Multi-Material Topology Optimization as a Concept Generation and Design Tool

Vierhout, Garrett; Roper, Stephen; Li, Daozhong; Pamwar, Manish; Sangha, Balbir; Kim, Il Yong

doi:10.4271/2019-01-1095

Cited by 13 publications

(6 citation statements)

References 17 publications

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“…where 1 E , 2 E , 12 G are the longitudinal, transverse and shear moduli, respectively, and 12  and 21  are the Poisson's ratio.…”

Section: B Lamination Parametersmentioning

confidence: 99%

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Simultaneous Topology And Composite Lay-Up Optimization

Bohrer¹,

Kim²

2021

Progress in Canadian Mechanical Engineering. Volume 4

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With the advances in manufacturing and design methods, engineers have been constantly pushed to improve mechanical components performance by minimizing part weight, maximize stiffness and optimize material usage. Tools such as topology optimization has been widely used to support the development of new components. While the optimization process for metallic components is well stablished, composite materials optimization still possess challenges to designers, especially due to the plies stacking sequence definition. The recent advances in 3D printed composite additive manufacturing have brought a new alternative to the composite manufacturing adding geometric freedom and challenges on the definition of the optimum material layout and lay-up. Thus, this paper expands upon existing mathematical methods by providing an algorithm to simultaneously minimizing the material distribution and the laminate stacking sequence of composite plates. Lamination parameters are used as design variables to optimize the laminate stacking sequence avoiding local optimum solutions and reducing the number of designable variables. Once the optimum topology and set of lamination parameters are defined, angle retrieval is performed to define the optimum plies orientation. Two problem examples are solved to illustrate the applicability of this approach.

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“…where 1 E , 2 E , 12 G are the longitudinal, transverse and shear moduli, respectively, and 12  and 21  are the Poisson's ratio.…”

Section: B Lamination Parametersmentioning

confidence: 99%

“…Topology optimization (TO) has been reported by many authors as a method to generate unconventional load paths [9][10][11][12]. TO was used by [13], for instance, in the conceptual design of an automotive engine cradle showing significant mass reduction results.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Topology And Composite Lay-Up Optimization

Bohrer¹,

Kim²

2021

Progress in Canadian Mechanical Engineering. Volume 4

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“…Equation (14) presents the compliance sensitivities, where ∼ is the element strain energy vector. Equation 15provides the sensitivity of the interpolated elastic modulus (shown in (4)) with respect to the pseudo-density,…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…With MMTO, the added design freedom always yields TO results of similar or superior performance compared to the standard SMTO using SIMP. Several researchers verified this by comparing the performance of SMTO and MMTO for industry problems 3,13‐16 . For the MMTO method described above, M − 1 design vectors are required to solve an M phase MMTO problem, which includes one void phase; or m design vectors for an m material MMTO problem.…”

Section: Introductionmentioning

confidence: 97%

“…Several researchers verified this by comparing the performance of SMTO and MMTO for industry problems. 3,[13][14][15][16] For the MMTO method described above, M − 1 design vectors are required to solve an M phase MMTO problem, which includes one void phase; or m design vectors for an m material MMTO problem. The size of each design vector is equal to the total number of finite elements in the model, n. Thus, the total number of design variables in an m material MMTO are equal to the product of m design vectors and n finite elements.…”

Section: Introductionmentioning

confidence: 99%

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Material interface control in multi‐material topology optimization using pseudo‐cost domain method

Shah

Pamwar

Sangha

et al. 2020

Numerical Meth Engineering

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The recent drive for producing lightweight and high performance designs on reduced timelines has promoted the need for computational design generation tools such as Multi-Material Topology Optimization (MMTO). However, MMTO has drawn some industry skepticism as it assumes different material elements to be perfectly fused together. To address this concern, in this article, a novel pseudo-cost domain (PCD) method is proposed which mathematically determines individual material interfaces in MMTO solutions. The proposed methodology employs a user defined joint cost model to weigh the distinct material interfaces relative to each other. An innovative approach to tailor the MMTO design considering the relative cost of each material interface is presented. The proposed methodology can consider any number of materials and their respective interfaces, and it is defined in such a way that increasing the number of materials has minimal effect on computational time. The methodology is formulated in a smooth and differentiable manner and the sensitivity expressions required by gradient-based optimization solvers are presented. A series of example problems are provided to demonstrate the efficacy of the proposed methodology.

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