Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Fatigue failure is one of the most critical issues in industry nowadays as 60 to 90 percent of failures in metals are due to fatigue. Therefore, different methods and approaches are developed to estimate the fatigue life of metallic parts. In this research, a case-hardened steel splined shaft is studied to estimate the fatigue life that the shaft will withstand before failure. The purpose of the research is to develop an advanced fatigue prediction method for splines.A static experimental test was performed on the splined shaft for analyzing the load-strain behavior of the shaft and determining the suitable load cases of the study. A dynamic test of pure torsional load was carried out to collect experimental results for validating the generated fatigue methods and investigating the failure behavior of the shaft. Stress analysis was performed on the part for investigating critical areas and the effect of the different spline teeth designs on the resulting stress. Two finite element models were analyzed using two software, MSC Marc software with a geometry of straight spline teeth and Spline LDP with an involute spline teeth model. DIN 5466-1 spline standard’s analytical solution was used for verification purposes. Stress and strain-based approaches were used to estimate fatigue life. The most suitable method was evaluated against experimental test results.The research findings show that the most critical stress areas on the shaft are the spline root fillet and relief. When the part fails due to fatigue the crack initiates at the root fillet and propagates to the relief. It is also shown that involute teeth spline gives higher stress than straight teeth for the same load due to less contact area.The conclusion of the research could be summarized in: the stress-based method (Wöhler curve) is giving good accuracy and proved a reliable method. While among six different approaches used of strain-based methods, four-point correlation method is giving the best correlation to test results. Hence, it is recommended to use four-point correlation method for fatigue analysis for its accuracy and for considering both elastic and plastic behavior of the material.

The main objective of this paper is to equip the trade policy analyst with an appropriate method of seasonally adjusting trade data with weekly observations. To that end, a structural time series model containing a trend, seasonal and irregular component is specified. The seasonal component is represented by a time-varying periodic spline. Casting the model in state-space form enables time-varying parameters as well as use of the powerful Kalman filter for trend estimation. The resulting trend can then be interpreted as a seasonally adjusted series. A simulation exercise shows that the correct trend is identified with an average absolute error of 0.4 percent. An application to Swedish imports during 2017-2021 shows that the model produces a reasonable trend estimate when applied in 'real-time' and that its application is preferred to smoothing the series using a simple moving average.

In the representation of scattered data by smooth pp (:= piecewise polynomial) functions, perhaps the most important problem is to find an optimal triangulation of the given sample sites (called vertices). Of course, the notion of optimality depends on the desirable properties in the approximation or modeling problems. In this paper, we are concerned with optimal approximation order with respect to the given order r of smoothness and degree k of the polynomial pieces of the smooth pp functions. We will only consider C1 pp approximation with r = 1 and k = 4. The main result in this paper is an efficient method for triangulating any finitely many arbitrarily scattered sample sites, such that these sample sites are the only vertices of the triangulation, and that for any discrete data given at these sample sites, there is a C1 piecewise quartic polynomial on this triangulation that interpolates the given data with the fifth order of approximation.

In this article, we study the construction of piecewise linear prewavelets over type-2 triangulations. Different from a so-called semi-prewavelet approach, we investigate the orthogonal conditions directly and obtain parameterized prewavelets with a smaller support. The conditions for parameterized prewavelet basis on the parameters are also given.

