Fractals and Additive Manufacturing

Ullah, Aman; D’Addona, Doriana M.; Harib, Khalifa H.; Lin, Than

doi:10.20965/ijat.2016.p0222

Cited by 16 publications

(16 citation statements)

References 14 publications

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“…This section presents the mathematical settings to generate IFS-based fractals. IFS-based fractals are created by some strictly contracting affine maps, as described in [71][72][73][74]. Predefined probabilities control the frequency of participation of each map.…”

Section: Settings Of Ifs-based Fractalsmentioning

confidence: 99%

Utilizing Fractals for Modeling and 3D Printing of Porous Structures

et al. 2021

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Porous structures exhibiting randomly sized and distributed pores are required in biomedical applications (producing implants), materials science (developing cermet-based materials with desired properties), engineering applications (objects having controlled mass and energy transfer properties), and smart agriculture (devices for soilless cultivation). In most cases, a scaffold-based method is used to design porous structures. This approach fails to produce randomly sized and distributed pores, which is a pressing need as far as the aforementioned application areas are concerned. Thus, more effective porous structure design methods are required. This article presents how to utilize fractal geometry to model porous structures and then print them using 3D printing technology. A mathematical procedure was developed to create stochastic point clouds using the affine maps of a predefined Iterative Function Systems (IFS)-based fractal. In addition, a method is developed to modify a given IFS fractal-generated point cloud. The modification process controls the self-similarity levels of the fractal and ultimately results in a model of porous structure exhibiting randomly sized and distributed pores. The model can be transformed into a 3D Computer-Aided Design (CAD) model using voxel-based modeling or other means for digitization and 3D printing. The efficacy of the proposed method is demonstrated by transforming the Sierpinski Carpet (an IFS-based fractal) into 3D-printed porous structures with randomly sized and distributed pores. Other IFS-based fractals than the Sierpinski Carpet can be used to model and fabricate porous structures effectively. This issue remains open for further research.

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Section: Settings Of Ifs-based Fractalsmentioning

confidence: 99%

Utilizing Fractals for Modeling and 3D Printing of Porous Structures

et al. 2021

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“…Some authors have also worked in the other direction. For example, Ullah et al [56][57][58] and Ullah [59] have created some point-clouds the using the mathematical processes called iterative function systems and Monte Carlo simulation. They have used the point-clouds as the base models and manufactured the self-similar objects (e.g., fractals) and porous structures.…”

Section: Surface Model Creation Techniques For Pcammentioning

confidence: 99%

Analytical Point-Cloud Based Geometric Modeling for Additive Manufacturing and Its Application to Cultural Heritage Preservation

et al. 2018

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Point-cloud is a valuable piece of information for geometric modeling and additive manufacturing of different types of objects. In most cases, a point-cloud is obtained by using the 3D scanners or by using image processing. Alternatively, one can rely on an analytical approach for creating the required point-cloud. In this study, we develop an analytical method that uses both equation and algorithm-based approaches for creating a point-cloud for modeling a given object (or shape). The analytically created point-cloud can then be processed by using a commercially available CAD package to create a virtual model (or solid CAD model) of the object. Finally, the virtual model can be used to create a physical model (or replica) of the underlying object using a commercially available additive manufacturing device (e.g., a 3D printer). The abovementioned procedure of analytical point-cloud based geometric modeling for additive manufacturing can be applied to preserve artifacts having cultural significance. In particular, we consider the Ainu motifs that represent the cultural heritage of Ainus living in the northern part of Japan (Hokkaido). We first classify the motifs and then model them in the form of a point-clouds using both equations and a recursive process (algorithm) proposed in this study. Finally, we create the CAD model and physical models of the artifacts having Ainu motifs on them. This way, we show the effectiveness of the analytical point-cloud based geometric modeling for additive manufacturing.

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“…To generate a tessellated 3D model, there are two ways: a solid model from CAD software using boundary representation (B-rep) is tessellated; and point clouds from a coordinate measuring machine (CMM) or a laser scanner are triangularized using reverse-engineering (RE) technology [18,19]. The design requirements are fundamental to creating an AM part.…”

Section: Key Attributes For Producibility Repeatability and Reprodumentioning

confidence: 99%

Toward a Digital Thread and Data Package for Metals-Additive Manufacturing

Kim

Witherell

et al. 2017

Smart and Sustainable Manufacturing Systems

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Additive manufacturing (AM) has been envisioned by many as a driving factor of the next industrial revolution. Potential benefits of AM adoption include the production of low-volume, customized, complicated parts/products, supply chain efficiencies, shortened time-to-market, and environmental sustainability. Work remains, however, for AM to reach the status of a full production-ready technology. Whereas the ability to create unique 3D geometries has been generally proven, production challenges remain, including lack of (1) data manageability through information management systems, (2) traceability to promote product producibility, process repeatability, and part-to-part reproducibility, and (3) accountability through mature certification and qualification methodologies. To address these challenges in part, this paper discusses the building of data models to support the development of validation and conformance methodologies in AM. We present an AM information map that leverages informatics to facilitate part producibility, process repeatability, and part-to-part reproducibility in an AM process. We present three separate case studies to demonstrate the importance of establishing baseline data structures and part provenance through an AM digital thread.

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Fractals and Additive Manufacturing

Cited by 16 publications

References 14 publications

Utilizing Fractals for Modeling and 3D Printing of Porous Structures

Utilizing Fractals for Modeling and 3D Printing of Porous Structures

Analytical Point-Cloud Based Geometric Modeling for Additive Manufacturing and Its Application to Cultural Heritage Preservation

Toward a Digital Thread and Data Package for Metals-Additive Manufacturing

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