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== Abstract ==
Multiscale topological material design, aiming at obtaining optimal distribution of the material at several scales in structural materials is still a challenge. In this case, the cost function to be minimized is placed at the macro-scale (compliance function), but the design variables (material distribution) lie at both the macro-scale and the micro-scale. The large number of involved design variables and the multi-scale character of the analysis, resulting into a multiplicative cost of the optimization process, often make such approaches prohibitive, even if in 2D cases.
In this work, an integrated approach for multi-scale topological design of structural linear materials is proposed. The approach features the following properties:
The “topological derivative” is considered the basic mathematical tool to be used for the purposes of determining the sensitivity of the cost function to material removal. In conjunction with a level-set-based “algorithm” it provides a robust and well-founded setting for material distribution optimization.
The computational cost associated to the multiscale optimization problem is dramatically reduced by resorting to the concept of the online/offline decomposition of the computations. A “Computational Vademecum” containing the micro-scale solution for the topological optimization problem in a RVE for a large number of discrete macroscopic stress-states, is used for solving that problem by simple consultation.
Coupling of the optimization problem at both scales is solved by a simple iterative “fixedpoint” scheme, which is found to be robust and convergent.
The proposed technique is enriched by the concept of “manufacturability”, i.e.: obtaining sub-optimal solutions of the original problems displaying homogeneous material over finite sizes domains at the macrostructure: the “structural components”.
The approach is tested by application to some engineering examples, involving minimum compliance design of material and structure topologies, which show the capabilities of the proposed framework.
== Recording of the presentation ==
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|-
| {{#evt:service=youtube|id=https://youtu.be/6LAbAo5m5ZQ|alignment=center}}
|- style="text-align: center;"
| Location: Technical University of Catalonia (UPC), Vertex Building.
|- style="text-align: center;"
| Date: 1 - 3 September 2015, Barcelona, Spain.
|}
== General Information ==
* Location: Technical University of Catalonia (UPC), Barcelona, Spain.
* Date: 1 - 3 September 2015
* Secretariat: [//www.cimne.com/ International Center for Numerical Methods in Engineering (CIMNE)].
== External Links ==
* [//congress.cimne.com/complas2015/frontal/default.asp Complas XIII] Official Website of the Conference.
* [//www.cimnemultimediachannel.com/ CIMNE Multimedia Channel]
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Published on 07/06/16
Licence: CC BY-NC-SA license
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