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

Autor: Simone Morganti, Alberto Sibileau, Alberto García-González, Ferdinando Auricchio, Pedro Díez
Přispěvatelé: Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental, Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
Rok vydání: 2018
Předmět:
74 Mechanics of deformable solids::74P Optimization [Classificació AMS]
Optimal design
Proper generalized decomposition
Computer science
Explicit parametric solution
Computational Mechanics
Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC]
3D printing
74 Mechanics of deformable solids::74C Plastic materials
materials of stress-rate and internal-variable type [Classificació AMS]
Ocean Engineering
02 engineering and technology
Crystal structure
01 natural sciences
Lattice (order)
Applied mathematics
Strength of materials
Architectured materials
0101 mathematics
Resistència de materials
Parametric statistics
business.industry
Applied Mathematics
Mechanical Engineering
Metamaterial
021001 nanoscience & nanotechnology
Parametric lattice structure
010101 applied mathematics
Computational Mathematics
Algebraic equation
Computational Theory and Mathematics
0210 nano-technology
business
Plastics
Matemàtiques i estadística::Investigació operativa::Optimització [Àrees temàtiques de la UPC]
Zdroj: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname
ISSN: 1432-0924
0178-7675
DOI: 10.1007/s00466-017-1534-9
Popis: 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.
Databáze: OpenAIRE
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