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V.H. Yanes Francisco¹ and F.J. Montans Leal^1,2

¹Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Polotécnica de Madrid, Spain
²Department of Mechanical and Aerospace Engineering, University of Florida, Florida, USA

doi:10.4203/ccc.9.2.1

V.H. Yanes Francisco, F.J. Montans Leal, "Computational Procedure for Finite Element Analysis of Functionally Graded Metamaterials", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 9, Paper 2.1, 2024, doi:10.4203/ccc.9.2.1

Keywords: finite element analysis, metamaterials, hierarchical functions, numerical optimization, computational mechanics, macroelement techniques, structural analysis.

Abstract

The extremely fine meshes needed to run problems with details on two scales have promoted several computational homogenization techniques. However, these techniques typically require periodicity of the deformations and the separation of scales. In functionally graded metamaterials, two scales become relevant, but since every metamaterial cell may differ slightly from the neighboring ones, neither the separation of scales nor periodicity conditions may be assumed to hold. Nevertheless, the fact that every metamaterial cell differs only slightly and that we are typically concerned with the global behavior may be considered to speed up the computational procedure. This paper introduces a novel method specifically designed for metamaterials to address these challenges by structuring the metamaterial in macroelements, the stiffness matrix of elements being reduced prior to assembling in the global matrix. The advantage is taken from the fact that macroelement matrices differ only in a few terms. This strategy significantly improves computational efficiency, enabling the handling of very large meshed structures in metamaterials with improved performance compared to conventional FEA techniques.

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Front Page Browse CCC CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Conferences ISSN 2753-3239 CCC: 9 PROCEEDINGS OF THE FIFTEENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: P. Iványi, J. Kruis and B.H.V. Topping Paper 2.1 Computational Procedure for Finite Element Analysis of Functionally Graded Metamaterials V.H. Yanes Francisco¹ and F.J. Montans Leal^1,2 ¹Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Polotécnica de Madrid, Spain ²Department of Mechanical and Aerospace Engineering, University of Florida, Florida, USA doi:10.4203/ccc.9.2.1 Full Bibliographic Reference for this paper V.H. Yanes Francisco, F.J. Montans Leal, "Computational Procedure for Finite Element Analysis of Functionally Graded Metamaterials", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 9, Paper 2.1, 2024, doi:10.4203/ccc.9.2.1 Keywords: finite element analysis, metamaterials, hierarchical functions, numerical optimization, computational mechanics, macroelement techniques, structural analysis. Abstract The extremely fine meshes needed to run problems with details on two scales have promoted several computational homogenization techniques. However, these techniques typically require periodicity of the deformations and the separation of scales. In functionally graded metamaterials, two scales become relevant, but since every metamaterial cell may differ slightly from the neighboring ones, neither the separation of scales nor periodicity conditions may be assumed to hold. Nevertheless, the fact that every metamaterial cell differs only slightly and that we are typically concerned with the global behavior may be considered to speed up the computational procedure. This paper introduces a novel method specifically designed for metamaterials to address these challenges by structuring the metamaterial in macroelements, the stiffness matrix of elements being reduced prior to assembling in the global matrix. The advantage is taken from the fact that macroelement matrices differ only in a few terms. This strategy significantly improves computational efficiency, enabling the handling of very large meshed structures in metamaterials with improved performance compared to conventional FEA techniques. download the full-text of this paper (PDF, 23825 Kb) go to the previous paper go to the next paper return to the table of contents return to the volume description
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