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published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

Ma Mun Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 86-88). / Abstract also in Chinese. / Abstract --- p.i / Declaration --- p.ii / Acknowledgement --- p.iii / List of Figures --- p.iv / List of Tables --- p.ix / Table of Contents --- p.x / Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Motivation --- p.1 / Chapter 1.2. --- Thesis Roadmap --- p.3 / Chapter 1.3. --- Contribution / Chapter 2. --- System Architecture --- p.6 / Chapter 2.1. --- Tracker system --- p.6 / Chapter 2.1.1. --- Spatial Information --- p.6 / Chapter 2.1.2. --- Transmitter (Xmtr) --- p.6 / Chapter 2.1.3. --- Receiver (Recvr) --- p.7 / Chapter 2.2. --- Glove System --- p.7 / Chapter 2.2.1. --- CyberGlove Interface Unit (CGIU) --- p.7 / Chapter 2.2.2. --- Bend Sensors --- p.7 / Chapter 2.3. --- Integrating the tracker and the glove system --- p.9 / Chapter 2.3.1. --- System Layout --- p.9 / Chapter 3. --- Deformable Model --- p.11 / Chapter 3.1. --- Elastic models in computer --- p.11 / Chapter 3.2. --- Virtual object model --- p.17 / Chapter 3.3. --- Force displacement relationship --- p.18 / Chapter 3.3.1. --- Stress-strain relationship --- p.19 / Chapter 3.3.2. --- Stiffness matrix formulation --- p.20 / Chapter 3.4. --- Solving the linear system --- p.24 / Chapter 3.5. --- Implementation --- p.26 / Chapter 3.5.1. --- Data structure --- p.26 / Chapter 3.5.2. --- Global stiffness matrix formulation --- p.27 / Chapter 3.5.3. --- Re-assemble of nodal displacement --- p.30 / Chapter 4. --- Collision Detection --- p.32 / Chapter 4.1. --- Related Work --- p.31 / Chapter 4.2. --- Spatial Subdivision --- p.37 / Chapter 4.3. --- Hierarchy construction --- p.38 / Chapter 4.3.1. --- Data structure --- p.39 / Chapter 4.3.2. --- Initialisation --- p.41 / Chapter 4.3.3. --- Expanding the hierarchy --- p.42 / Chapter 4.4. --- Collision detection --- p.45 / Chapter 4.4.1. --- Hand Approximation --- p.45 / Chapter 4.4.2. --- Interference tests --- p.47 / Chapter 4.4.3. --- Searching the hierarchy --- p.51 / Chapter 4.4.4. --- Exact interference test --- p.51 / Chapter 4.5. --- Grasping mode --- p.53 / Chapter 4.5.1. --- Conditions for Finite Element Analysis (FEA) --- p.53 / Chapter 4.5.2. --- Attaching conditions --- p.53 / Chapter 4.5.3. --- Collision avoidance --- p.54 / Chapter 4.6. --- Repeating deformation in different orientation --- p.56 / Chapter 5. --- Enhancing performance --- p.59 / Chapter 5.1. --- Data communication --- p.60 / Chapter 5.1.1. --- Client-server model --- p.60 / Chapter 5.1.2. --- Internet protocol suite --- p.61 / Chapter 5.1.3. --- Berkeley socket --- p.61 / Chapter 5.1.4. --- Checksum problem --- p.62 / Chapter 5.2. --- Use of parallel tool --- p.62 / Chapter 5.2.1. --- Parallel code generation --- p.63 / Chapter 5.2.2. --- Optimising parallel code --- p.64 / Chapter 6. --- Implementation and Results --- p.65 / Chapter 6.1. --- Supporting functions --- p.65 / Chapter 6.1.1. --- Read file --- p.66 / Chapter 6.1.2. --- Keep shape --- p.67 / Chapter 6.1.3. --- Save as --- p.67 / Chapter 6.1.4. --- Exit --- p.67 / Chapter 6.2. --- Visual results --- p.67 / Chapter 6.3. --- An operation example --- p.75 / Chapter 6.4. --- Performance of parallel algorithm --- p.78 / Chapter 7. --- Conclusion and Future Work --- p.84 / Chapter 7.1. --- Conclusion --- p.84 / Chapter 7.2. --- Future Work --- p.84 / Reference --- p.86 / Appendix A Matrix Inversion --- p.89 / Appendix B Derivation of Equation 6.1 --- p.92 / Appendix C Derivation of (6.2) --- p.93

Thesis (Ph.D)--Computing, Georgia Institute of Technology, 2009. / Committee Chair: Vuduc, Richard; Committee Member: Biros, George; Committee Member: Davatzikos, Christos; Committee Member: Tannenbaum, Allen; Committee Member: Zhou, Hao Min. Part of the SMARTech Electronic Thesis and Dissertation Collection.

