Algebraic level sets for CAD/CAE integration and moving boundary problems

Boundary representation (B-rep) of CAD models obtained from solid modeling kernels are commonly used in design, and analysis applications outside the CAD systems. Boolean operations between interacting B-rep CAD models as well as analysis of such multi-body systems are fundamental operations on B-rep geometries in CAD/CAE applications. However, the boundary representation of B-rep solids is, in general, not a suitable representation for analysis operations which lead to CAD/CAE integration challenges due to the need for conversion from B-rep to volumetric approximations. The major challenges include intermediate mesh generation step, capturing CAD features and associated behavior exactly and recurring point containment queries for point classification as inside/outside the solid. Thus, an ideal analysis technique for CAD/CAE integration that can enable direct analysis operations on B-rep CAD models while overcoming the associated challenges is desirable. ^ Further, numerical surface intersection operations are typically necessary for boolean operations on B-rep geometries during the CAD and CAE phases. However, for non-linear geometries, surface intersection operations are non-trivial and face the challenge of simultaneously satisfying the three goals of accuracy, efficiency and robustness. In the class of problems involving multi-body interactions, often an implicit knowledge of the boolean operation is sufficient and explicit intersection computation may not be needed. Such implicit boolean operations can be performed by point containment queries on B-rep CAD models. However, for complex non-linear B-rep geometries, the point containment queries may involve numerical iterative point projection operations which are expensive. Thus, there is a need for inexpensive, non-iterative techniques to enable such implicit boolean operations on B-rep geometries. ^ Moreover, in analysis problems with evolving boundaries (ormoving boundary problems), interfaces or cracks, blending functions are used to enrich the underlying domain with the known behavior on the enriching entity. The blending functions are typically dependent on the distance from the evolving boundaries. For boundaries defined by free form curves or surfaces, the distance fields have to be constructed numerically. This may require either a polytope approximation to the boundary and/or an iterative solution to determine the exact distance to the boundary. ^ In this work a purely algebraic, and computationally efficient technique is described for constructing signed distance measures from Non-Uniform Rational B-Splines (NURBS) boundaries that retain the geometric exactness of the boundaries while eliminating the need for iterative and non-robust distance calculation. The proposed technique exploits the NURBS geometry and algebraic tools of implicitization. Such a signed distance measure, also referred to as the Algebraic Level Sets, gives a volumetric representation of the B-rep geometry constructed by purely non-iterative algebraic operations on the geometry. This in turn enables both the implicit boolean operations and analysis operations on B-rep geometries in CAD/CAE applications. Algebraic level sets ensure exactness of geometry while eliminating iterative numerical computations. Further, a geometry-based analysis technique that relies on hierarchical partition of unity field compositions (HPFC) theory and its extension to enriched field modeling is presented. The proposed technique enables direct analysis of complex physical problems without meshing, thus, integrating CAD and CAE. The developed techniques are demonstrated by constructing algebraic level sets for complex geometries, geometry-based analysis of B-rep CAD models and a variety of fracture examples culminating in the analysis of steady state heat conduction in a solid with arbitrary shaped three-dimensional cracks. ^ The proposed techniques are lastly applied to investigate the risk of fracture in the ultra low-k (ULK) dies due to copper (Cu) wirebonding process. Maximum damage induced in the interlayer dielectric (ILD) stack during the process steps is proposed as an indicator of the reliability risk. Numerical techniques based on enriched isogeometric approximations are adopted to model damage in the ULK stacks using a cohesive damage description. A damage analysis procedure is proposed to conduct damage accumulation studies during Cu wirebonding process. Analysis is carried out to identify weak interfaces and potential sites for crack nucleation as well as damage nucleation patterns. Further, the critical process condition is identified by analyzing the damage induced during the impact and ultrasonic excitation stages. Also, representative ILD stack designs with varying Cu percentage are compared for risk of fracture

Cubic B-Spline Curves with Shape Parameter and Their Applications

The present studies on the extension of B-spline mainly focus on Bezier methods and uniform B-spline and are confined to the adjustment role of shape parameters to curves. Researchers pay little attention to nonuniform B-spline. This paper discusses deeply the extension of the quasi-uniform B-spline curves. Firstly, by introducing shape parameters in the basis function, the spline curves are defined in matrix form. Secondly, the application of the shape parameter in shape design is analyzed deeply. With shape parameters, we get another means for adjusting the curves. Meanwhile, some examples are given. Thirdly, we discuss the smooth connection between adjacent B-spline segments in detail and present the adjusting methods. Without moving the control points position, through assigning appropriate value to the shape parameter, C1 continuity of combined spline curves can be realized easily. Results show that the methods are simple and suitable for the engineering application

Shape analysis of the corpus callosum of autistic and normal subjects in neuroimaging.

