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Deterministic And Random Isogeometric Analysis Of Fluid Flow In Unsaturated Soils, Shahriar Shahrokhabadi
Deterministic And Random Isogeometric Analysis Of Fluid Flow In Unsaturated Soils, Shahriar Shahrokhabadi
Theses and Dissertations
The main objective of this research is to use IGA as an efficient and robust alternative for numerical simulation of unsaturated seepage problems. Moreover, this research develops an IGA-based probabilistic framework that can properly account for the variability of soil hydraulic properties in the simulations. In the first part, IGA is used in a deterministic framework to solve a head-based form of Richards’ equation. It is shown that IGA is able to properly simulate changes in pore pressure at the soils interface. In the second part of this research, a new probabilistic framework, named random IGA (RIGA), is developed. A …
Modeling Stokes Flow Using Hierarchical Structure-Preserving B-Splines, Kendrick Monroe Shepherd
Modeling Stokes Flow Using Hierarchical Structure-Preserving B-Splines, Kendrick Monroe Shepherd
Theses and Dissertations
A new spline space, the hierarchical structure-preserving B-spline space, is introduced and implemented in the analysis of Stokes flow. The space, when properly constrained, is shown to be stable and to have at least optimal convergence rates in the velocity field and suboptimal convergence rates in the pressure field. However, results show that superoptimal convergence can often be expected in the pressure field, likely due to error reduction in the velocity field. Like other hierarchical spline spaces, these splines are shown to greatly increase accuracy and to drastically lower computation times for analyses on domains whose solution fields have singularities …
An Investigation Of Nurbs-Based Deformable Image Registration, Travis J. Jacobson
An Investigation Of Nurbs-Based Deformable Image Registration, Travis J. Jacobson
Theses and Dissertations
Deformable image registration (DIR) is an essential tool in medical image processing. It provides a means to combine image datasets, allowing for intra-subject, inter-subject, multi-modality, and multi-instance analysis, as well as motion detection and compensation. One of the most popular DIR algorithms models the displacement vector field (DVF) as B-splines, a sum of piecewise polynomials with coefficients that enable local shape control. B-splines have many advantageous properties in the context of DIR, but they often struggle to adequately model steep local gradients and discontinuities. This dissertation addresses that limitation by proposing the replacement of conventional B-splines with a generalized formulation …
Application Of Machine Learning And Parametric Nurbs Geometry To Mode Shape Identification, Robert Mceuen Porter
Application Of Machine Learning And Parametric Nurbs Geometry To Mode Shape Identification, Robert Mceuen Porter
Theses and Dissertations
In any design, the dynamic characteristics of a part are dependent on its geometric and material properties. Identifying vibrational mode shapes within an iterative design process becomes difficult and time consuming due to frequently changing part definition. Although research has been done to improve the process, visual inspection of analysis results is still the current means of identifying each vibrational mode determined by a modal analysis. This research investigates the automation of the mode shape identification process through the use of parametric geometry and machine learning.In the developed method, displacement results from finite element modal analysis are used to create …
Application Of Parametric Nurbs Geometry To Mode Shape Identification And The Modal Assurance Criterion, Evan D. Selin
Application Of Parametric Nurbs Geometry To Mode Shape Identification And The Modal Assurance Criterion, Evan D. Selin
Theses and Dissertations
The dynamic characteristics of a part are highly dependent on geometric and material properties of the part. The identification and tracking of vibrational mode shapes within an iterative design process becomes difficult and time consuming due to the frequently changing part definition. Currently, visual inspection of analysis results is used as the means to identify the shape of each vibrational mode determined by the modal analysis. This thesis investigates the automation of the mode shape identification process through the use of parametric geometry and the Modal Assurance Criterion. Displacement results from finite element modal analysis are used to create parametric …
Isogeometric Finite Element Analysis Using T-Splines, Jingang Li
Isogeometric Finite Element Analysis Using T-Splines, Jingang Li
Theses and Dissertations
Non-uniform rational B-splines (NURBS) methodology is presented, on which the isogeometric analysis is based. T-splines are also introduced as a surface design methodology, which are a generalization of NURBS and permit local refinement. Isogeometric analysis using NURBS and T-splines are applied separately to a structural mechanics problem. The results are compared with the closed-form solution. The desirable performance of isogeometric analysis using T-splines on engineering analysis is demonstrated.
Arbitrary Degree T-Splines, Gordon Thomas Finnigan
Arbitrary Degree T-Splines, Gordon Thomas Finnigan
Theses and Dissertations
T-Splines is a freeform surface type similar to NURBS, that allows partial rows of control points. Up until now, T-Splines have only been formally defined for the degree three case. This paper extends the definition to support all odd, even, and mixed degree T-Spline surfaces, making T-Splines a proper superset of all standard NURBS surfaces.
Reducing Curvature In Complex Tool Paths By Deviating From Cam-Produced Tool Paths Within A Tolerance Band, George Benjamin Naseath
Reducing Curvature In Complex Tool Paths By Deviating From Cam-Produced Tool Paths Within A Tolerance Band, George Benjamin Naseath
Theses and Dissertations
This thesis develops an algorithm to decrease high-curvature sections in tool paths for complex parts to achieve shorter machining times resulting in higher production rates. In the research sample cases, the algorithm decreased machining times by 1% to 9% for design-induced sections of high curvature and by 16% to 75% for CAM induced ripples using high path tolerances. High-curvature sections in tool paths are caused by complex part geometry, noise, and discontinuities in the model. The curvature is decreased by deviating the tool path within an allowable path tolerance. The feedrate along the tool path is directly related to the …
A Geometry-Based Motion Planner For Direct Machining And Control, Robert M. Cheatham
A Geometry-Based Motion Planner For Direct Machining And Control, Robert M. Cheatham
Theses and Dissertations
Direct Machining And Control (DMAC) is a new method of controlling machine tools directly from process planning software. A motion planning module is developed for the DMAC system that operates directly off path geometry without pre-tessellation. The motion planner is developed with the intent to process Bezier curves. The motion planning module includes a deterministic predictor-corrector-type curve interpolator, a dynamics limiting module, and a two-pass jerk-limited speed profiling algorithm. The methods are verified by machining an automotive surface in a clay medium and evaluating the resultant machine dynamics, feed rate, and chordal error throughout the machining process.
T-Spline Simplification, David L. Cardon
T-Spline Simplification, David L. Cardon
Theses and Dissertations
This work focuses on generating approximations of complex T-spline surfaces with similar but less complex T-splines. Two approaches to simplifying T-splines are proposed: a bottom-up approach that iteratively refines an over-simple T-spline to approximate a complex one, and a top-down approach that evaluates existing control points for removal in producing an approximations. This thesis develops and compares the two simplification methods, determining the simplification tasks to which each is best suited. In addition, this thesis documents supporting developments made to T-spline research as simplification was developed.
T-Spline Merging, Heather Ipson
T-Spline Merging, Heather Ipson
Theses and Dissertations
Geometric models, such as for use in CAD/CAM or animation, are often constructed in a piece-wise fashion. Historically, these models have been made of NURBS surfaces. For various reasons it is problematic and often times mathematically impossible to combine several NURBS models into one continuous surface. The recent invention of a surface type called T-splines has made the combining of NURBS surfaces into a single continuous surface possible, but much of the mathematics has yet to be explored. This thesis explores the mathematics and algorithms necessary to merge multiple NURBS, T-spline, or T-NURCC surfaces into a single continuous surface. This …