Finite Element Methods in Structural Engineering

Mathematical formulation of the finite element method for linearly elastic solids. Element and system analysis. Isoparametric mapping and numerical integration of the stiffness relation. Accuracy and convergence. Bar elements, plane stress and plane strain elements, axisymmetric elements, solid elements, beam and plate elements with shear deformation, thin-plate elements, and simple shell elements. Case studies with ABAQUS covering key topics in the course, including modelling, selection of element type and discretization, application of loads and introduction of boundary conditions, as well as accuracy, robustness, and control of results.

Knowledge: The candidate shall be able to explain the mathematical basis of the finite element method, the accuracy and convergence properties of isoparametric elements, and how the finite element method can be used in the analysis of elastic bodies.

Skills: The candidate shall be able to carry out strength analysis of components, details, and structures with the finite element method, select the correct element type and mesh size, perform convergence studies, and check the validity of the numerical model.

General competence: The candidate shall be able to explain and critically discuss the use of the finite element method in the analysis of structures, and check, interpret and present results from stress analysis with the finite element method.

Digital competence: Skilled use of finite element program (ABAQUS) for strength analysis of structures: Modeling, linear elastic solids, plane stress and plane strain elements, axisymmetric elements, solid elements, plate elements, shell elements, interpretation of results, accuracy and convergence. Programming with Python: ABAQUS scripting interface.

Sustainability competence: The course serves to give the students appropriate skills to design safe and cost-effective structures.

Lectures, homework assignments and case studies with Abaqus. 2/3 of the case studies must be approved to be admitted to the exam. Teaching is given in English if students who do not speak Norwegian take the course. If the teaching is given in English, the exam papers are only given in English. The student's answers can be in Norwegian or English.