Algorithms for Design and Interrogation of Functionally Gradient Material Objects

Abstract

Solid Freeform Fabrication (SFF) processes have demonstrated the ability to produce parts with locally controlled composition. In the limit, processes such as Three-Dimensional Printing(3DP) can create parts with composition to the length scale of 100 μm. To exploit this potential, new methods for automatic design of Functionally Gradient Material (FGM) parts need to be developed. This paper presents an efficient method for design and composition interrogation of FGM solids. The design tool based on the distance function from the surface of the part requires enhanced efficiency, and so does the interrogation of the part. The approach for improving efficiency includes preprocessing the model with bucket sorting and 3D digital distance transform, and an efficient point classification algorithm. Based on these tools, an efficient algorithm for distance function computation is developed for the design of FGM through distance to the surface of the part or distance to an .STL surface boundary. An efficient algorithm to evaluate composition at a point, along a ray or on a plane is also presented.

Feature Based Modeling of Heterogeneous Objects

“…This method was further extended to create more general heterogeneous objects including multi-material, FGM and fiber bundles [9]. Jackson et al proposed a local composition control (LCC) approach to represent heterogeneous object in which a mesh model was divided into tetrahedrons and different material compositions were evaluated on the nodes of the tetrahedrons by using Bernstein polynomials [10][11][12]. Chiu [13] developed a material tree structure to store different compositions inside an object.…”

“…Samanta and Koc [33] also proposed a feature-based design and material blending scheme for free-form heterogeneous object modeling. Liu et al extended their work in [12] by taking parameterized functions with respect to distance(s) and functions that use Laplace equation to smoothly blend various boundary conditions as the material composition functions. This method made the designers to edit geometry and composition simultaneously [21].…”

An Integrated 2D and 3D Shape-based Search Framework and Applications

“…Boolean operators to facilitate the modeling procedure were defined [2]. Jackson et al proposed a local composition control (LCC) approach to represent heterogeneous object in which a mesh model was divided into tetrahedrons and different material compositions were evaluated on the nodes of the tetrahedrons by using Bernstein polynomials [3,4]. Chiu [5] developed a material tree structure to store different compositions of an object.…”

“…The feature-based modeling scheme was extended to heterogeneous object representation through boundary conditions of a virtual diffusion problem in the solid, and then designers could use it to control the material distribution [8]. Liu et al extended their work in [4] by taking parameterized functions in terms of distance(s) and functions using Laplace equation to blend smoothly various boundary conditions, through which designers could edit geometry and composition simultaneously [9]. Kou and Tan suggested a hierarchical representation for heterogeneous object modeling by using B-rep to represent geometry and a heterogeneous feature tree to express the material distributions [10].…”

Rapid Prototyping Technology

“…Boolean operators to facilitate the modeling procedure were defined (Kumar (1997), Kuman (1998)). Jackson et al proposed a local composition control (LCC) approach to represent heterogeneous object in which a mesh model was divided into tetrahedrons and different material compositions were evaluated on the nodes of the tetrahedrons by using Bernstein polynomials (Jackon (2000), Liu (2000)). Chiu et.…”