Topology and shape optimization methods using evolutionary algorithms: a review

Munk, David J.; Vio, Gareth A.; Steven, Grant P.

doi:10.1007/s00158-015-1261-9

Cited by 168 publications

(79 citation statements)

References 212 publications

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“…However, if sensitivity number is used to optimize shell structures, the thickness distribution in the shell must be continuous. 33 Therefore, individual elements cannot be rejected from the structure. This conflicts with the aims of the current optimization study, wherein we are considering wholesale changes in topology.…”

Section: (B)eso-based Optimization Methodsmentioning

confidence: 99%

Ground Structure Approaches for the Evolutionary Optimization of Aircraft Wing Structures

Sóbester

Ikonen

2016

16th AIAA Aviation Technology, Integration, and Operations Conference

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Aircraft wings have seen very few changes in the topological arrangement of the internal structures during the past decades. However, the traditional topology consisting of longitudinal spars and transverse ribs has not been conclusively shown to be the optimal. The purpose of this study is to develop a tool to explore the space of alternative internal structure topologies. We consider a pair of two-step optimization methods. First, a large set of potential structural members, i.e. a ground structure, is built inside the outer mold line of the wing. Second, an evolutionary optimization method is applied to search for the optimal subset of structural members. Two methods are used: a genetic algorithm (GA) and an evolutionary structural optimization (ESO) heuristic. The objective in both cases is to minimize the structural mass of the wing subject to stress and buckling constraints, which are evaluated by automated finite element analysis. The methods are applied to the structural design of the 3D printed wing of a small unmanned aerial vehicle (sUAV) and benchmarked against manually designed internal structures.

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Section: (B)eso-based Optimization Methodsmentioning

confidence: 99%

Ground Structure Approaches for the Evolutionary Optimization of Aircraft Wing Structures

Sóbester

Ikonen

2016

16th AIAA Aviation Technology, Integration, and Operations Conference

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“…There are now several different approaches to topology optimization (Sigmund and Maute 2013;Deaton and Grandhi 2014), including density-based methods (Bendsøe and Sigmund 2004), Evolutionary Structural Optimization (ESO) (Munk et al 2015) and level-set methods (van Dijk et al 2013). Density-based and ESO methods utilize element-wise design variables to indicate where material exists.…”

Section: Introductionmentioning

confidence: 99%

Minimum length-scale constraints for parameterized implicit function based topology optimization

Dunning

2018

Struct Multidisc Optim

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This paper introduces explicit minimum length-scale constraint functions suitable for parameterized implicit function based topology optimization methods. Length-scale control in topology optimization has many potential benefits, such as removing numerical artifacts, mesh independent solutions, avoiding thin, or single node hinges in compliant mechanism design and meeting manufacturing constraints. Several methods have been developed to control length-scale when using density-based or signed-distance-based level-set methods. In this paper a method is introduced to control length-scale for parameterized implicit function based topology optimization. Explicit constraint functions to control the minimum length in the structure and void regions are proposed and implementation issues explored in detail. Several examples are presented to show the efficacy of the proposed method. The examples demonstrate that the method can simultaneously control minimum structure and void length-scale, design hinge free compliant mechanisms and control minimum length-scale for three dimensional structures.

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“…Rozvany (2001), Munk et al (2015), and Bendsøe and Sigmund (2003) give a good overview of the eld and its development. We briey cover that history here.…”

Section: Classical Approaches To Structural Optimisationmentioning

confidence: 99%

“…He found that in order to minimise the weight, frames should have their elements meet at right angles. Since this seminal article, much work has been done in the eld examining a variety of methods and descriptions including frames, planar sections, plates and continuous structures (Bendsøe and Sigmund, 2003;Munk et al, 2015). Of interest to the ideas described in this thesis is the relatively general continuum optimisation problem which has been approached in a number of ways, including: with pure shape optimisation; a relaxed formulation with the material distribution method; heuristic evolution with evolutionary structural optimisation; and using level-set methods to describe and evolve designs.…”

Section: Overviewmentioning

confidence: 99%

“…Elements are removed when they are inecient, with the quantication of eciency depending on the problem. For example, in the case of stress minimisation, eciency may in some cases be determined with the von Mises stress (Xie and Steven, 1994;Munk et al, 2015), so elements that are transferring less stress are removed while those transferring more stress are retained.…”

Section: Overviewmentioning

confidence: 99%

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Microstructure Interpolation for Macroscopic Optimisation

Cramer¹

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Recent advances in additive manufacturing now allow the physical construction of designs with features on the scale of tens of micrometres. It is impractical to design macroscopic objects with such feature sizes by hand, yet designs exploiting this new manufacturing ability can be produced through computational algorithms, such as with structural optimisation. While the computational ability of structural optimisation techniques is improving, the direct optimisation of a structure spanning two or more length scales is still dicult. Despite this, the new nescale manufacturing capability can be exploited using multiscale structural optimisation to nd the best high resolution design for a particular application.A multiscale design consists of microstructures which are repeatedly placed to create the design according to a macroscopic description. Previous work in multiscale optimisation has focused either on homogeneous microstructures that do not vary throughout the macroscopic design;analytically dened microstructures whose variation is well-known such as square lattices; or top-down multiscale design. In top-down multiscale design the macroscopic requirements at various locations prescribe the microstructural optimisation problems to be solved.We seek to solve some of the issues associated with top-down multiscale designs while allowing ii a wider space of microstructures than those that are analytically dened. We present a novel bottom-up method for multiscale structural optimisation over two length scales, which we call microstructure interpolation for macroscopic optimisation (MIMO). Shape interpolation, or morphing, between optimised microstructures produces a continuous set of microstructures that smoothly varies in both geometry and mechanical properties. The smooth set is used for macroscopic optimisation similar to the material distribution method (see Figure 1).The output of any multiscale optimisation method must be transformed into a single unied description before a physical product can be manufactured. This transformation requires smooth transitions between the various microstructures to be well dened; the smoothness is assumed but not enforced in many existing top-down methods. The MIMO approach trades the generality of existing multiscale methods for a stronger unied interpretation: while the space of allowed microstructures is diminished compared to existing top-down methods, the microstructures vary smoothly throughout the design. This smoothness makes it clear how the microstructures can be transitioned between neighbouring macroscopic elements ensuring connectedness in the unied two-scale design. The MIMO method is also straightforward to apply to problems where a functionally graded material is desired.In this thesis the MIMO method is developed and tested. We rstly perform shape interpolation between a number of elastically isotropic microstructures optimised for bulk modulus. They are parameterised by their volume fraction and vary in stiness. The interpolated microstructures have sm...

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Topology and shape optimization methods using evolutionary algorithms: a review

Cited by 168 publications

References 212 publications

Ground Structure Approaches for the Evolutionary Optimization of Aircraft Wing Structures

Ground Structure Approaches for the Evolutionary Optimization of Aircraft Wing Structures

Minimum length-scale constraints for parameterized implicit function based topology optimization

Microstructure Interpolation for Macroscopic Optimisation

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