## Graduate Research

### Publications

- A Comparative Study of Maritime Operations in India, H. Mukundan, Master's Thesis
in Ocean Systems Management, February 2007.

- Riser Modal Identification in CFD and Full-Scale Experiments, D. Lucor, H. Mukundan and M. Triantafyllou, Journal of Fluids and Structures, (In Press).
- Intersections With Validated Error Bounds For Building Interval Solid Models, H. Mukundan, K. H. Ko and N. M. Patrikalakis, ASME 25th Computers and Information in Engineering Conference (CIE), Long Beach, California, USA, September 2005.
- DNS-based Multi-Modal Decomposition of VIV, D. Lucor, H. Mukundan and M. Triantafyllou, Fourth Conference on Bluff Body Wakes and Vortex Induced Vibrations (BBVIV4), Santorini, Greece, June 2005.
- Surface
- Surface Intersection with Validated Error Bounds, H. Mukundan, Joint Master's Thesis
with MIT Ocean Engineering and Mechanical Engineering Departments, February 2005.

- Approximation of Involute Curves for CAD-System Processing,
F. Higuchi, S. Gofuku, T. Maekawa, H. Mukundan, and N. M. Patrikalakis, Engineering with Computers, 2007.
To appear.

- Tracing
Surface Intersections with a Validated ODE System Solver,
H. Mukundan, K. H. Ko, T. Maekawa, T. Sakkalis, and N. M. Patrikalakis, Proceedings of the Ninth EG/ACM Symposium on Solid Modeling and
Applications, G. Elber and G. Taubin, editors. Genoa, Italy, June 2004.
Eurographics Press.

- Surface
to Surface Intersections, N.
M. Patrikalakis, T. Maekawa, K. H. Ko, and H. Mukundan. Computer-Aided
Design and Applications, Vol. 1, No. 1-4, pp. 449-458, 2004.

- Surface
to Surface Intersections, N. M. Patrikalakis, T. Maekawa, K. H. Ko and H. Mukundan, International CAD Conference and
Exhibition, CAD'04. L. Piegl, editor. Pattaya Beach, Thailand, May
2004.

**Descriptions**

**Research Topic 1: Surface-Surface Intersections**

Complex CAD models permeate all walks of our life. For example, the delivery of the Boeing 777 airplane has been hailed in the popular press as the first production of a 'paperless' airplane, meaning that computerized models supplanted the traditional paper drawings of the engineering design room. Surface to surface intersection is a fundamental process required to build and interrogate such complex CAD models. Specifically intersections are needed in representing complex objects using the boundary representation (B-rep) method, in finite element discretization, computer animation, feature recognition, manufacturing simulation, numerically controlled machining, collision avoidance and scientific visualization for implicitly defined objects and for contouring multivariate functions that represent some properties of a system. The next ambitious step is to eliminate many of the physical prototypes used for destructive testing and engineering analyses prior to releasing an airplane. These tests on physical prototypes are expensive. An appealing, cost-effective alternative is to reliably simulate the complex behavior of turbulence, stress and strain on computerized geometric models of these aircraft. Progress towards that goal has been delayed by inaccuracies introduced in the geometric input to these simulations, specifically along intersection boundaries.

The idea is to define new representations for intersecting rational parametric surfaces (splines) within computer-aided design (CAD) geometric objects. 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. A method to achieve a continuous gapfree boundary with a definite numerically verified upper bound for the intersection curve error in parameter space was developed. 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).

Research Topic 2: Vortex Induced Vibrations

Research Topic 2: Vortex Induced Vibrations

Vortex-induced vibration (VIV) of ocean structures is a major factor affecting all stages of development of offshore structures (conceptualization, design, analysis, construction and monitoring) and governs the arrangement of risers, details during fabrication, method of installation and instrumentation. Advances to deeper waters in search for crude oil has resulted in multi-billion dollar offshore projects off the Gulf of Mexico, for example: Independence Hub (2450m), Atlantis (2100m), Nakika (2000m), Thunder Horse (1900m), Hoover/Diana (1400m) to name a few. Under such water depths, long flexible cylinders are increasingly required (umbilics, risers, conductor tubes, pipeline spans), and prediction of VIV response increasingly important.

Historically, the complex problem of VIV (fluid-structure interaction) is subdivided into two simply stated problems: a hydrodynamics problem which quantifies the action of the fluid on the structure, and secondly a structural dynamics problem, which predicts the response of the structure given excitation from the fluid. This research project hope to make significant improvements in predicting VIV response or long flexible cylinders.

Historically, the complex problem of VIV (fluid-structure interaction) is subdivided into two simply stated problems: a hydrodynamics problem which quantifies the action of the fluid on the structure, and secondly a structural dynamics problem, which predicts the response of the structure given excitation from the fluid. This research project hope to make significant improvements in predicting VIV response or long flexible cylinders.

## Under Graduate Research

### Publication

- Finite Element Analysis of a Rudder, Mukundan, H., Undergraduate Thesis for the completion of Bachelor of Technology in Ocean Engineering and Naval Architecture, July 2002.

### Description

**Brief history of the reseach topic.**

The first part of my
project deals with finding out the possible reason for the failure of
rudders. This essentially involves a linear static analysis and leads
to the question of dynamic amplification. I have tried to answer the
question of modelling the rudder in water, which brings us to the
concept of added mass. I have proposed a new way or method for the
modelling of added mass and added mass moment of inertia.

The second part is a kind of parametric analysis on the variation of rudder Eigen frequency as a function of the Torsional stiffness due to the steering gear and also as a function of the depth of immersion of the rudder in water.

A formula has been proposed to evaluate the first Torsional mode natural frequency of the rudder. This formula is verified for the case of two rudders also.

The fourth part of my project is to find out the share of bending moment which the rudder trunk receives from the stock. I have done a non linear contact analysis which gives us the force and wherefrom we can get the moment.

I hope that my work will be useful for people needing information on Rudder Structural strength calculation.

The second part is a kind of parametric analysis on the variation of rudder Eigen frequency as a function of the Torsional stiffness due to the steering gear and also as a function of the depth of immersion of the rudder in water.

A formula has been proposed to evaluate the first Torsional mode natural frequency of the rudder. This formula is verified for the case of two rudders also.

The fourth part of my project is to find out the share of bending moment which the rudder trunk receives from the stock. I have done a non linear contact analysis which gives us the force and wherefrom we can get the moment.

I hope that my work will be useful for people needing information on Rudder Structural strength calculation.