Applying functional principal components to structural topology optimization

Alaimo, Gianluca; Auricchio, Ferdinando; Bianchini, Ilaria; Lanzarone, Ettore

doi:10.1002/nme.5801

Cited by 9 publications

(11 citation statements)

References 43 publications

(77 reference statements)

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“…The idea behind the use of FCPA in STO is to solve the equilibrium (2) in a reduced space for as many gradientbased iterations as possible. Such a reduced space, whose dimension is given by a limited number of principal displacement components, is generated by applying FPCA to a set of previously obtained solutions (Alaimo et al 2018;Bianchini et al 2015).…”

Section: Fpca For Reduced Modelmentioning

confidence: 99%

“…On the other hand, however, their bottleneck is the computational effort, as they require solving FEA a large number of times. For example, in a minimum compliance problem, up to 97% of the total computational time could be spent for numerically solving the equilibrium equations (Alaimo et al 2018;Petersson 1999).…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we propose and test a reduced basis method that relies on functional PCA (FPCA). FPCA for FEA is quite new in STO since it has only been exploited for the variable thickness sheet design problem in combination with a simulated annealing optimization heuristic (Alaimo et al 2018); moreover, it was initially developed for uncertainty quantification (Bianchini et al 2015). We extend the use of FPCA in STO by applying it to the class of gradientbased optimization methods, which are the most commonly used.…”

Section: Introductionmentioning

confidence: 99%

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A gradient-based optimization method with functional principal component analysis for efficient structural topology optimization

Montanino

Alaimo

Lanzarone

2021

Struct Multidisc Optim

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Structural topology optimization (STO) is usually treated as a constrained minimization problem, which is iteratively addressed by solving the equilibrium equations for the problem under consideration. To reduce the computational effort, several reduced basis approaches that solve the equilibrium equations in a reduced space have been proposed. In this work, we apply functional principal component analysis (FPCA) to generate the reduced basis, and we couple FPCA with a gradient-based optimization method for the first time in the literature. The proposed algorithm has been tested on a large STO problem with 4.8 million degrees of freedom. Results show that the proposed algorithm achieves significant computational time savings with negligible loss of accuracy. Indeed, the density maps obtained with the proposed algorithm capture the larger features of maps obtained without reduced basis, but in significantly lower computational times, and are associated with similar values of the minimized compliance.

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Section: Fpca For Reduced Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A gradient-based optimization method with functional principal component analysis for efficient structural topology optimization

Montanino

Alaimo

Lanzarone

2021

Struct Multidisc Optim

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“…Indeed, the approach allows to construct an optimal basis of the solutions space and to project the full FEA problem into a smaller space spanned by this basis. The same approach was also used to reduce the computational effort of iterative optimization algorithms for STO [32].…”

Section: Prediction Models To Identify Patient-specific Functional Prmentioning

confidence: 99%

“…Finally, considering the reduced basis approach to solve FEA problems in the presence of uncertain parameters [31] or for STO [32], results are promising. We assessed the applicability of the proposed approach on several test cases, obtaining satisfactory results.…”

Section: Prediction Modelsmentioning

confidence: 99%

Hospital Factory for Manufacturing Customised, Patient-Specific 3D Anatomo-Functional Models and Prostheses

Lanzarone

Marconi

Conti

et al. 2019

Factories of the Future

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The fabrication of personalised prostheses tailored on each patient is one of the major needs and key issues for the future of several surgical specialties. Moreover, the production of patient-specific anatomo-functional models for preoperative planning is an important requirement in the presence of tailored prostheses, as also the surgical treatment must be optimised for each patient. The presence of a prototyping service inside the hospital would be a benefit for the clinical activity, as its location would allow a closer interaction with clinicians, leading to significant time and cost reductions. However, at present, these services are extremely rare worldwide. Based on these considerations, we investigate enhanced methods and technologies for implementing such a service. Moreover, we analyse the sustainability of the service and, thanks to the development of two prototypes, we show the feasibility of the production inside the hospital.

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Efficient stress‐constrained topology optimization using inexact design sensitivities

Amir

2021

Numerical Meth Engineering

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An efficient computational approach to stress‐constrained topology optimization is presented. Using a multigrid‐preconditioned Krylov solver for the state and adjoint problems, the number of Krylov iterations is reduced significantly by enforcing early termination of the iterative solves. The criterion for early termination is based on the convergence of the design sensitivities with respect to Krylov iterations. Consequently, the progress of optimization is not affected by the inexact resolution of the state and adjoint problems. The proposed approach is demonstrated on several design problems that possess different characteristics of the maximum stress. Optimization results obtained with early termination show very good agreement with those obtained with an accurate direct solver—in terms of objective value, constrained maximum stress and overall number of design cycles. Savings of 80% in the number of Krylov iterations are achieved, compared to the number of iterations required to satisfy the force residual convergence criterion to a common tolerance. The approach is directly applicable to high‐resolution problems that are solved on parallel computational environments. A MATLAB code for reproducing the results is freely available at https://github.com/odedamir/topopt-stress-inexact-sensitivities

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Applying functional principal components to structural topology optimization

Cited by 9 publications

References 43 publications

A gradient-based optimization method with functional principal component analysis for efficient structural topology optimization

A gradient-based optimization method with functional principal component analysis for efficient structural topology optimization

Hospital Factory for Manufacturing Customised, Patient-Specific 3D Anatomo-Functional Models and Prostheses

Efficient stress‐constrained topology optimization using inexact design sensitivities

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