Surface-surface intersection with validated error bounds

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 97-100).This thesis presents a robust method for tracing intersection curve segments between continuous rational parametric surfaces, typically rational polynomial parametric surface patches. Using a validated ordinary differential equation (ODE) system solver based on interval arithmetic, we obtain a continuous, validated upper bound for the intersection curve segment in the parametric space of each surface. Application of the validated ODE solver in the context of eliminating the pathological phenomena of straying and looping is discussed. We develop a method to achieve a continuous gap-free boundary with a definite numerically verified upper bound for the intersection curve error in parameter space. This bound in parametric space is further mapped to an upper bound for the intersection curve error in 3D model space, denoted as model space error, which assists in defining robust boundary representation models of complex three-dimensional solids. In addition, we also discuss a method for controlling this model space error so that it takes values below a predefined threshold (tolerance). Application of the above method to various examples is further demonstrated.by Harish Mukundan.S.M

VIV of marine risers : motion and force reconstruction from field and experimental data

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.Includes bibliographical references (p. 199-205).Vortex-induced vibration (VIV) of long flexible cylindrical structures enduring ocean currents is ubiquitous in the offshore industry. Though significant effort has gone into understanding this complicated fluid-structure interaction problem, major challenges remain in modeling and predicting the response of such structures. The work presented in this thesis provides a systematic approach to estimate and analyze the vortex-induced motions and forces on a marine riser, and develop suitable methods to improve riser VIV modeling and response prediction. In the first part of the thesis, a systematic framework is developed, which allows reconstruction of the riser motion from a limited number of sensors placed along its length. A perfect reconstruction criterion is developed, which allows us to classify when the measurements from the sensors contain all information pertinent to VIV response, and when they do not, in which case additional, analytical methods must be employed. Reconstruction methods for both scenarios are developed and applied to experimental data. The methods are applied to: develop tools for in-situ estimation of fatigue damage on marine risers; improve understanding of the vortex shedding mechanisms, including the presence of traveling waves and higher-harmonic forces; and estimate the vortex-induced forces on marine risers. In the second part of the thesis, a method is developed to improve the modeling of riser VIV by extracting empirical lift coefficient databases from field riser VIV measurements. The existing experiment-based lift coefficient databases are represented in a flexible parameterized form using a set of carefully chosen parameters. Extraction of the lift coefficient parameters is posed as an optimization problem, where the error between the prediction using a theoretical model and the experimental data is minimized.(cont.) Predictions using the new databases are found to significantly reduce the error in estimating the riser cross-flow response. Finally, data from a comprehensive experiment is utilized to show that the riser response is resonant in the harmonic component, but non-resonant in the third-harmonic component. It is shown that this happens because the spatial dependence of the third-harmonic fluid force component is dominated by the first-harmonic wavelengths. This finding has significant implications for modeling the higher-harmonic forces and the resulting fatigue damage estimation methodologies.by Harish Mukundan.Ph.D

A comparative study of maritime operations in India

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (p. 89-93).This thesis studies the maritime sector of India, specifically using China as a basis for comparison. Chinese economic impact is studied under the two major headings: the effective use of non-living and living resources. Next, an overview of the current maritime profile of India is presented followed by a comparative discussion to understand the reasons for India to lag behind China in the maritime field. The outlook for global shipping, taking into account the possibility of strong economic growth in India, is presented. This is performed by comparing the expected impact on global shipping due to India, to the one observed in 2004 due to China. This comparative analysis foresees a plausible shipping boom in select cargo types namely liquid and dry bulk cargo. No boom in containers shipping is expected. Conditions of expected global shipping growth rates and Indian growth rates which may yield another shipping boom are presented.by Harish Mukundan.S.M

INTERSECTIONS WITH VALIDATED ERROR BOUNDS FOR BUILDING INTERVAL SOLID MODELS

Interval arithmetic has been considered as a step forward to counter numerical robustness problem in geometric and solid modeling. The interval arithmetic boundary representation (Brep) scheme was developed to tackle this problem. In constructing an interval B-rep solid, robust and efficient computation of intersections between the bounding surfaces of the solid is a critical issue. To address this problem, a marching method based on a validated interval ordinary differential equation (ODE) solver was proposed, motivated by its potential for the interval B-rep model construction. In this paper, we concentrate on the issue of error control in model space using the validated ODE solver, and further explain that the validated ODE solver can be used in the construction of an interval B-rep solid model using such an error control

Abstract Approximation of Involute Curves for CAD-System Processing

In numerous instances, accurate algorithms for approximating the original geometry is required. One typical example is a circle involute curve which represents the underlying geometry behind a gear tooth. The circle involute curves are by definition transcendental and cannot be expressed by algebraic equations, and hence it cannot be directly incorporated into commercial CAD systems. In this paper an approximation algorithm for circle involute curves in terms of polynomial functions is developed. The circle involute curve is approximated using a Chebyshev approximation formula [11], which enables us to represent the involute in terms of polynomials, and hence as a Bézier curve. In comparison with the current B-spline approximation algorithms for circle involute curves, the proposed method is found to be more accurate and compact, and induces fewer oscillations