Design of Auxetic Structures via Mathematical Optimization
ABSTRACT The optimization and manufacturing of an auxetic structure is presented. An inverse homogenization method is used to obtain the optimized geometry shown in the figure. The resulting structure is then produced using selective electron beam melting. The numerically predicted properties are experimentally verified.
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ABSTRACT: Additive manufacturing (AM) could be a novel method of fabricating composite and porous materials having various effective performances based on mechanisms of their internal geometries. Materials fabricated by AM could rapidly be used in industrial application since they could easily be embedded in the target part employing the same AM process used for the bulk material. Furthermore, multi-material AM has greater potential than usual single-material AM in producing materials with effective properties. Negative thermal expansion is a representative effective material property realized by designing a composite made of two materials with different coefficients of thermal expansion. In this study, we developed a porous composite having planar negative thermal expansion by employing multi-material photopolymer AM. After measurement of the physical properties of bulk photopolymers, the internal geometry was designed by topology optimization, which is the most effective structural optimization in terms of both minimizing thermal stress and maximizing stiffness. The designed structure was converted to a three-dimensional STL model, which is a native digital format of AM, and assembled as a test piece. The thermal expansions of the specimens were measured using a laser scanning dilatometer. The test pieces clearly showed negative thermal expansion around room temperature.
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ABSTRACT: Materials and microstructures with specific configurations are able to have negative Poisson’s ratio. This paper proposes a topology optimization methodology of frame structures to design a planar periodic structure that exhibits negative Poisson’s ratio. Provided that beam section of each existing member is chosen from a set of some given candidates, we can reduce the topology optimization problem to a mixed-integer linear programming problem. Since the proposed approach treats frame structures and stress constraints are rigorously addressed, the optimal solution contains no hinge region. A heuristic method with local search is used to solve large-scale problems. Numerical examples and fabrication test demonstrate that planar periodic frame structures exhibiting negative Poisson’s ratio can be successfully obtained by the proposed method.Optimization and Engineering 09/2013; 15(3). DOI:10.1007/s11081-013-9225-7 · 0.96 Impact Factor
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ABSTRACT: Purpose – Optimization techniques can be used to design geometrically complex components with a wide variety of optimization criteria. However, such components have been very difficult and costly to produce. Layered fabrication technologies such as electron beam melting (EBM) open up new possibilities though. This paper seeks to investigate the integration of structural optimization and direct metal fabrication process. Design/methodology/approach – Mesh structures were designed, and optimization problems were defined to improve structural performance. Finite element analysis code in conjunction with nonlinear optimization routines were used in MATLAB. Element data were extracted from an STL-file, and output structures from the optimization routine were manufactured using an EBM machine. Original and optimized structures were tested and compared. Findings – There were discrepancies between the performance of the theoretical structures and the physical EBM structures due to the layered fabrication approach. A scaling factor was developed to account for the effect of layering on the material properties. Practical implications – Structural optimization can be used to improve the performance of a design, and direct fabrication technologies can be used to realise these structures. However, designers must realize that fabricated structures are not identical to idealized CAD structures, hence material properties much be adjusted accordingly. Originality/value – Integration of structural optimization and direct metal fabrication was reported in the paper. It shows the process from design through manufacturing with integrated analysis.Rapid Prototyping Journal 03/2008; 14(2):114-122. DOI:10.1108/13552540810862082 · 1.16 Impact Factor