Engelska Studiehandboken kurser

Mechanical Engineering

MTM081 Computational Methods in Mechanics (F) 6.0 ECTS credits

DENNA SIDA FINNS OCKSÅ PÅ SVENSKA

General information about studying at Luleå university

TIMEPERIOD: Q 3

LANGUAGE: English/Swedish

EXAMINER
H O Åkerstedt Univ lekt

PREREQUISITES
Basic mathematical knowledge in real and complex analysis. Ordinary differential equations. Partial differential equations. Mechanics and continuum mechanics.

COURSE AIM
The aim is to get the student familiar with some approximate analytical and numerical methods of importance in solving problems in mechanics and continuum mechanics. The course should also give the student some practice in using MATLAB for numerical computations and MAPLE for symbolic computing.

CONTENTS
Finite difference methods for solution of differential equations (25%): Stability, convergence, vibrating string, heat conduction. Galerkin methods (20%): Weighted residuals, conventional Galerkin methods, FEM methods, Spectral methods. Approximate solution of differential equations (35%): Lindstedt-Poincares method, Renormalisation, Method of multiple scales. Power series solutions near singularities.WKB method, Liouville-Greens and Langers transformations. Matched asymptotic series, Boundary layers, inner and outer expansions, matching principles, composite solution. Chaos in mechanical systems (5%): Convection and Lorenz equations, strange attractors, discrete mappings, bifurcations, Feigenbaum numbers. Integrals (15%): Integration by parts, Laplaces method, stationary phase.

TEACHING
The education consists of lectures in which the basic mathematical concepts are introduced. To each topic the student is supposed to do some compulsory problems.

EXAMINATION
For grade 3 compulsory problems. For higher marks a written examination.
COURSE GRADE SCALE: U,3,4,5

ITEMS/CREDITS


Laboratory work                                             	1.5ECTS
Writen exam                                                 	4.5ECTS

COURSE LITTERATURE
Bush A.W: Perturbation methods for engineers and scientists, CRC press. Fletcher C.A.J: Computational Techniques for Fluid Dynamics. Vol I, Springler Enander o Hägglund: Användarhandledning för MATLAB

REMARKS

Last modified : 97-06-05 by Jan Lindberg

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