A method using successive iteration of analysis and design for large-scale topology optimization considering eigenfrequencies

Kang, Zhan; He, Jingjie; Shi, Lin; Miao, Zhaohui

doi:10.1016/j.cma.2020.112847

Cited by 37 publications

(9 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a related work, dimension reduction is achieved by using mode superposition and Ritz vectors for topology optimization under dynamic responses 37 . Recently, Kang et al 38 presented a promising approximate method for eigenfrequency topology optimization where convergence of the eigensolver is not strictly enforced and is gradually refined with the progress of optimization.…”

Section: Introductionmentioning

confidence: 99%

Efficient stress‐constrained topology optimization using inexact design sensitivities

Amir

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

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

show abstract

Section: Introductionmentioning

confidence: 99%

Efficient stress‐constrained topology optimization using inexact design sensitivities

Amir

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Convergence to 0-1 designs was not achieved and the efficiency of the augmented Lagrangian solver needs to be investigated further, but the results are encouraging. Another encouraging result was presented by Kang et al (2020), who solved eignefrequency topology optimization without enforcing convergence of the eigensolver in each design iteration. The solution of the eigenproblem was gradually improved with the progress of optimization ś resembling the one-shot approach.…”

Section: Limitationsmentioning

confidence: 98%

One-shot procedures for efficient minimum compliance topology optimization

Amir

2023

Preprint

View full text Add to dashboard Cite

In this paper, a one-shot approach for minimum compliance topology optimization is investigated. In the convex case of variable thickness sheet optimization, an optimality criteria scheme with a single step of an iterative state solver converges to the same solutions as an accurate procedure. This remarkable behavior is explained by the crucial role of the geometric multigrid preconditioner, that generates accurate design sensitivities on a coarse scale. When applied to SIMP-based topology optimization, a one-shot procedure yields designs with the same primary load-transferring features as an accurate procedure. The difference is in the absence and presence of thin features that have a relatively minor impact on the objective. Several practical remedies are suggested that can close the small performance gaps between the one-shot procedure and an accurate one. The solution scheme is directly applicable to large-scale problems executed on parallel computers, allowing for significant computational savings.

show abstract

“…The involvement of more and more modes requires solving for more and more eigenvalues which is prohibitively expensive. Various approaches to resolve this issue have been investigated, also for similar dynamic problems [26,27,28]. For the buckling problem, however, a multilevel approach where the costly eigenvalue problem is only solved at the coarsest scale [29], promises reduced CPU times corresponding to solving much cheaper multiload linear problems, again paving the way for future applications in the giga-scale.…”

Section: Extended Summary With Referencesmentioning

confidence: 99%

EML webinar overview: Topology Optimization — Status and Perspectives

Sigmund

2020

Extreme Mechanics Letters

View full text Add to dashboard Cite

 Users may download and print one copy of any publication from the public portal for the purpose of private study or research.  You may not further distribute the material or use it for any profit-making activity or commercial gain  You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

show abstract

A method using successive iteration of analysis and design for large-scale topology optimization considering eigenfrequencies

Cited by 37 publications

References 59 publications

Efficient stress‐constrained topology optimization using inexact design sensitivities

Efficient stress‐constrained topology optimization using inexact design sensitivities

One-shot procedures for efficient minimum compliance topology optimization

EML webinar overview: Topology Optimization — Status and Perspectives

Contact Info

Product

Resources

About