Goal‐oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis

Ju, Xiaozhe; Mahnken, Rolf

doi:10.1002/nme.5996

Cited by 2 publications

(4 citation statements)

References 41 publications

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“…Here, z h is the FE solution of the approximate dual problem (C2), which is not directly useful for the error representation (44) due to the Galerkin orthogonality. For this reason, we use, in this work, a patch recovery approach developed in our previous works 61,63 to construct an approximate solution of…”

Section: B4 Interaction Direct Derivativementioning

confidence: 99%

“…In this manner, the load term

\overset{F}{true}

can be equivalently replaced by the second term in Equation , which can be easily localized into its element contributions. For a numerical efficiency, the patch recovery can be used to approximate the enhanced primal problem in a similar manner as for the enhanced dual solution

{\overset{bold-italicz}{true}}_{h^{+}}

in Appendix C.…”

Section: Goal‐oriented Adaptivity On the Macroscalementioning

confidence: 99%

“…[48][49][50][51] For applications to multiscale problems, we refer to related works. 39,40,44,47,52,53 The issue of numerical verification is addressed by the adaptive FEM, which is developed to estimate and adaptively control the discretization error, see, eg, other works [54][55][56][57][58][59] for the general framework of a posteriori error estimate and some related works [48][49][50][51][60][61][62] for goal-oriented error estimate.…”

Section: Introductionmentioning

confidence: 99%

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Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity

Mahnken

2019

Numerical Meth Engineering

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Summary Homogenization methods are drawing increasing attention for simulation of heterogeneous materials like composites. For balancing the accuracy and the numerical efficiency of such strategies, we deal with both model and discretization errors of the finite element method (FEM) on a macroscale. Within a framework of goal‐oriented adaptivity, we consider linear elastic heterogeneous materials, for which first‐order homogenization schemes apply. A novel model hierarchy is proposed based on mean‐field and full‐field homogenization methods. For the former, we consider several well‐established schemes like Mori‐Tanaka or self‐consistent as basic models, and for the latter, as superior models, unit cell problems are solved via the FEM under an a priori chosen boundary condition. For a further stage of the model hierarchy, we consider hierarchical unit cells within the frame of the FEM toward an adaptive selection of the unit cell size. By means of several numerical examples, we illustrate the effectiveness of the proposed adaptive approach.

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Section: B4 Interaction Direct Derivativementioning

confidence: 99%

“…In this manner, the load term

\overset{F}{true}

{\overset{bold-italicz}{true}}_{h^{+}}

in Appendix C.…”

Section: Goal‐oriented Adaptivity On the Macroscalementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity

Mahnken

2019

Numerical Meth Engineering

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“…In the actual application process, the main incongruous actuator group behaviors are as follows: When a symmetrical flatness defect is detected by shapemeter roll, the work roll tilting may participate in the flatness regulating process [7][8][9]. However, the additional flatness change is caused by work roll tilting, which will consume the regulating margin of other actuators in the flatness closed-loop control system [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Collaboration Strategy Based on Conflict Resolution for Flatness Actuator Group

Yan

Wang

et al. 2021

Mathematical Problems in Engineering

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During the flatness control process, there are frequently some uncoordinated regulating behaviors in the flatness actuator group. This has a bad influence on the flatness control accuracy and the flatness control efficiency. Therefore, a collaboration strategy based on conflict resolution for the flatness actuator group has been proposed in this paper. First of all, the feature of flatness measurement value is extracted through establishing the actual flatness condition discriminating factor. After that, the coordination cooperation that is appropriate to the actual flatness condition is developed for the flatness actuator group. Finally, the optimal adjustment of the actuator population is solved by the coordinated algorithm of Topkis-Veinott and genetic algorithm collaborative optimization. The collaboration strategy proposed in this paper has been successfully applied to a flatness control system of a 1450 mm five-stand cold rolling mill.

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Goal‐oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis

Cited by 2 publications

References 41 publications

Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity

Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity

Collaboration Strategy Based on Conflict Resolution for Flatness Actuator Group

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