published_or_final_version / Statistics / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 135-138).

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 1999. / Includes bibliographical references. Also available on the Internet.

Engineers have utilized CAE technique as an analysis tool to refine the engineering design over decades. However, CAE alone is not the key to open the door for the final goal. In order to achieve the practical solution to the real-time engineering problem, we need to integrate CAD, CAE and optimization techniques into a single framework. / In the optimization algorithm part, apart from the general parametric steepest descent (ST) algorithm, we also study the least square (LSQ) based optimization algorithm. As a result, we can solve the problem arisen from the variant dimensional sizes of the different design variables by using the weighted sensitivity information. / In the problem of the structural optimizations, three categories of the approaches can be identified: size, shape and topology optimizations. For size optimization, explicit dimensions are usually chosen as the design variables, for example, the thickness of a beam or the diameter of a cylinder. For shape optimization, the shape related parameters of the geometrical boundary are always considered to be the design variables, like the positions of the control points for a Bezier curve. However, these two methods are lack of the capability to handle the topological changes of the geometry. On the contrary, topology optimization is the generalization of size and shape optimizations, which offers a more flexible and powerful tool to determine the best layout of the materials and the topology to the design problem, and it is becoming increasingly important in the conceptual design phase. In other words, topology optimization gives one the inspiration for the locations where we put holes to reach the best design. / In this thesis, we put forward the algebraic level set (ALS) model with the consideration of the constructive solid geometry (CSG) model so that it is consistent with half-space primitive concept in CSG. Based on general shape derivative, we propose the general shape design sensitivity analysis (SDSA) formulations for general geometric primitives that are represented implicitly, such as line and circle primitives in two-dimensional space and plane primitive in three-dimensional space. We then extend the relevant formulations into corresponding parametrically represented primitives as they are widely used in today's mainstream CAD systems. / The material density method and the boundary-variation method are the popular methods adopted in both academia and industrial community. Even though the former method is dominant in industry, the latter method is more preferable these years owing to its boundary description nature. Undoubtedly, the level set based method is the most promising technique of the boundary-variation type. Scientists successfully developed the optimization algorithms based on the level set method (LSM) in the past few years. With the implicit representation of the LSM, topological changes of the design can be handled easily and the geometrical complexity is then reserved. / The numerical examples for the design optimization problem are successfully implemented with both the implicit geometric representation (2D cases) and the parametric geometric representation (3D cases), which proves the feasibility of the proposed framework. The results show that both shape and topology optimizations of a design could be accomplished in a natural way. / The optimal result given by conventional topology optimization usually involves tedious post-processing to form CAD geometry. Using our parameterizations with basic primitives and the proposed optimization algorithms, we can deliver comparatively complicated shapes with rich topological information. Therefore, the detail design could be conducted directly later. / Zhang, Jiwei. / "December 2010." / Adviser: Yu Michael Wang. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 119-129). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains xvi, 131 p.; also includes graphics (some col.). Includes abstract and vita. Advisor: Tamal K. Dey, Dept. of Computer and Information Science. Includes bibliographical references (p. 126-131).