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Paper A: In this paper, the development and implementation of a contact algorithm based on C2-continuous surface representations is discussed. In 3D contact simulations involving models with arbitrarily curved surfaces (as in the case of vessel walls), the discretization of the contact surfaces by means of facet-based techniques could lead to numerical instabilities and finally loss of quadratic convergence. These instabilities arise mainly due to the sliding of contractor (slave) nodes over the boundaries of target (master) contact facets, where jumps of the normal vector are experienced. The paper addresses successfully this problem, by discretization of the target surfaces by means of C2-continuous parameterization schemes. Initially, the uniform cubic B-spline surfaces are introduced. Next, in an attempt for more accurate representations of the geometric models of the contact surfaces, a new parameterization based on the expression of cubic B-splines is developed. The two approaches are implemented into a finite element framework and more specifically, into the multipurpose finite element analysis program FEAP. The special merits of the developed algorithms and the advantages of the smooth surfaces over facet-based approaches are exhibited through a classical contact mechanics problem, considering incompressibility, finite deformations and large slidings. Next, a simulation of balloon angioplasty with stenting is presented, where the contact between both medical devices (balloon and stent) with the arterial wall is modeled. The arterial wall is modeled in this first approach, as hyperelastic, homogeneous, isotropic, while a cylindrically orthotropic model is developed to capture the nonlinear, anisotropic behavior of the balloon catheter under pressure. Two stents with the same geometry but different strut thickness, are studied. Both are considered elasto-plastic. The performed simulations point out the outcome of the balloon angioplasty and stenting in terms of luminal gain and mechanical strains. Finally, a comparison between the two stent configurations is presented. Paper B: The second paper makes use of the contact tool developed in Paper A and focuses on the changes of the mechanical environment of the arterial wall due to stenting, as a function of a set of stent design parameters. In particular, Paper B presents a detailed geometric and material model of a postmortem human iliac artery, composed by distinct tissue components, each associated with specific mechanical properties. The constitutive formulation for the artery considers anisotropic, highly nonlinear mechanical characteristics under supraphysiological loadings. The material and structural parameters of the arterial model are obtained through uniaxial tensile tests on stripes extracted from the several arterial tissues that form the stenosis, axially and circumferentially oriented. Through cooperation with a well-established stent manufacturing company, an iliac stent was acquired. The dimensions of the stent are measured under a reflected-light microscope, while it is parameterized in such a way as to enable new designs to be simply generated through variations of its geometric parameters. The 3D balloon-stent-artery interaction is simulated by making use of the smooth contact surfaces with C2-continuity, as previously mentioned. Next, scalar quantities attempt to characterize the arterial wall changes after stenting, in form of contact forces induced by the stent struts, stresses within the individual components and luminal change. These numerically derived quantities allow the determination of the most appropriate stent configuration for an individual stenosis. Therefore, the proposed methodology has the potential to provide a scientific basis for optimizing treatment procedures, stent material and geometries on a patient-specific level. / <p>QC 20101118</p>

The present study proposes a novel approach to Coverage Path Planning for unmanned aerial vehicle (UAV) inspired by the Orienteering Problem. The main goal is to develop an algorithm suitable for Search and Rescue Missions, which can produce a search pattern with dynamical constrains, that is not limited to the traditional back-and-forth motion or spiral patterns. This method leads to a more flexible and diverse coverage of the Area of Interest. In order to generate dynamically correct trajectories, we utilize cubic splines as motion primitives to solve the Orienteering Problem. To accomplish this, we implement and test three different types of cubic splines, namely Catmull-Rom, Freya, and B-splines. To determine the coverage of the search area, the sensor's projection (footprint) is evaluated along the spline trajectory onto a costmap. This method accounts for the footprint's orientation and size, which depend on the UAV's attitude to some extent. This version of the Orienteering Problem using splines for dynamical control and calculating coverage, we call the Mapping Motion Orienteering Problem (MMOP). \\The heuristic method Simulated Annealing is used to address the combinatorial challenges of the MMOP, and two cost functions are tested for optimization. The study shows that the choice of spline has a significant impact on the algorithm's efficacy, and B-splines are the most effective in generating dynamic and adaptable trajectories. However, the study also shows that the Simulated Annealing algorithm with identical settings produced varied resulting paths. Finally, further research is needed to solve the challenges faced with the computational time, which heavily depends on factors such as the sampling rate for the footprint along the path and the resolution of the costmap and footprint itself.

In this thesis, all the possible semi-prewavelets over uniform refinements of regular triangulations have been studied. A corresponding theorem is given to ensure the linear independence of a set of different pre-wavelets obtained by summing pairs of these semi-prewavelets. This provides efficient multiresolutions of the spaces of functions over various regular triangulation domains since the bases of the orthogonal complements of the coarse spaces can be constructed very easily.

Many computer graphic API’s, including OpenGL, emphasize modeling with rectangular patches, which are especially useful in Computer Aided Geomeric Design (CAGD). However, not all shapes are rectangular; some are triangular or more complex. This paper extends the OpenGL library to support the modeling of triangular patches, Coons patches, and Box-splines patches. Compared with the triangular patch created from degenerate rectangular Bezier patch with the existing functions provided by OpenGL, the triangular Bezier patches can be used in certain design situations and allow designers to achieve high-quality results that are less CPU intense and require less storage space. The addition of Coons patches and Box splines to the OpenGL library also give it more functionality. Both patch types give CAGD users more flexibility in designing surfaces. A library for all three patch types was developed as an addition to OpenGL.