Finite Element Methods in Strength Analysis

The course gives the theoretical framework for the finite element method, and formulates elements for beams, plates, shells, axisymmetric and three-dimensional structures. Element properties, convergence requirements and modelling errors are discussed. The course emphasizes modelling, choice of element type, discretization, introduction of loads and boundary conditions, accuracy, robustness and results control. An introduction in using Abaqus for two- and three-dimensional structures and typical structural details will be given.

The course Finite Element Method for strength analysis shows how the basic linear theory behind the method combined with numerical calculations leads to the key variables such as displacements, strains and stresses in various structures, primarily the membrane, plate, shell and solid structures. This course constitutes a necessary basis for the secondary topic Nonlinear Finite Element analysis. The finite element method for strength analysis has the following learning objectives: Knowledge: - Establishment of interpolation polynomials in terms of natural coordinates for isoparametric elements - Requirements for convergence and accuracy - Establishment of stiffness relationship for the C0-elements and C1-elements - Numerical integration of stiffness matrix and load vector - Calculation of stresses and strains in the element - Elements convergence properties and ability to represent various deformational patterns in order to choose proper element type and density of the Finite Element mesh - How elements shape and integration of the stiffness matrix affects the accuracy and convergence properties. Skills: The candidate is able to: - Derive the element stiffness relation - Calculate the stiffness matrix and load vector - Establish interpolation polynomials for C0 Lagrange and Serendipity elements and C1 plate elements - Transform displacements, stresses and strains - Use generalized displacements - Establish and check a Finite Element model - Use the computer program Abaqus to solve linear strength two- and three-dimensional structural problems. General competence: The candidate master: - The general basis for the displacement-based finite element method - The computational scheme in linear element calculations - Understanding of the consequences of the assumptions made in the element types upon accuracy and convergence - Present, interpret and judge whether the Finite Element results are reasonable or not.

Lectures and homework assignments (including analytical and computational problems). 2/3 of the homework assignments must be approved to take the final exam. If there is a re-sit examination, the examination form may be changed from written to oral. The lectures and exercises are in English when students who do not speak Norwegian take the course. If the teaching is given in English the Examination papers will be given in English only. Students are free to choose Norwegian or English for written assessments.