MM8100 - Calculus of Variations and Variational Principles for Continuum based Analysis Software


Examination arrangement

Examination arrangement: Oral exam
Grade: Passed / Not Passed

Evaluation Weighting Duration Grade deviation Examination aids
Oral exam 100/100 1 hours E

Course content

The course consists of variational calculus and the variational principles that are the foundation for most continuum based simulation programs. This also includes tensor theory and the most common tensors used in linear and nonlinear solid mechanics. Topics are: Euler Equation. Natural and essential boundary conditions. General constraint conditions. Minimum potential energy. Hellinger-Riessner and Hu-Washizu principle. Generalized multifield principles. Tensor algebra. Co-variant and contra-variant vector systems. Stress and strain measures. Additional topics may be selected for the individual candidates. A passing grade is required on the project work before taking the exam.

Learning outcome

Knowledge: This subject are aimed give comprehensive understanding of the theory behind simulation software.

Skills: Ability to comprehend theory from multiple sources, and be able to combine and expand on this for new applications.

General Competence: Be able to communicate and present obtained knowledge.

Learning methods and activities

Guided private study and project work. To pass the course a score of at least 70 percent is required.

Compulsory assignments

  • Project work

Further on evaluation

For a re-take of an examination, all assessments during the course must be re-taken.

Required previous knowledge

All students taking this course must be enrolled in a PhD program at NTNU or a different university.

Course materials

This information are given at the beginning of the course.

Credit reductions

Course code Reduction From To
DIO2001 7.5
More on the course



Version: 1
Credits:  7.5 SP
Study level: Doctoral degree level


Term no.: 1
Teaching semester:  SPRING 2025

Language of instruction: English

Location: Trondheim

Subject area(s)
  • Technological subjects
Contact information
Course coordinator: Lecturer(s):

Department with academic responsibility
Department of Mechanical and Industrial Engineering


Examination arrangement: Oral exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Autumn ORD Oral exam 100/100 E
Room Building Number of candidates
Spring ORD Oral exam 100/100 E
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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