(Created 2010-07-25.)
 THE FINITE ELEMENT METHOD - STRUCTURAL ANALYSIS VSMN30
Credits: 7,5. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course might be given in English. VSMN30 overlaps following cours/es: FHL064 and VSM040. Optional for: Pi4, Pi4bs, V4at, V4ko. Course coordinator: Kent Persson, kent.persson@byggmek.lth.se, Structural Mechanics. Prerequisites: VSMN25 The Finite Element Method - Flow Analysis and VSMA05 Structural Mechanics or FHL013 Solid Mechanics, Basic Course. Recommended prerequisits: VSMF05 Engineering Modelling: Analysis of Structures. The course might be cancelled if the number of applicants is less than 15. Assessment: A mid-term test and one design assignment. Home page: http://www.byggmek.lth.se.

Aim
The aim of the course is to continue the knowledge gained in the course ""Finite Element Method - Flow analysis" by giving detailed theoretical and practical knowledge to be able to model and analyse general solid mechanics problems described from a physical context. Problems within the field of engineering that will be studied are based on stresses, strains, 2- and 3-dimensional elasticity problems, beams and plates.

Knowledge and understanding
For a passing grade the student must

• be able to define linear static structural mechanics problems in 1d-3d and interpret their physical terms.

• from physical relations be able to formulate a mathematical model for the problem.

• be able to transfer a mathematical model, through the weak formulation, to a finite element formulation.

• be able to explain convergence, completeness and compatibility requirements for approximating functions.

• be able to describe the formulation of isoparametric elements and numerical integration.

• be able to define and utilise various types of boundary conditions and loadings.

Skills and abilities
For a passing grade the student must

• be able to create finite element models of real solid mechanics problems from a physical described context.

• be able to perform finite element analyses of various types of engineering problems.

Judgement and approach
For a passing grade the student must

• be able to analyse and interpret results from a finite element simulation.

• be able to estimate the reliability of a finite element analysis.

Contents
The course consists of lectures, exercise sessions and one compulsory design assignments. The knowledge from the course "Finite Element Method - Flow analysis" is increased by gradually introducing more advanced problems to this basic knowledge, such as, two- and three-dimensional solid mechanics problems. Solid mechanics problems that are studied: stresses and strains, 2 and 3D elasticity, beams and plates. At the end of the course the theory for isoparametric finite elements and numerical integration is introduced. The design assignment illustrate the procedure of transferring a design problem into a model suitable for finite element analysis.

Literature
Ottosen, N., Petersson, H.: Introduction to the Finite Element Method, Prentice Hall 1992.
Olsson, K.-G and Heyden, S.: Introduction to the finite element method, problems, Byggnadsmekanik, Lund 2001.
CALFEM ver. 3.4 - A finite element toolbox, KFS i Lund AB, 2004.