Explicit fourth-order stiffness representation in non-linear dynamics

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

139 Downloads (Pure)


In momentum-based time integration methods, the internal forces appear naturally as an approximate representation of the time integral of the internal forces over the integration interval. It is highly desirable that this force integral also represents the increment of the internal energy. A simple global form of the effective internal force is presented, in which it is represented by its algebraic mean value plus a higher order term in the form of the product of the increment of the tangent stiffness matrix at the interval end-points and the corresponding displacement increment. This explicit representation is of fourth order, and leads to the exact energy increment for systems with quartic internal energy function.
Original languageEnglish
Title of host publicationProceedings of the 26th Nordic Seminar on Computational Mechanics
EditorsA. Logg, K.A. Mardal
Number of pages4
PublisherCenter for Biomedical Computing, Simula Research Laboratory
Publication date2013
ISBN (Print)978-82-92593-12-7
Publication statusPublished - 2013
Event26th Nordic Seminar on Computational Mechanics - Oslo, Norway
Duration: 23 Oct 201325 Oct 2013
Conference number: 26


Conference26th Nordic Seminar on Computational Mechanics
Internet address


  • Time integration
  • Energy conservation
  • Non-linear dynamics

Fingerprint Dive into the research topics of 'Explicit fourth-order stiffness representation in non-linear dynamics'. Together they form a unique fingerprint.

Cite this