Extended exact solutions for least-weight truss layouts—Part I: Cantilever with a horizontal axis of symmetry

Numerical layout optimization provides a computationally efficient and generally applicable means of identifying the optimal arrangement of bars in a truss. When the plastic layout optimization formulation is used, a wide variety of problem types can be solved using linear programming. However, the solutions obtained are frequently quite complex, particularly when fine numerical discretizations are employed. To address this, the efficacy of two rationalization techniques are explored in this paper: (i) introduction of 'joint lengths', and (ii) application of geometry optimization. In the former case this involves the use of a modified layout optimization formulation, which remains linear, whilst in the latter case a non-linear optimization post-processing step, involving adjusting the locations of nodes in the layout optimized solution, is undertaken. The two rationalization techniques are applied to example problems involving both point and distributed loads, self-weight and multiple load cases. It is demonstrated that the introduction of joint lengths reduces structural complexity at negligible computational cost, though generally leads to increased volumes. Conversely, the use of geometry optimization carries a computational cost but is effective in reducing both structural complexity and the computed volume.

Section: Chan Cantilever With Two Load Casesmentioning

confidence: 99%

Rationalization of trusses generated via layout optimization

Gilbert

2015

“…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%

“…Unsurprisingly, the number of Michell structures to have been identified to date is not large, see e.g. Michell (1904), Chan (1962), Chan (1967), Hemp (1973), Lewiński et al (1994), and Rozvany (1998). Furthermore, whilst some notable exceptions exist, see Hemp (1974), Chan (1975), Sokół and Lewiński (2010), and Tyas et al (2011), the majority of known Michell structures are designed to support only a single external point load.…”

Section: Introductionmentioning

confidence: 99%

Optimum structure for a uniform load over multiple spans

Pichugin

Tyas

Gilbert

et al. 2015

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.

“…(6.7) and (6.8) in Graczykowski and Lewiński (2006a); the functions G n (λ, μ) are defined by (1) in Lewiński et al (1994a). Let us define the functions…”

Section: Geometry Of the Domain Rbdcnarmentioning

confidence: 99%

“…2 was constructed. By using (2.3) and (7)- (14) in Lewiński et al (1994a) one can rearrange (2.8) to the form …”

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

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.