Early detection of human disease in today’s society can have an enormous impact on the severity of the disease that is manifested. Disease such as Autism and Dyslexia, which have no current cure or proven mechanism as to how they develop, can often have an adverse physical and physiological impact on the lifestyle of a human being. Although these disease are not fully curable, the severity handicaps that accompany them can be significantly reduced with the proper therapy, and thus the earlier that the disease is detected the faster therapy can be administered. The research in this thesis is an attempt at studying discriminatory shape measures of some brain structures that are known to carry changes from autistics to normal individuals. The focus will be on the corpus callosum. There has been considerable research done on the brain scans (MRI, CT) of autistic individuals vs. control (normal) individuals to observe any noticeable discrepancies through statistical analysis. The most common and powerful tool to analyze structures of the brain, once a specific region has been segmented, is using Registration to match like structures and record their error. The ICP algorithm (Iterative Closest Point) is commonly used to accomplish this task. Many techniques such as level sets and statistical methods can be used for segmentation. The Corpus Callosum (CC) and the cortical surface of the brain are currently where most Autism analysis is performed. It has been observed that the gyrification of the cortical surface is different in the two groups, and size as well as shape of the CC. An analysis approach for autism MRI is quite extensive and involves many steps. This thesis is limited to examination of shape measures of the CC that lend discrimination ability to distinguish between normal and autistic individuals from T1-weigheted MRI scans. We will examine two approaches for shape analysis, based on the traditional Fourier Descriptors (FD) method and shape registration (SR) using the procrustes technique. MRI scans of 22 autistic and 16 normal individuals are used to test the approaches developed in this thesis. We show that both FD and SR may be used to extract features to discriminate between the two populations with accuracy levels over 80% up to 100% depending on the technique

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

A sharp interface isogeometric strategy for moving boundary problems

The proposed methodology is first utilized to model stationary and propagating cracks. The crack face is enriched with the Heaviside function which captures the displacement discontinuity. Meanwhile, the crack tips are enriched with asymptotic displacement functions to reproduce the tip singularity. The enriching degrees of freedom associated with the crack tips are chosen as stress intensity factors (SIFs) such that these quantities can be directly extracted from the solution without a-posteriori integral calculation. As a second application, the Stefan problem is modeled with a hybrid function/derivative enriched interface. Since the interface geometry is explicitly defined, normals and curvatures can be analytically obtained at any point on the interface, allowing for complex boundary conditions dependent on curvature or normal to be naturally imposed. Thus, the enriched approximation naturally captures the interfacial discontinuity in temperature gradient and enables the imposition of Gibbs-Thomson condition during solidification simulation. The shape optimization through configuration of finite-sized heterogeneities is lastly studied. The optimization relies on the recently derived configurational derivative that describes the sensitivity of an arbitrary objective with respect to arbitrary design modifications of a heterogeneity inserted into a domain. The THB-splines, which serve as the underlying approximation, produce sufficiently smooth solution near the boundaries of the heterogeneity for accurate calculation of the configurational derivatives. (Abstract shortened by ProQuest.

