Course syllabus for Finite element simulations in design

• Summarize what the Finite Element Method (FEM) is and exemplify what it could be used for.
• Describe the theoretical basis of FEM and explain strong form, weak form, and FE-form.
• Compare FEM to Finite Element Analysis (FEA) and illustrate the steps involved in each.
• Identify and choose relevant boundary conditions for a given problem. 
• Select and motivate the appropriate choice of element type for a given analysis. 
• Judge the quality of a given mesh. Can identify and motivate regions where the mesh density must be high.
• Explain essential and natural boundary conditions, also list these conditions for all studied elements. Exemplify boundary conditions of mixed type. 
• Recognize the governing equations for different mathematical models and explain their constituents.
• Perform a convergence study and evaluate the results.
• Derive FE-equations for linearized buckling and free vibration.
• Construct FE-models and perform: 
• static structural analysis to determine deformations, stresses, and strains.
• linearized buckling analysis to estimate critical buckling loads and buckling modes.
• free-vibration analysis to estimate natural-frequencies and modal shapes.
• steady-state thermal analysis to determine temperature and heat flow.
• sequential thermo-mechanical analysis to determine thermal stresses.
• Use FEA to guide the design of a component, with respect to given criteria, in an iterative process.
• Summarize the following element types: bars, beams, plates, shells, 2D solids (plane stress/strain, axisymmetry) and 3D solids.
• Explain the difference between linear and nonlinear problems and how they are solved. List sources leading to a nonlinear FE-problems.
• Set up, solve and evaluate results from FEA containing:
• Contact formulations (Penalty, Lagrange, Augmented-Lagrange). 
• Linear material models (Hooke's law, Fourier's law), elastic-plastic models (elastic-ideally-plastic, linear hardening), fiber reinforced composites (transverse isotropy).
• Prepare CAD-geometry for FEA (defeaturing and repairing).
• Explain what topology optimization is and be able to perform an analysis where the compliance is minimized. 

• Theoretical basics of the Finite Element Method (FEM).
• Practice using commercial software to set up and perform Finite Element Analysis (FEA). 
• Common types of FE-analyses: static structural analysis, steady-state heat flow, linearized buckling, natural vibration analysis.
• Iterative design based on one or more criteria: stiffness/deformation, allowable stress, fatigue, weight, etcetera.
• Introduction to non-linear problems.
• Modeling aspects: choosing boundary conditions (loads and supports), preparing CAD geometry, meshing, choosing element types, contact formulations. 
• Common material models for metals, polymers and fiber reinforced composites.
• Introduction to topology optimization.

The course contains about 40 h of lectures and about 30 h of computer labs. The lectures cover the theory and exemplify practical aspects of FEA. During the computer labs, students work on hand-in assignments under teacher supervision.

The course relates to the UN's sustainable development goals, especially:

• Goal 9: Industry, Innovation and Infrastructure
• Goal 11: Sustainable Cities and Communities
• Goal 12: Sustainable Consumption and Production

Will be notified prior to the course start. 

A written exam determines the final grade. To pass the course, all the computer assignments need to be approved.