Stress-based topology optimization with discrete geometric components

Zhang, Shanglong; Gain, Arun L.; Norato, Julián A.

doi:10.1016/j.cma.2017.06.025

Cited by 69 publications

(46 citation statements)

References 24 publications

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“…This is a trait of geometry projection methods we have observed before (Norato et al 2015;Zhang et al 2017a), and it is likely due to the more restrictive representation of possible geometries imposed by the discrete geometric components. To illustrate this dependency, we show in Fig.…”

Section: Long Cantilever Beammentioning

confidence: 99%

“…Besides other benefits (described in Zhang et al 2017a), this approximation has the advantage that it approximates the true maximum from below. This helps the method produce designs with less gaps between shapes in the optimal designs.…”

Section: Geometry Projectionmentioning

confidence: 99%

“…While we consider compliance minimization for simplicity in this work, we note that stress considerations can be incorporated in geometry projection methods (Zhang et al 2017a). The set denotes the design envelope, i.e.…”

Section: Optimization Problemmentioning

confidence: 99%

“…Since the maximum function is not differentiable, we replace it with a lower-bound Kreisselmeier-Steinhauser (KS) approximation (as in Zhang et al 2017a):…”

Section: Geometry Projectionmentioning

confidence: 99%

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Topology optimization with supershapes

Norato

2018

Struct Multidisc Optim

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This work presents a method for the continuum-based topology optimization of structures whereby the structure is represented by the union of supershapes. Supershapes are an extension of superellipses that can exhibit variable symmetry as well as asymmetry and that can describe through a single equation, the so-called superformula, a wide variety of shapes, including geometric primitives. As demonstrated by the author and his collaborators and by others in previous work, the availability of a feature-based description of the geometry opens the possibility to impose geometric constraints that are otherwise difficult to impose in density-based or level set-based approaches. Moreover, such description lends itself to direct translation to computer aided design systems. This work is an extension of the author's group previous work, where it was desired for the discrete geometric elements that describe the structure to have a fixed shape (but variable dimensions) in order to design structures made of stock material, such as bars and plates. The use of supershapes provides a more general geometry description that, using a single formulation, can render a structure made exclusively of the union of geometric primitives. It is also desirable to retain hallmark advantages of existing methods, namely the ability to employ a fixed grid for the analysis to circumvent re-meshing and the availability of sensitivities to use robust and efficient gradient-based optimization methods. The conduit between the geometric representation of the supershapes and the fixed analysis discretization is, as in previous work, a differentiable geometry projection that maps the supershapes parameters onto a density field. The proposed approach is demonstrated on classical problems of 2-dimensional compliance-based topology optimization.

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Section: Long Cantilever Beammentioning

confidence: 99%

Section: Geometry Projectionmentioning

confidence: 99%

Section: Optimization Problemmentioning

confidence: 99%

“…Since the maximum function is not differentiable, we replace it with a lower-bound Kreisselmeier-Steinhauser (KS) approximation (as in Zhang et al 2017a):…”

Section: Geometry Projectionmentioning

confidence: 99%

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Topology optimization with supershapes

Norato

2018

Struct Multidisc Optim

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“…Several methods have recently been developed that utilize components, or voids, to parameterize the design (Guo et al 2014a;Zhang et al 2016aZhang et al , 2017a. These methods allow the exact position of the boundary to be known throughout the optimization.…”

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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A geometry projection method for the topology optimization of curved plate structures with placement bounds

Zhang

Gain

Norato

2018

Numerical Meth Engineering

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Summary Single‐curvature plates are commonly encountered in mechanical and civil structures. In this paper, we introduce a topology optimization method for the stiffness‐based design of structures made of curved plates with fixed thickness. The geometry of each curved plate is analytically and explicitly represented by its location, orientation, dimension, and curvature radius, and therefore, our method renders designs that are distinctly made of curved plates. To perform the primal and sensitivity analyses, we use the geometry projection method, which smoothly maps the analytical geometry of the curved plates onto a continuous density field defined over a fixed uniform finite element grid. A size variable is ascribed to each plate and penalized in the spirit of solid isotropic material with penalization, which allows the optimizer to remove a plate from the design. We also introduce in our method a constraint that ensures that no portion of a plate lies outside the design envelope. This prevents designs that would otherwise require cuts to the plates that may be very difficult to manufacture. We present numerical examples to demonstrate the validity and applicability of the proposed method.

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Stress-based topology optimization with discrete geometric components

Cited by 69 publications

References 24 publications

Topology optimization with supershapes

Topology optimization with supershapes

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

A geometry projection method for the topology optimization of curved plate structures with placement bounds

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