Credits: 7.5. Responsible teacher: Ralf Denzer. Prerequisites: Basic Courses in Mathematics, especially Calculus in Several Variables, and Solid Mechanics. Teaching: Lectures 28 h, problem sessions 28 h. Individual study: 150 h. Assessment: Written examination and compulsory assignment which are graded. Study period: vt2. Old course code: FHL064
To qualify for a final grade it is required that the project assignment is fulfilled. The report is graded on the scale 0 to 5 points.
Aims of the course
The finite element method (FEM) is a numerical method able to solve differential equations, i.e. boundary value problems. The method is today the most powerful numerical method within solid mechanics; this since arbitrary geometries and complex material models can be treated. Within the modern industry the finite element method is the key factor in many construction phases. The emphasis in the course in placed on the understanding of the fundamental principles of the FEM and its numerical issues. The course allows the participant to implement its own finite element program and thereby gain understanding of the method in great detail. Moreover, the course builds the corner stones for our Advanced Courses Computational Inelasticity FHLN05 and Non-Linear Finite Element Analysis FHLN20, Structural Optimization FHLN01 and Fracture Mechanics FHLN25.
Manifestation of the course
The course consists of a series of seminars starting with the so-called direct method where no mathematical reformulation is needed. After this introduction different field problems defined by differential equations are considered. To establish the finite element formulation the equivalent weak formulation will be introduced where use of weighted residual methods are made, special emphasis is placed on the Galerkin method. This treatment will lead to the FE-formulation. In this process of establishing the FE-formulation, both the mathematical treatment of the equations as well as the different key issues/approximations (isoparametric mapping, elements choices etc.) are discussed in detail.
Problem sessions are given parallel to the seminars were both the theoretical and numerical issues are discussed.
The project treat a structural problem by the finite element method. The project is presented in a written report, and the report is graded with respect to the technical contents. The structural and linguistic qualities of the presentations may also have an influence on the final grade --- positive or negative. The project work is carried through in groups of two students.
The format of the seminars is based on the assumption that the students have studied the material at hand in advance, so that a profound understanding can be achieved in discussion between teachers and students.
The course program is available here and the course schedule can be generated by TimeEdit.