descriptionPublicationkeyboard_double_arrow_right Article 10 Jan 2018 English Publisher:Springer Science and Business Media LLCJournal:Computational Mechanics, volume 62, pages 871-891 (issn: 0178-7675, eissn: 1432-0924,

Authors: Sibileau, Alberto; García González, Alberto; Auricchio, Ferdinando; Morganti, Simone; Díez, Pedro;

doi: 10.1007/s00466-017-1534-9

handle: 2117/117361 , 11571/1211490

Explicit parametric solutions of lattice structures with proper generalized decomposition (PGD)

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Abstract

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-017-1534-9 Architectured materials (or metamaterials) are constituted by a unit-cell with a complex structural design repeated periodically forming a bulk material with emergent mechanical properties. One may obtain specific macro-scale (or bulk) properties in the resulting architectured material by properly designing the unit-cell. Typically, this is stated as an optimal design problem in which the parameters describing the shape and mechanical properties of the unit-cell are selected in order to produce the desired bulk characteristics. This is especially pertinent due to the ease manufacturing of these complex structures with 3D printers. The proper generalized decomposition provides explicit parametic solutions of parametric PDEs. Here, the same ideas are used to obtain parametric solutions of the algebraic equations arising from lattice structural models. Once the explicit parametric solution is available, the optimal design problem is a simple post-process. The same strategy is applied in the numerical illustrations, first to a unit-cell (and then homogenized with periodicity conditions), and in a second phase to the complete structure of a lattice material specimen. Peer Reviewed

Related Organizations

Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
University of Pavia
Italy

Keywords

:74 Mechanics of deformable solids::74P Optimization [Classificació AMS], Classificació AMS::74 Mechanics of deformable solids::74C Plastic materials, explicit parametric solution, Proper generalized decomposition, Explicit parametric solution, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], Ocean Engineering, :74 Mechanics of deformable solids::74C Plastic materials, materials of stress-rate and internal-variable type [Classificació AMS], 510, Computational Theory and Mathematic, Strength of materials, Architectured materials, proper generalized decomposition, Resistència de materials, materials of stress-rate and internal-variable type, Mechanical Engineering, Applied Mathematics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització, Classificació AMS::74 Mechanics of deformable solids::74P Optimization, 3D printing, Architectured material, Parametric lattice structure, Classificació AMS::74 Mechanics of deformable solids::74C Plastic materials, materials of stress-rate and internal-variable type, parametric lattice structure, Compliance or weight optimization in solid mechanics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, Computational Mathematic, architectured materials, Homogenization in equilibrium problems of solid mechanics, Plastics, :Matemàtiques i estadística::Investigació operativa::Optimització [Àrees temàtiques de la UPC]

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