Simultaneous optimisation of structural topology and material grading using level set method

Dunning, Peter D.; Brampton, Christopher J.; Kim, Hyunsun

doi:10.1179/1743284715y.0000000022

Cited by 18 publications

(7 citation statements)

References 48 publications

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“…It has been applied to optimize structure and material simultaneously. For example, structural topology and material selection have been simultaneously optimized by designing the material phase (Sigmund 2001;Wang and Wang 2004), or the continuous grading between two materials (Dunning et al 2015;Sigmund and Torquato 1997). Topology optimization has also been combined with the design of layered fiber composite material (De Leon et al 2012;Lund 2009;Peeters et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Simultaneous material and structural optimization by multiscale topology optimization

Sivapuram

Dunning

Kim

2016

Struct Multidisc Optim

256

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This paper introduces a new approach to multiscale optimization, where design optimization is applied at two scales: the macroscale, where the structure is optimized, and the microscale, where the material is optimized. Thus, structure and material are optimized simultaneously. We approach multiscale design optimization by linearizing and formulating a new way to decompose into macro and microscale design problems in such a way that solving the decomposed problems separately lead to an overall optimum solution. In addition, the macro and microstructural designs are coupled tightly through homogenization and inverse homogenization. This approach is generic in that it allows any number of unique microstructures and can be applied to a wide range of design problems. An advantage of decomposing the problem in this physical way is that it is potentially straight forward to specify additional design requirements at a specific scale or in specific regions of the design domain. The decomposition approach also allows an easy parallelization of the computational methodology and this enables the computational time to be maintained at a practical level. We demonstrate the proposed approach using the level-set topology optimization at both scales, i.e. macrostructural topological design and microstructural topology of architected material. A series of optimization problems, minimizing compliance and compliant mechanism are solved for verification and investigation of potential benefits.

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Section: Introductionmentioning

confidence: 99%

Simultaneous material and structural optimization by multiscale topology optimization

Sivapuram

Dunning

Kim

2016

Struct Multidisc Optim

256

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“…Another point worth mentioning is that producing part in functionally graded material is enabled by AM and there are different topology optimization approaches readily designing this type of structures [160][161][162][163][164].…”

Section: Multi-materials Topology Optimizationmentioning

confidence: 99%

Current and future trends in topology optimization for additive manufacturing

Liu

Gaynor

Chen

et al. 2018

Struct Multidisc Optim

659

249

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Manufacturing-oriented topology optimization has been extensively studied the past two decades, in particular for the conventional manufacturing methods, e.g., machining and injection molding or casting. Both design and manufacturing engineers have benefited from these efforts because of the close-tooptimal and friendly-to-manufacture design solutions. Recently, additive manufacturing (AM) has received significant attention from both academia and industry. AM is characterized by producing geometrically complex components layer-by-layer, and greatly reduces the geometric complexity restrictions imposed on topology optimization by conventional manufacturing. In other words, AM can make near-full use of the freeform structural evolution of topology optimization. Even so, new rules and restrictions emerge due to the diverse and intricate AM processes, which should be carefully addressed when developing the AM-specific topology optimization algorithms. Therefore, the motivation of this perspective paper is to summarize the state-of-art topology optimization methods for a variety of AM topics. At the same time, this paper also expresses the authors' perspectives on the challenges and opportunities in these topics. The hope is to inspire both researchers and engineers to meet these challenges with innovative solutions.

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“…An elegant alternative is the introduction of microstructures that are continuously graded in space-analogous to the transition from classical multimaterial topology optimization defining a unique material at each point (e.g., Refs. [52][53][54]) to a continuous grading of materials [55]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Topology Optimization of Graded Truss Lattices Based on On-the-Fly Homogenization

Telgen

Sigmund

Kochmann

2022

Journal of Applied Mechanics

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We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order homogenization approach, which replaces the discrete truss by an effective continuum description to be treated by finite elements in a macroscale boundary value problem. By defining the local truss architecture through a set of Bravais vectors, we formulate the optimization problem with regards to the spatially varying basis vectors and demonstrate its feasibility and performance through a series of benchmark problems in 2D (though the method is sufficiently general to also apply in 3D, as discussed). Both the displacement field and the topology are continuously varying unknown fields on the macroscale, and a regularization is included for well-posedness. We argue that prior solutions obtained from aligning trusses along the directions of principal stresses are included as a special case. The outlined approach results in heterogeneous truss architectures with a smoothly varying unit cell, enabling easy fabrication with a tunable length scale (the latter avoiding the ill-posedness stemming from classical nonconvex methods without an intrinsic length scale).

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Simultaneous optimisation of structural topology and material grading using level set method

Cited by 18 publications

References 48 publications

Simultaneous material and structural optimization by multiscale topology optimization

Simultaneous material and structural optimization by multiscale topology optimization

Current and future trends in topology optimization for additive manufacturing

Topology Optimization of Graded Truss Lattices Based on On-the-Fly Homogenization

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