On the approximate reanalysis technique in topology optimization

Senne, Thadeu A.; Gomes, Francisco A. M.; Santos, Sandra A.

doi:10.1007/s11081-018-9408-3

Cited by 17 publications

(11 citation statements)

References 19 publications

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“…One of the earliest contributions in this direction was provided by Wang et al 28 who recycled Krylov subspaces, thus exploiting the small changes between subsequent linear systems. Later on, Kirsch's approximate reanalysis methodology 29,30 was integrated into topology optimization for minimum compliance 31,32 . It should be noted that Kirsch's Combined Approximations (CA) is essentially a reduced basis method where the basis vectors are constructed using previous (in the sense of optimization cycles) stiffness matrices.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Efficient stress‐constrained topology optimization using inexact design sensitivities

Amir

2021

Numerical Meth Engineering

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“…For instance, Fujii et al (2018) demonstrated the robustness of their topology optimization method based on a covariance matrix adaptation evolution strategy against the choice of the initial guess. One of the main arguments against using evolutionary methods is that it tends to take more iterations to arrive at a solution; however, recent works on approximate reanalysis of structures could be of help (Senne et al, 2019).…”

Section: Challenges and Recent Trendsmentioning

confidence: 99%

Revisiting non-convexity in topology optimization of compliance minimization problems

Abdelhamid

Czekanski

2021

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Purpose This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods. Design/methodology/approach Starting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum. Findings The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application. Originality/value In this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

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“…Our approach rests upon a sequential piecewise linear programming (SPLP) algorithm [16] that, aside from having a stopping criterion with theoretical support, has proven to be efficient and robust. In a previous work [28], the approximate reanalysis technique has been applied in combination with the SPLP algorithm to solve three benchmark structure problems under small displacements. In the current work, besides addressing two structures, we have also applied the devised strategies to the design of two mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Inexact Newton combined approximations in the topology optimization of geometrically nonlinear elastic structures and compliant mechanisms

Senne¹,

Gomes²,

Santos³

2021

Preprint

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This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a sequential piecewise linear programming (SPLP) algorithm. Five distinct strategies have been proposed to control the frequency of the factorizations of the Jacobian matrices of the nonlinear equilibrium equations. Aiming at speeding up the overall iterative scheme while keeping the accuracy of the approximate solutions, three of the strategies also use an ICA scheme for the adjoint linear system associated with the sensitivity analysis. The robustness of the proposed reanalysis strategies is corroborated by means of numerical experiments with four benchmark problems -two structures and two compliant mechanisms. Besides assessing the performance of the strategies considering a fixed budget of iterations, the impact of a theoretically supported stopping criterion for the SPLP algorithm was analyzed as well.

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On the approximate reanalysis technique in topology optimization

Cited by 17 publications

References 19 publications

Efficient stress‐constrained topology optimization using inexact design sensitivities

Efficient stress‐constrained topology optimization using inexact design sensitivities

Revisiting non-convexity in topology optimization of compliance minimization problems

Inexact Newton combined approximations in the topology optimization of geometrically nonlinear elastic structures and compliant mechanisms

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