the fully dense regions representing the optimized topology. The final material distribution can be described by the probability distribution function, f f , given by (14) and the corresponding final cumulative distribution is given by (15) A gradual transition from the initial distribution to the final distribution can be achieved through the use of the beta function (17) where Γ is the gamma function. The corresponding cumulative distribution function, also known as the incomplete beta function, is given by …”

Section: Prescribed Materials Redistribution Methodsmentioning

confidence: 99%

“…Following the initial pioneering work of Michell [1] and a flourish of advances in the 1950's and 1960's (Cox [2]; Hemp [3]; Prager [4]; Chan [5]), the analysis of absolute minimum-weight truss structures entered a period of relative neglect until the 1990's since when it has become a subject of renewed interest; see for example the work by Rozvany et al [6][7][8]; Lewinski et al [9]; Lewinski and Rozvany [10][11][12]; Graczykowski and Lewinski [13][14][15]; Dewhurst [16,17]; Dewhurst and Srithongchai [18]; Srithongchai and Dewhurst [19]; Dewhurst et al [20].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional cylindrical truss structures: a case study for topological optimization

Dewhurst

Taggart

Waterman

et al. 2009

WIT Transactions on the Built Environment

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A general minimum-weight cylindrical structural layout for the support of any combination of axial and torsional loading has been developed. The principal intention in this work is to provide a test case for 3-dimensional numerical topological optimization. It is anticipated that the solution may present a challenge, since for the small angular spacing of the truss elements the internal radial force component is always of the order of magnitude of the angular spacing for any arbitrary selected pair of helix families. Moreover for a wide range of solutions slender members are an essential part of the topology.A novel finite element topology optimization procedure is presented based on the application of Beta probability density and cumulative distribution functions. The procedure utilizes a family of Beta functions which provide a smooth transition from a uniform to a bi-modal density distribution, with constant probability mean to conserve constant mass.

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Michell cantilevers constructed within trapezoidal domains—Part III: force fields

Cited by 18 publications

References 5 publications

Optimum structure for a uniform load over multiple spans

Optimum structure for a uniform load over multiple spans

On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight

Three-dimensional cylindrical truss structures: a case study for topological optimization

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