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==1 Title, abstract and keywords==
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== Abstract ==
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Multiscale topological material design, aiming at obtaining optimal distribution of the material at
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several scales in structural materials is still a challenge. In this case, the cost function to be
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minimized is placed at the macro-scale (compliance function)  [<span id='cite-1'></span>[[#1|1]]], but the design variables (material
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distribution) lie at both the macro-scale and the micro-scale  [<span id='cite-2'></span>[[#2|2]]]. The large number of involved design
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variables and the multi-scale character of the analysis, resulting into a multiplicative cost of the
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optimization process, often make such approaches prohibitive, even if in 2D cases.
  
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Your paper should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.
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In this work, an integrated approach for multi-scale topological design of structural linear materials is proposed. The approach features the following properties:
  
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Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.
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- The “topological derivative” is considered the basic mathematical tool to be used for the
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purposes of determining the sensitivity of the cost function to material removal  [<span id='cite-3'></span>[[#3|3]]]. In
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conjunction with a level-set-based “algorithm”  [<span id='cite-4'></span>[[#4|4]]] it provides a robust and well-founded
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setting for material distribution optimization  [<span id='cite-5'></span>[[#5|5]]].
  
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An abstract is required for every paper; it should succinctly summarize the reason for the work, the main findings, and the conclusions of the study. Abstract is often presented separately from the article, so it must be able to stand alone. For this reason, references and hyperlinks should be avoided. If references are essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself.
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- 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.
  
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==2 The main text==
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- Coupling of the optimization problem at both scales is solved by a simple iterative “fixedpoint” scheme, which is found to be robust and convergent.
  
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- 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”.
  
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Most of the papers in Scipedia are written in English (write your manuscript in American or British English, but not a mixture of these). Anyhow, specific journals in other languages can be published in Scipedia. In any case, the documents published in other languages must have an abstract written in English.
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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.
  
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===2.1 Subsections===
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== Recording of the presentation ==
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{| style="font-size:120%; color: #222222; border: 1px solid darkgray; background: #f3f3f3; table-layout: fixed; width:100%;"
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Divide your article into clearly defined and numbered sections. Subsections should be numbered 1.1, 1.2, etc. and then 1.1.1, 1.1.2, ... Use this numbering also for internal cross-referencing: do not just refer to 'the text'. Any subsection may be given a brief heading. Capitalize the first word of the headings.
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===2.2 General guidelines===
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|- style="text-align: center;"  
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| Location: Technical University of Catalonia (UPC), Vertex Building.  
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Some general guidelines that should be followed in your manuscripts are:
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| Date: 1 - 3 September 2015, Barcelona, Spain.
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Please insert tables as editable text and not as images. Tables should be placed next to the relevant text in the article. Number tables consecutively in accordance with their appearance in the text (<span id='cite-_Ref382560620'></span>[[#_Ref382560620|table 1]], table 2, etc.) and place any table notes below the table body. Be sparing in the use of tables and ensure that the data presented in them do not duplicate results described elsewhere in the article.
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{| style="margin: 1em auto 1em auto;border: 1pt solid black;border-collapse: collapse;"
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| style="text-align: center;"|Thickness
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| style="text-align: center;"|3.175 mm
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| style="text-align: center;"|Young Modulus
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| style="text-align: center;"|12.74 MPa
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| style="text-align: center;"|Poisson coefficient
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| style="text-align: center;"|0.25
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| style="text-align: center;"|1107 kg/m<sup>3</sup>
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<span style="text-align: center; font-size: 75%;">Table 1: Material properties</span></div>
 
