Some Approaches for Shape Finding in Optimal Structural Design

“…As mentioned already by , isotropic approaches used by Mlejnek et al (1991), Rozvany et al (1992) or Maute and Ramm (1994) sometimes show considerable dependencies on meshes. Orthotropic approaches, such as the rectangular microhole model introduced by Bendsee and Kikuchi (1988) or the rank two layered model used by Bendsee (1989), possess better convergence properties.…”

Section: Orthotropic Approachmentioning

confidence: 96%

Adaptive topology optimization

Maute

Ramm

1995

Structural Optimization

160

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Topology optimization of continuum structures is often reduced to a material distribution problem. Up to now this optimization problem has been solved following a rigid scheme. A design space is parametrized by design patches, which are fixed during the optimization process and are identical to the finite element discretization. The structural layout is determined, whether or not there is material in the design patches. Since many design patches are necessary to describe approximately the structural layout, this procedure leads to a large number of optimization variables. Furthermore, due to a lack of clearness and smoothness, the results obtained can often only be used as a conceptual design idea.To overcome these shortcomings adaptive techniques, which decrease the number of optimization variables and generate smooth results, are introduced. First, the use of pure mesh refinement in topology optimization is discussed. Since this technique still leads to unsatisfactory results, a new method is proposed that adapts the effective design space of each design cycle to the present material distribution. Since the effective design space is approximated by cubic or Bdzier splines, this procedure does not only decrease the number of design variables and lead to smooth results, but can be directly joined to conventional shape optimization. With examples for maximum stiffness problems of elastic structures the quality of the proposed techniques is demonstrated.

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“…Introducing a fictive porosity and with a defined mass limit (mean porosity) the stiffness variation can be transformed into a density variation. The similarity to the homogenization approach of Bendsoe and Kikuchi and the method of Mlejnek is obvious [9,10,11,34,40].…”

Section: The Topology Optimization Theorymentioning

confidence: 96%

“…Therefore large efforts have to be put into the sensitivity analylsis up to now. So far no method [8,9,10,11,33,34,40,41,54,55] can be considered as a standard for calculating the optimum topology due to the above mentioned difficulties regarding the mathematical approaches. Essentially because of the expensive calculation efforts these approaches only can handle extremely simplified models.…”

Section: Topology Optimizationmentioning

confidence: 99%