Free Form Deformation Techniques for 3D Shape Optimization Problems

The purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we choose to use the Free Form Deformation parametrization, a recent technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the technique by developing a link among different specialized softwares, in order to establish a path, from the geometry definition, to the method implementation, and finally to the simulation and to the optimization of the problem. In particular, we have studied a bulb and a rudder of a race sailing boat as model problems

Geometrical representations for efficient aircraft conceptual design and optimisation

Geometrical parameterisation has an important role in the aircraft design process due to its impact on the computational efficiency and accuracy in evaluating different configurations. In the early design stages, an aircraft geometrical model is normally described parametrically with a small number of design parameters which allows fast computation. However, this provides only a course approximation which is generally limited to conventional configurations, where the models have already been validated. An efficient parameterisation method is therefore required to allow rapid synthesis and analysis of novel configurations. Within this context, the main objectives of this research are: 1) Develop an economical geometrical parameterisation method which captures sufficient detail suitable for aerodynamic analysis and optimisation in early design stage, and2) Close the gap between conceptual and preliminary design stages by bringing more detailed information earlier in the design process. Research efforts were initially focused on the parameterisation of two-dimensional curves by evaluating five widely-cited methods for airfoil against five desirable properties. Several metrics have been proposed to measure these properties, based on airfoil fitting tests. The comparison suggested that the Class-Shape Functions Transformation (CST) method is most suitable and therefore was chosen as the two-dimensional curve generation method. A set of blending functions have been introduced and combined with the two-dimensional curves to generate a three-dimensional surface. These surfaces form wing or body sections which are assembled together through a proposed joining algorithm. An object-oriented structure for aircraft components has also been proposed. This allows modelling of the main aircraft surfaces which contain sufficient level of accuracy while utilising a parsimonious number of intuitive design parameters ... [cont.]

The Quantification of Displacement of the Anterior Teeth in the Human Dentition

The credibility of bite mark analysis as a forensic science is under fire in our legal system. The basis of opinions regarding the probability of a dental pattern observed in bite mark evidence matching a suspect\u27s dentition has not been objectively substantiated. Though guidelines and standards are in place, bite mark analyses have failed to provide basic scientific methods in order to be deemed of evidentiary value. Forensic scientists need to take a step back and develop valid and reliable methodologies that provide a statistical approach for defining dental characteristics in the human dentition. For this study, three computer-generated, mathematically derived curves were chosen to describe and quantify in a statistical manner the dental characteristic of displacement of eight anterior teeth in the human dentition. The Bezier, ellipse, and polynomial curves were digitally applied to scanned images from 75 dentitions comprising 150 wax exemplars of dental imprints of a male population, ages 18-44. Measurements of each tooth were made using Adobe Photoshop® software to provide maximum standardization and objectivity. Statistical tests established the best-fit-curve for determining displacement of the anterior teeth. Of the three curves, the polynomial curve had the lowest average of variance and the lowest sum of the absolute value of displacement from the curve for the anterior teeth; thus, it was shown to be the best-fit-curve based on the statistical variance for measuring displacement of the anterior teeth. Allowing for tooth displacement to be a measurable dental characteristic that can be scientifically quantified, the polynomial curve provides a valid and reliable methodology for bite mark analysis in future population studies. The polynomial curve may significantly enhance the judicial process associated with bite mark evidence by providing a scientific basis for objective interpretation of a unique dental characteristic based on an individual curve and the individuality of a bite pattern or imprint from a victim and/or suspect(s)

3D Scanning of transparent objects

Many practical tasks in industry, such as automatic inspection or robot vision, often require scanning of three-dimensional shapes with non-contact techniques. However, transparent objects, such as those made of glass, still pose difficulties for classical scanning techniques. The reconstruction of surface geometry for transparent objects is complicated by the fact that light is transmitted through, refracted and in some cases reflected by the surface. Current approaches can only deal relatively well with sub-classes of objects. The algorithms are still very specific and not generally applicable. Furthermore, many techniques require considerable acquisition effort and careful calibration. This thesis proposes a new method of determining the surface shape of transparent objects. The method is based on local surface heating and thermal imaging. First, the surface of the object is heated with a laser source. A thermal image is acquired, and pixel coordinates of the heated point are calculated. Then, the 3D coordinates of the surface are computed using triangulation and the initial calibration of the system. The process is repeated by moving the transparent object to recover its surface shape. This method is called Scanning From Heating. Considering the laser beam as a point heating source and the surface of the object locally at at the impact zone, the Scanning From Heating method is extended to obtain the surface normals of the object, in addition to the 3D world coordinates. A scanner prototype based on Scanning From Heating method has been developed during the thesis