Course content

Numerical solution methods in nonlinear finite element analysis. The course focus mainly on modeling of material and geometrical nonlinearities, and numerical methods for simulation of these phenomena. Implicit and explicit methods are presented, with main focus on implicit methods and equilibrium iterations. Simple finite elements are used to exemplify derivations of tangent stiffness relationships.

Learning outcome

Knowledge:
The candidates will have a good understanding of the most common stress and strain measures used in nonlinear finite element programs, and how these are employed in different finite element formulations that account for nonlinear geometry. Further, they will have detailed knowledge on central nonlinear material models (elastic and elastoplastic), including typical numerical methods that are used in implementation of the models. The students will have detailed knowledge of solution methods for static problems, and some knowledge on solution methods for dynamic problems.

Skills:
The candidates will be able to derive nonlinear finite element formulations from the governing equations, where geometric and material nonlinearity are accounted for. They can assess and quality assure that the computed results are realistic and have a reasonable level of accuracy.

General competence:
The candidates can apply advanced commercial nonlinear finite element software with a good understanding of the presumptions and assumptions the software is based on. They can assess the quality of the simulation results. If necessary, they should be able to develop their own nonlinear finite element program. The students have a good basis for reading scientific articles within the subject. Furthermore, they are able to publish research at an international level, where use and development of nonlinear finite element software is central.

Learning methods and activities

Lectures and mandatory homework assignments. 2/3 of the homework assignments must be approved to take the final exam. 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. To pass the course a score of at least 70 percent is required.

Compulsory assignments

• Exercises

Recommended previous knowledge

KT8305 Continuum Mechanics or similar.

Course materials

T. Belytschko, W.K. Liu and B. Moran, Nonlinear Finite Elements for Continua and Structures, Wiley, 2000
B. Skallerud: Compendium.