The present work outlines a methodology of shape synthesis using intrinsic geometry concepts for engineering design of two-dimensional and three-dimensional curves as well as three-dimensional surfaces. Using concepts of intrinsic geometry of curves, the shape of a curve can be defined in terms of intrinsic parameters such as the curvature and torsion as a function of the arc length. The method of shape synthesis proposed here consists of selecting a shape model, defining a set of shape design variables and then evaluating the Cartesian coordinates of a curve. It is assumed that the end-point coordinates and tangents are specified for design of curves. A shape model is conceived as a set of continuous piecewise linear segments of the curvature, each segment defined as a function of the arc length. The shape design variables are the values of curvature and/or arc length at some of the end-points of the linear segments. The proposed method of shape synthesis is general in nature. It has been shown how this method can be used to find the optimal shape of planar and spatial Variable Geometry Truss (VGT) manipulators for pre-specified position and orientation of the end-effectors. It is expected that the proposed methodology could be used for problems of shape optimization. The shape design of a three-dimensional curve is accomplished by modeling it as a generalized helix. The base of the helix lies in a plane perpendicular to the skew direction between the end-point tangents. The base curve is designed as a planar curve consisting of a set of linear curvature segments. The gradient of the helix can be modeled by choosing any one of the following three curves: (i) a parabolically blended curve, (ii) a cubically blended curve and (iii) a pair of Bezier curves. The proposed method has been shown to be useful for designing the shape of a Variable Geometry Truss-type manipulator. The method can also be used for a variety of other applications such as the path of a manipulator end-effector, or the geometry of a highway clover loop. A three-dimensional surface is considered as a surface swept by a generatrix curve when it moves along a directrix curve. In the present work a generatrix curve is considered to be a planar curve and it is defined using the intrinsic geometry concepts of shape models and shape variables. Four different types of surfaces have been proposed. (i) linearly swept surfaces, (ii) surfaces of revolution, (iii) generalized swept surfaces and (iv) transition surfaces. In each case, the generatrix can have a variable shape as it moves along the directrix. The proposed approach has been found suitable for modeling deformed geometries such as fabric drape surfaces. By controlling the variation of the shape design variables of the generatrix curve, it has been found that the proposed definition of surfaces can be used to design variable-shape three-dimensional surfaces. The present work is an attempt to develop definitions of planar curves, space curves and surfaces which are based on the intrinsic geometry concepts. It has been found that in engineering analysis and design-optimization work, an engineer is able to represent and manipulate the shape effectively using an intrinsic form of geometry as compared to a parametric form. / Ph. D.

This dissertation focuses on the mathematical design of a unified shape kernel for geometric computing, with possible applications to computer aided design (CAM) and manufacturing (CAM), solid geometric modelling, free-form modelling of curves and surfaces, feature-based modelling, finite element meshing, computer animation, etc. The generality of such a unified shape kernel grounds on a shape theory for objects in some Euclidean space. Shape does not mean herein only geometry as usual in geometric modelling, but has been extended to other contexts, e. g. topology, homotopy, convexity theory, etc. This shape theory has enabled to make a shape analysis of the current geometric kernels. Significant deficiencies have been then identified in how these geometric kernels represent shapes from different applications. This thesis concludes that it is possible to construct a general shape kernel capable of representing and manipulating general specifications of shape for objects even in higher-dimensional Euclidean spaces, regardless whether such objects are implicitly or parametrically defined, they have ‘incomplete boundaries’ or not, they are structured with more or less detail or subcomplexes, which design sequence has been followed in a modelling session, etc. For this end, the basic constituents of such a general geometric kernel, say a combinatorial data structure and respective Euler operators for n-dimensional regular stratified objects, have been introduced and discussed.

Thesis (Ph.D.) - University of Glasgow, 2008. / Ph.D. thesis submitted to the Faculty of Information and Mathematical Sciences, Department of Statistics, University of Glasgow, 2008. Includes bibliographical references. Print version also available.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 98-99). Also available via the Internet.

Presented is a model for predicting SMA-induced deformations in an unsymmetric cross ply laminate. A previously developed theory is used to predict the room-temperature shape of the cross-ply laminate by minimizing its total potential energy. Then, using the principle of virtual work, equations relating the shape of the laminate to a force applied on supports fastened to the laminate are derived. Induced strains and displacements are predicted as a function of the applied force. Experiments where the force is generated by known weights are conducted. Good correlations are established between the experimental results and the predictions. The developed theory is able to predict with good accuracy the shape, strains and, displacements of an unsymmetric cross-ply laminate to the force applied on the laminate. This theory is then used to develop a model relating the laminate response to forces produced by a SMA actuator, the actuator being a SMA wire. To describe the mechanics of the SMA actuator, constitutive equations derived by other researchers are used. These constitutive equations relate the temperature of the wire to forces generated in it. Experiments where a SMA wire is used as an actuator are conducted. These experiments consist of resistively heating a SMA wire attached to supports fastened to the laminate. During these experiments, laminate deformations are measured as a function of the applied voltage. Comparisons with the temperature-based constitutive model predictions are not made since the relation between the applied voltage and the SMA temperature is very difficult to establish. However, the experiments show that a SMA used in conjunction with cross-ply unsymmetric laminates can induce very large changes in the laminate shapes. Thus, the concept of using a SMA actuator to control the shape of cross-ply unsymmetric laminates is validated. / Master of Science