Multi-material thermomechanical topology optimization with applications to additive manufacturing: Design of main composite part and its support structure

Giraldo-Londoño, Oliver; Mirabella, Lucia; Dalloro, Livio; Paulino, Gláucio H.

doi:10.1016/j.cma.2019.112812

Cited by 54 publications

(13 citation statements)

References 49 publications

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“…For example, it could be extended to topology optimization with material selection, specifically using the NN framework proposed in [35]. Furthermore, inclusion of thermo-elastic properties [36], auxetic properties [37], coating properties [38], global warming indices [13] can also be considered. Inclusion of uncertainty in material properties is also of significant interest.…”

Section: Discussionmentioning

confidence: 99%

Integrating Material Selection with Design Optimization via Neural Networks

Chandrasekhar¹,

Sridhara²,

Suresh³

2021

Preprint

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The engineering design process often entails optimizing the underlying geometry while simultaneously selecting a suitable material. For a certain class of simple problems, the two are separable where, for example, one can first select an optimal material, and then optimize the geometry. However, in general, the two are not separable. Furthermore, the discrete nature of material selection is not compatible with gradient-based geometry optimization, making simultaneous optimization challenging. In this paper, we propose the use of variational autoencoders (VAE) for simultaneous optimization. First, a data-driven VAE is used to project the discrete material database onto a continuous and differentiable latent space. This is then coupled with a fully-connected neural network, embedded with a finite-element solver, to simultaneously optimize the material and geometry. The neuralnetwork's built-in gradient optimizer and back-propagation are exploited during optimization. The proposed framework is demonstrated using trusses, where an optimal material needs to be chosen from a database, while simultaneously optimizing the cross-sectional areas of the truss members.Several numerical examples illustrate the efficacy of the proposed framework. The Python code used in these experiments is available at github.com/UW-ERSL/MaTruss

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Section: Discussionmentioning

confidence: 99%

Integrating Material Selection with Design Optimization via Neural Networks

Chandrasekhar¹,

Sridhara²,

Suresh³

2021

Preprint

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“…4 is the sum of a constant term that can be neglected for optimization, a monotonically decreasing convex function in exponential intermediate variables, ξ ℓi ( z ℓi ) = z ℓi −α , α > 0 , and a monotonically (linearly) increasing function. For decomposition of the objective gradient, we adopt the scheme proposed in (70), which uses approximate second-order information to account for the curvature of the objective function such that the negative and positive components, respectively, are…”

Section: Gradient-based Solution Schemementioning

confidence: 99%

“…Since the derivatives of the objective function in Eq. 1 may become positive in regions of material mixing (62,63), we integrate sensitivity separation into the ZPR update scheme (70,71) by decomposing the objective function gradient into positive and negative components to arrive at the following nonmonotonic, convex approximation of the objective function…”

Section: Gradient-based Solution Schemementioning

confidence: 99%

Optimal and continuous multilattice embedding

2021

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Because of increased geometric freedom at a widening range of length scales and access to a growing material space, additive manufacturing has spurred renewed interest in topology optimization of parts with spatially varying material properties and structural hierarchy. Simultaneously, a surge of micro/nanoarchitected materials have been demonstrated. Nevertheless, multiscale design and micro/nanoscale additive manufacturing have yet to be sufficiently integrated to achieve free-form, multiscale, biomimetic structures. We unify design and manufacturing of spatially varying, hierarchical structures through a multimicrostructure topology optimization formulation with continuous multimicrostructure embedding. The approach leads to an optimized layout of multiple microstructural materials within an optimized macrostructure geometry, manufactured with continuously graded interfaces. To make the process modular and controllable and to avoid prohibitively expensive surface representations, we embed the microstructures directly into the 3D printer slices. The ideas provide a critical, interdisciplinary link at the convergence of material and structure in optimal design and manufacturing.

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“…With small modifications, we could define a new set of arithmetic properties, providing a base material for computer implementations. Moreover, even after introducing 𝛿 klb , we kept the consistency of the indexes according to the definition of diagonal hyper-dual numbers, presented in Equations ( 14)- (16).…”

Section: C1 Arithmeticmentioning

confidence: 99%

“…Ordinary numerical procedures, such as the finite difference approximation using real numbers, intrinsically introduce errors, which might affect the convergence behavior. Giraldo-Londoño et al 16 and Andrei 17 obtained an approximation of the diagonal of the Hessian using Broyden-Fletcher-Goldfarb-Shanno algorithm and finite difference method, respectively. Other differentiation methods using complex 18,19 and dual numbers 20 have been considered as an alternative to obtain accurate results; however, these methods are limited to calculate first-order derivatives.…”

Section: Introductionmentioning

confidence: 99%

Second‐order design sensitivity analysis using diagonal hyper‐dual numbers

Endo

Fancello

Muñoz-Rojas

2021

Numerical Meth Engineering

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Although sensitivity analysis provides valuable information for structural optimization, it is often difficult to use the Hessian in large models since many methods still suffer from inaccuracy, inefficiency, or limitation issues. In this context, we report the theoretical description of a general sensitivity procedure that calculates the diagonal terms of the Hessian matrix by using a new variant of hyper‐dual numbers as derivative tool. We develop a diagonal variant of hyper‐dual numbers and their arithmetic to obtain the exact derivatives of tensor‐valued functions of a vector argument, which comprise the main contributions of this work. As this differentiation scheme represents a general black‐box tool, we supply the computer implementation of the hyper‐dual formulation in Fortran. By focusing on the diagonal terms, the proposed sensitivity scheme is significantly lighter in terms of computational costs, facilitating the application in engineering problems. As an additional strategy to improve efficiency, we highlight that we perform the derivative calculation at the element‐level. This work can contribute to many studies since the sensitivity scheme can adapt itself to numerous finite element formulations or problem settings. The proposed method promotes the usage of second‐order optimization algorithms, which may allow better convergence rates to solve intricate problems in engineering applications.

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Multi-material thermomechanical topology optimization with applications to additive manufacturing: Design of main composite part and its support structure

Cited by 54 publications

References 49 publications

Integrating Material Selection with Design Optimization via Neural Networks

Integrating Material Selection with Design Optimization via Neural Networks

Optimal and continuous multilattice embedding

Second‐order design sensitivity analysis using diagonal hyper‐dual numbers

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