On Michell trusses

Hegemier, G. A.; Prager, William

doi:10.1016/0020-7403(69)90006-x

Cited by 89 publications

(28 citation statements)

References 6 publications

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“…In other words, the method avoids the optimisation of sizing and geometry by instead doing a sizing-only optimisation for a highly redundant truss. Hegemier and Prager [29] showed that a truss of a single load with maximum stiffness is fully stressed, meaning that volume minimisation with equal stress limits in tension and compression is equivalent to a compliance minimisation with a prescribed volume [6].…”

Section: Topology Optimisationmentioning

confidence: 99%

Sustainability Based on Biomimetic Design Models

Almeida

Oliveira

2016

Handbook of Sustainability in Additive Manufacturing

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Ecodesign is an approach to designing products with special consideration for the environmental impacts of the product's life cycle. In a lifecycle assessment, the life cycle of a product is usually divided into procurement, manufacture, use, and disposal. Ecodesign is a growing responsibility and understanding of our ecological footprint on the planet. It is imperative to search for new productive solutions that are environmentally friendly and lead to a reduction in the consumption of materials and energy while maintaining the desired performance of the products. Bearing this in mind, additive manufacturing has the capability of producing components with the lowest amount of raw material needed and the highest geometrical complexity. This work aims to present novel bioinspired design methodologies for the production of additive manufacturing products with lower amounts of material and higher performance. The bioinspired design considers natural cellular-based concepts for the definition of novel product definitions.

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Section: Topology Optimisationmentioning

confidence: 99%

Sustainability Based on Biomimetic Design Models

Almeida

Oliveira

2016

Handbook of Sustainability in Additive Manufacturing

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“…As can be seen the deformation and stress states in Figure 3 refer to the original state and thus are proportional; the distortion state has not yet appeared. The states of deformation, stresses and distortions calculated after 13 steps of the simulation process are demonstrated in Figures 4(a), (b) and (c), respectively and the simulated shape modification is shown in Figure 5 Further generalization of considerations from the previous Section allows us to define the optimal remodelling problem in the wider class of admissible distortions when constraints (6) are neglected. Therefore, the rule (6) generating the increments of local distortions can be modified analogously to the simulation rule (3) as follows:…”

Section: Simulation Procedures For 2d Continuummentioning

confidence: 99%

Optimal structural remodelling — simulation by virtual distortions

Holnicki‐Szulc

1989

Commun. appl. numer. methods

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“…The only problem investigated in the paper of Hegemier and Prager (1969) by using Hooke's law was the problem of Michell's truss stiffness (compliance). The problem concerns the subject matter of this section and will be examined below.…”

Section: Optimal Layout Problems For Physically Nonlinear Trussesmentioning

confidence: 99%

“…It is essential for the analogy that according to experimental data (Kachanov 1960) the stress-strain velocity relation is concave. Optimization problems for structures in stationary creep were investigated by Hegemier and Prager (1969) and Prager (1968) for the homogeneous relation only.…”

Section: Introductionmentioning

confidence: 99%

On optimal physically nonlinear trusses

Selyugin

1995

Structural Optimization

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Optimization problems for physically nonlinear hyperelastic trusses statically loaded by a single system of loads are investigated. Several possible formulations of the problems for a prescribed truss layout are considered. It is demonstrated that the problems lead to the design of equal absolute stress values in some rods and of active technology constraints in other rods. Some general properties of the trusses are examined. Optimal physically nonlinear hyperelastic truss layout problems under static loading are also considered. It is shown that the well-known results of Maxwell, Michell and Prager concerning linear-elastic structures are generalized for the considered problems. It is demonstrated that the results of the paper are extended to optimization probl~ems for structures in stationary creep with an arbitrary concave stress-strain velocity relation.

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On Michell trusses

Cited by 89 publications

References 6 publications

Sustainability Based on Biomimetic Design Models

Sustainability Based on Biomimetic Design Models

Optimal structural remodelling — simulation by virtual distortions

On optimal physically nonlinear trusses

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