Algorithms for design and interrogation of functionally graded material solids

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2000.Includes bibliographical references (leaves 109-112).A Functionally Gradient Material (FGM) part is a 3D solid object that has varied local material composition that is defined by a specifically designed function. Recently, research has been performed at MIT in order to exploit the potential of creating FGM parts using a modern fabrication process, 3D Printing, that has the capability of controlling composition to the length scale of 100 [mu]m. As part of the project of design automation of FGM parts, this thesis focuses on the issue of the development of efficient algorithms for design and composition interrogation. Starting with a finite element based 3D model, the design tool based on the distance function from the surface of the part and the design tool allowing the user to design within a .STL file require enhanced efficiency and so does the interrogation of the part. The approach for improving efficiency includes preprocessing the model with bucket sorting, digital distance transform of the buckets and an efficient point classification algorithm. Based on this approach, 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 a .STL surface boundary. Also an efficient algorithm for composition evaluation at a point, along a ray or on a plane is developed. The theoretical time complexities of the developed algorithms are analyzed and experimental numerical results are provided.by Hongye Liu.S.M

Feature-based design of solids with local composition control

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 2004.Includes bibliographical references (leaves 126-134).This thesis presents a parametric and feature-based methodology for the design of solids with local composition control (LCC). A suite of composition design features are conceptualized and implemented. The designer can use them singly or in combination, to specify the composition of complex components. Each material composition design feature relates directly to the geometry of the design, often relying on user interaction to specify critical aspects of the geometry. This approach allows the designer to simultaneously edit geometry and composition by varying parameters until a satisfactory result is attained. The identified LCC features are those based on volume, transition, pattern, and (user-defined) surface features. The material composition functions include functions parametrized with respect to distance or distances to user-defined geometric features; and functions that use Laplace's equation to blend smoothly various boundary conditions including values and gradients of the material composition on the boundaries. The Euclidean digital distance transform and the boundary element method are adapted to the efficient computation of composition functions. Theoretical and experimental complexity, accuracy and convergence analyses are presented. The developed model is a multi-level and graph-based representation, thereby allowing for controls on the model validity and efficiency in model management. The representations underlying the composition design features are analytic in nature and therefore concise. Evaluation for visualization and fabrication is performed only at the resolutions required for these purposes, thereby reducing the computational burden.by Hongye Liu.Ph.D