I strukturmekanikk simuleres ofte kompliserte strukturer ved bruk av numerisk diskretisering av grunnligningene. Regulering av modellene er avhengig av pålitelige simuleringsverktøy der de numeriske tilnærmelser arver de viktigste fysiske/geometriske egenskapene fra de kontinuerlige modellene. Hovedmålet i samarbeidet vil være å takle konkrete problemstillinger fra, for eksempel, marine systemer, utvikle og analysere modellene fra et geometrisk synspunkt og deretter designe numeriske metoder som er godt egnet for å gjøre troverdige simuleringer av de utvalgte fenomener. Stabilitet og effektiv implementasjon av de diskrete modellene vil også vektlegges.
Det finnes mange aktuelle problemstillinger innenfor marine operasjoner hvor dette er av interesse, spesielt marine systemer som er kombinasjoner av fleksible systemer og stive legemer.
A collaboration between the Departments of Engineering Cybernetics and Mathematical Sciences.
The computer simulation of complicated real life mechanical structures is achieved by first describing the physical problem with models of differential equations and then performing a numerical discretization. Testing and validation of the control strategies applied to operate the mechanical structures are essential goals of the simulations.
Control operations first come into play in the modeling phase, where they are designed based on physical principles and analyzed with mathematical tools. Their faithful reproduction under discretization is depending on qualitatively correct numerical tools able to transfer the most important physical and geometrical features from the continuous model to its discrete numerical approximation.
This project will foster a collaboration between mathematicians and control engineers. Concrete problems from marine control systems of interest in offshore operations will be addressed, and the models will be analyzed and developed also from a geometric point of view. Eventually the design of numerical schemes which are well suited for accurate simulations of the chosen phenomena will be undertaken. Stability and efficient implementation of the discrete models will also be studied.
There are several challenging problems within the field of marine operations where this methodology can be applied. Especially marine systems where flexible and rigid bodies interact.
Good programming skills and solid background in mathematics with specialization in numerical analysis and/or control engineering are very important prerequisites for this post.
For more information on the type of problems which will be addressed see under publications.
The successful candidate will be jointly supervised by stuff in the Departments of Engineering Cybernetics and Mathematical Sciences.
- Offshore Pipelay dynamics. PhD thesis G.A. Jensen (2010).
- Geometric modeling and simulation of rigid body and rod dynamics. PhD Thesis N. Sæfstøm (2009).
- Hamiltonian and multi-Hamiltonian formulation of a rod model using quaternions. Numerics No.8/09. Celledoni and Sæfstøm, to appear in CMAME.
- Modeling and control of suspended pipeline during pipe-lay operation based on a finite strain beam model, Jensen, Sæfstøm, Fossen, Nguyen. OCEAN ENGINEERING Volume: 37 Issue: 4 Pages: 365-377.
- Jensen, Sæfstrøm, Fossen, Nguyen, Modelling and Control of Suspended Pipeline during Pipe-lay Operation Based on a Finite Strain Beam, Proceedings of the American Control Conference; 2009-06-10 - 2009-06-12. IEEE/IET, 4717 - 4722, 2009, ISBN: 978-1-4244-4524-0 ISSN: 0743-1619, St. Luis.
- A geometricaly exact rod model and its Hamiltonian structure, Celledoni and Sæfstrøm, Proceedings of the ICNAAM conference 2009.
- FRB-FORTRAN routines for the exact computation of free rigid body motions, E. Celledoni and A. Zanna, ACM ToMS vol 37 nr. 2 (2010).
- N. Säfström, G.A. Jensen, T.D. Nguyen, T.I. Fossen, A Nonlinear Elastic Model Applied to Pipelay Operation in Ocean Engineering, In Proceedings of 21 Nordic Seminar on Computational Mechanics, NSCM-21.
- Professor Elena Celledoni (IMF)
- Professor Thor Inge Fossen (ITK)
- Dr. Gullik Jensen (ITK)
- Førsteamanuensis Anne Kværnø (IMF)
- Professor Carl M. Larsen (CeSOS)
- Dr. Tu Duc Nguyen (ITK)
- Professor Syvert Nørsett (IMF)
- Professor Brynjulf Owren (IMF)
- Dr. Niklas Säfström (IMF)
- Professor Asgeir Sørensen (CeSOS)
- Post doctoral fellow Olivier Verdier (IMF)
- Natalyia Ramzina (IMF)
We are organizing a one-day worshop on rigid body and rod dynamics. Modeling and simulation.
- September 2010. Takaharu Yaguchi, University of Tokyo,
Energy Preserving Methods based on Discrete Differential Forms.
- May 2010. Moody Chu, North Carolina State University,
Raleigh (USA), Semi-definite Programming Techniques for Structured Quadratic Inverse Eigenvalue Problems in Structural Mechanics.
- December 2009. Sigrid Leyendecker University of Kaiserslautern,
Structure Preserving Methods in Computational Multibody Dynamics and Optimal Control.