  
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Graphics may be inserted directly in the document and positioned as they should appear in the final manuscript.
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== General Information ==
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* Location: Technical University of Catalonia (UPC), Barcelona, Spain.
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* Date: 1 - 3 September 2015
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Supplementary material can be inserted to support and enhance your article. This includes video material, animation sequences, background datasets, computational models, sound clips and more. In order to ensure that your material is directly usable, please provide the files with a preferred maximum size of 50 MB. Please supply a concise and descriptive caption for each file.
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Citations in text will follow a citation-sequence system (i.e. sources are numbered by order of reference so that the first reference cited in the paper is [<span id='cite-1'></span>[[#1|1]]], the second [<span id='cite-2'></span>[[#2|2]]], and so on) with the number of the reference in square brackets. Once a source has been cited, the same number is used in all subsequent references. If the numbers are not in a continuous sequence, use commas (with no spaces) between numbers. If you have more than two numbers in a continuous sequence, use the first and last number of the sequence joined by a hyphen (e.g. [<span id='cite-1'></span>[[#1|1]], <span id='cite-3'></span>[[#3|3]]] or [<span id='cite-2'></span>[[#2|2]]-<span id='cite-2'></span>[[#4|4]]]).
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[[#cite-1|[1]]] Author, A. and Author, B. (Year) Title of the article. Title of the Journal. Article code. Available: [http://www.scipedia.com/ucode. http://www.scipedia.com/ucode.]
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[[#cite-1|[1]]] M. Bendsoe, O. Sigmund. Topology Optimization. Theory, Methods, and Applications,
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Springer Verlag, New York (2003).
 
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[[#cite-2|[2]]] Kato, J., Yachi, D., Terada, K., Kyoya, T. Topology optimization of micro-structure for
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composites applying a decoupling multi-scale analysis. Structural Multidisciplinary
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Optimization 49:595–608 (2014).
 
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[[#cite-3|[3]]] Amstutz, S., Giusti, S. M., Novotny, A. A. and de Souza Neto, E. A.), Topological derivative
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for multi-scale linear elasticity models applied to the synthesis of micro-structures. Int. J.
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Numer. Meth. Engng., 84: 733–756. doi: 10.1002/nme.2922, (2010).
 
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[[#cite-4|[4]]] Allaire, G., Jouve, F., Toader, A.-M. Structural optimization using sensitivity analysis and a
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level-set method, Journal of Computational Physics, 194 (1), pp. 363-393, (2004).
 
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[[#cite-5|[5]]] Author, E. (Year, Month date). Title of the article. In A. Editor, B. Editor, and C. Editor. Title of published proceedings. Paper presented at title of conference, Volume number, first page-last page. Place of publication.
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[[#cite-5|[5]]] Ferrer A., Cante, J.C., Oliver J., On multi-scale structural topology optimization and material
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design, Proc. of the Congress on Numerical Methods in Engineering (CMA_2015), Lisboa
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2015.
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[[#cite-6|[6]]] Institution or author. Title of the document. Year. [Online] (Date consulted: day, month and year). Available: [http://www.scipedia.com/document.pdf http://www.scipedia.com/document.pdf]. [Accessed day, month and year].
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Latest revision as of 11:39, 19 July 2016

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) [1], but the design variables (material distribution) lie at both the macro-scale and the micro-scale [2]. 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 [3]. In conjunction with a level-set-based “algorithm” [4] it provides a robust and well-founded setting for material distribution optimization [5].

- 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

Location: Technical University of Catalonia (UPC), Vertex Building.
Date: 1 - 3 September 2015, Barcelona, Spain.

General Information

External Links

References

[1] M. Bendsoe, O. Sigmund. Topology Optimization. Theory, Methods, and Applications, Springer Verlag, New York (2003).

[2] Kato, J., Yachi, D., Terada, K., Kyoya, T. Topology optimization of micro-structure for composites applying a decoupling multi-scale analysis. Structural Multidisciplinary Optimization 49:595–608 (2014).

[3] Amstutz, S., Giusti, S. M., Novotny, A. A. and de Souza Neto, E. A.), Topological derivative for multi-scale linear elasticity models applied to the synthesis of micro-structures. Int. J. Numer. Meth. Engng., 84: 733–756. doi: 10.1002/nme.2922, (2010).

[4] Allaire, G., Jouve, F., Toader, A.-M. Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, 194 (1), pp. 363-393, (2004).

[5] Ferrer A., Cante, J.C., Oliver J., On multi-scale structural topology optimization and material design, Proc. of the Congress on Numerical Methods in Engineering (CMA_2015), Lisboa 2015.

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