A computer algorithm is developed for clipping and capping N-sided polyhedra with arbitrary planes. The algorithm is then expanded to include the processing of general two and three dimensional geometric finite element model data. Data processing is included for the transformation of original model results to match the clipped and capped graphical display model. The algorithms are implemented in a FORTRAN program that may be directly substituted into the MOVIE.BYU/ARIZONA graphics system. The new SECTION program maintains all the functions of the original version while incorporating several major new features. These new features include the expansion of the geometric library to two and three dimensional elements and two new general forms for polygons and polyhedra. Another significant change in the processing is the implementation of the reentrant clipping and capping routines. This feature permits a previously clipped model to be clipped again and again by new and different clipping planes. The above features as well as enhanced input data schemes including a preliminary interface to NASTRAN are offered as a skeleton for future modifications. The major routines in the program have taken advantage of dynamic memory allocation via FORTRAN subroutine argument calls. Through this latter feature new capability can be concatenated to the end of the current processing in a prototype manner for rapid implementation and exploration.

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A general review of lattice dome geometry and connection details, leads to a modeling approach, which introduces intermediate elements to represent connections. The method provides improved modeling of joint behavior and flexibility for comparative studies. The discussion of lattice domes is further specialized for parallel lamella geometry. A procedure is developed for minimizing the number of different member lengths. This procedure is incorporated into a program, which generates the geometric data for a specified dome. The model is developed from a background which considers commercial space frame systems, static and dynamic loads, and modeling techniques using ABAQUS, a finite element program. An optional output of the generation program creates input data for ABAQUS. Modal analysis, static design loads, and earthquake loads are used in the evaluation of the model. / Master of Science

The first component of this work is a parallel algorithm for constructing non-uniform octree meshes for finite element computations. Prior to octree meshing, the linear octree data structure must be constructed and a constraint known as "2:1 balancing" must be enforced; parallel algorithms for these two subproblems are also presented. The second component of this work is a parallel matrix-free geometric multigrid algorithm for solving elliptic partial differential equations (PDEs) using these octree meshes. The last component of this work is a parallel multiscale Gauss Newton optimization algorithm for solving the elastic image registration problem. The registration problem is discretized using finite elements on octree meshes and the parallel geometric multigrid algorithm is used as a preconditioner in the Conjugate Gradient (CG) algorithm to solve the linear system of equations formed in each Gauss Newton iteration. Several ideas were used to reduce the overhead for constructing the octree meshes. These include (a) a way to lower communication costs by reducing the number of synchronizations and reducing the communication message size, (b) a way to reduce the number of searches required to build element-to-vertex mappings, and (c) a compression scheme to reduce the memory footprint of the entire data structure. To our knowledge, the multigrid algorithm presented in this work is the only matrix-free multiplicative geometric multigrid implementation for solving finite element equations on octree meshes using thousands of processors. The proposed registration algorithm is also unique; it is a combination of many different ideas: adaptivity, parallelism, fast optimization algorithms, and fast linear solvers. All the algorithms were implemented in C++ using the Message Passing Interface (MPI) standard and were built on top of the PETSc library from Argonne National Laboratory. The multigrid implementation has been released as an open source software: Dendro. Several numerical experiments were performed to test the performance of the algorithms. These experiments were performed on a variety of NSF TeraGrid platforms. Our largest run was a highly-nonuniform, 8-billion-unknown, elasticity calculation on 32,000 processors.

Indiana University-Purdue University Indianapolis (IUPUI) / Nanocomposite ceramics have been widely studied in order to tailor desired properties at high temperatures. Methodologies for development of material design are still under effect. While finite element modeling (FEM) provides significant insight on material behavior, few design researchers have addressed the design paradox that accompanies this rapid design space expansion. A surrogate optimization model management framework has been proposed to make this design process tractable. In the surrogate optimization material design tool, the analysis cost is reduced by performing simulations on the surrogate model instead of high fidelity finite element model. The methodology is incorporated to and the optimal number of silicon carbide (SiC) particles, in a silicon-nitride(Si3N4) composite with maximum fracture energy [2]. Along with a deterministic optimization algorithm, model uncertainties have also been considered with the use of robust design optimization (RDO) method ensuring a design of minimum sensitivity to changes in the parameters. These methodologies applied to nanocomposites design have a significant impact on cost and design cycle time reduced.