# TBM250 The Finite Element Method

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#### Showing course contents for the educational year 2014 - 2015 .

Course responsible: Tor Anders Nygaard
Teachers: Anders Myhr
ECTS credits: 10
Faculty: Department of Mathematical Sciences and Technology
Teaching language: EN, NO
(NO=norsk, EN=Engelsk)
Limits of class size:

70

Teaching exam periods:
This course starts in the August block. This course has teaching/evaluation in August block and the Autumn parallel
Course frequency: Annually
First time: Study year 2008-2009
Preferential right:

Technology students (M-MPP, M-BA, M-IØ).

Course contents:
Central topics are: Terminology, direct method for element matrices, compatibility, equilibrium, system matrices and boundary conditions. Galerkin method and interpolation functions. Energy methods. Derivation of structural dynamics matrices for beam elements. Solution algorithms. Solution of simple problems by hand and programming. Use of commercial software packages. Beam elements, plate/shell elements and volume elements. Boundary conditions and symmetry. Convergence criteria. Sources of errors and singularities. A number of compulsory problems must be solved in order to pass the course.
Learning outcome:

Having passed the course, the students will have gained basic understanding of how to use the Finite-Element-Method (FEM) in solving practical problems. This class also provides training in problem solving using commercial FEM- software packages.

Learning activities:
The course is based on a combination of lectures, demonstrations and exercises.
Teaching support:
The subject teachers are available, via e-mail or during office hours, for assistance in connection with exercises. Exercises are carried out under the guidance of both the subject teacher and with assistance from others at the department.
Syllabus:
The lecture notes cover the main aspects of the class. Recommended, but not compulsory supporting literature: Huebner et al: The finite element method for engineers (John Wiley and Sons, inc), ISBN 0-471-37078-9 : Introduction. Matrix algebra. Appendiks A, Ch 2.4, 2.5 Direct method applied to static beam systems. 1, 2.1, except triangular element, 2.2.4, 2.3 - 2.3.3 Boundary conditions 2.3.4 Math review, integration 1D og 2D. Notes Galerkins method for derivation of element equations. Ch 4 except variational methods in 4.2.2, ch 4.2.3 Elements and interpolation functions, with emphasis on cubic Hermite polynoms 5.1 - 5.8.1 Derivation of matrices for beam elements by the Galerkin method. Notes (not treated in book). Elasticity problems, 6.1 - 6.2.2. Structural dynamics, 6.7.1. Derivation of mass matrices for beam elements by the Galerkin method. Notes (not treated in book) Eigen frequencies 6.7.2. Examples Transient response by modal superposition 6.7.3. Structural damping (notes). Examples Symmetry, boundary conditions, grid generation, errors and singularities 10.1 - 10.6.5 Additional material is handed out throughout the class.
Prerequisites:

MATH111, MATH112, MATH113, FYS101, FYS102, FYS110, TBM120, INF120.

Recommended prerequisites:
Mandatory activity:

Compulsory exercises/problems.

Assessment:
Failed/Pass, based on exercises/compulsory problems. To pass the course, all compulsory problems have to be submitted  before the deadlines and approved.