Explicit fourth-order stiffness representation in non-linear dynamics

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    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


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