Single-Course Engelsk 10 ECTS

Introduction to Finite Element Analysis

Overall Course Objectives

The Finite Element Method is one of the most widely used numerical methods for designing and optimizing components and processes in traditional machine industry, production, devices for medical and biomechanical applications (Life-sciences) as well as civil infrastructure. It is an essential tool with significant societal contributions to areas such as the green transition, the healthcare sector, and Industry 4.0.

Students of this course will get a fundamental understanding of the theoretical background of the finite element method and its application to industrial problems. Using commercial finite element software, students will be able to conduct thermal and structural analyses in 2D and 3D. By means of both theory and numerical experiments, the students will be able to grasp the breadth of its capabilities, but importantly also its limits. Particular emphasis is put on concepts of numerical modeling philosophy, such as understanding, evaluating and controlling the different sources of analysis errors.

See course description in Danish

Perform structural and heat transfer modeling using available finite element software.
Explain the theory behind the most common options provided in the graphical user interface of commercial finite element software.
Recall the most common types of finite element analyses and choose appropriately for a given problem.
Describe the different meshing strategies and techniques, and apply them appropriately in order to create accurate and efficient finite element models.
Choose one or more suitable finite element types for a specific analysis.
Describe input and output file formats used by finite element software, and modify finite element models by editing of such files.
Explain how imported CAD model descriptions can affect the generated finite element mesh, identify and fix issues with imported CAD geometries.
Perform system simplifications in terms of geometry, loads and boundary conditions in a finite element model to achieve the required accuracy while minimizing computation time.
Verify a model and evaluate its accuracy, based on simple hand calculations, finite element theory, and mesh convergence studies.
Explain the logistics behind the implementation of the finite element method for numbering of degrees of freedom and connection of elements.
Post-process and report finite element analysis results in a structured, clear, concise and informative manner.

The course is based on theoretical lectures, computer exercises and project work. Initially, the stiffness method is introduced as a practical approach to the finite element method for simple elements. Subsequently, the general theory of finite element is presented by covering the concepts of virtual work, shape functions and numerical integration. The most common element types found in finite element software are discussed and tested. Moreover, simple and more advanced boundary conditions are explained in detail. A series of practical aspects are also covered such as import of CAD geometries, meshing techniques, file formats and post-processing. The basic theory behind different analysis types are also presented as well as the most common types of linear solvers employed in finite element analysis. In the first group project the students program a very simple finite element model using the stiffness method. During the three weeks period in January a larger project work is performed using commercial software.

02002/02003/62646/41502/41534/41814, Comprehensive knowledge is expected within general stress and strain states (41502/41534 or similar), knowledge of heat transfer (41814), as well as good computer programming background (02002/02003/62646 or similar experience).

Lectures, exercises with use of software and hand calculations, project work. Hand-in projects are performed in groups of three students.