期刊
COMPUTATIONAL MECHANICS
卷 62, 期 4, 页码 871-891出版社
SPRINGER
DOI: 10.1007/s00466-017-1534-9
关键词
Parametric lattice structure; Proper generalized decomposition; Explicit parametric solution; Architectured materials; 3D printing
资金
- Ministerio de Economia y Competitividad [DPI2014-51844-C2-2-R, DPI2017-85139-C2-2-R]
- Generalitat de Catalunya [2014-SGR-1471]
- European Education, Audiovisual and Culture Executive Agency (EACEA) under the Erasmus Mundus Joint Doctorate Simulation in Engineering and Entrepreneurship Development (SEED) [FPA 2013-0043]
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.
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