A Generalized Lanczos-QR Technique for Structural Analysis

S. Vissing

    Research output: Book/ReportPh.D. thesisResearch

    Abstract

    Within the field of solid mechanics such as structural dynamics and linearized as well as non-linear stability, the eigenvalue problem plays an important role. In the class of finite element and finite difference discretized problems these engineering problems are characterized by large matrix systems with very special properties. Due to the finite discretization the matrices are sparse and a relatively large number of problems also has real and symmetric matrices. The matrix equation for an undamped vibration contains two matrices describing tangent stiffness and mass distributions. Alternatively, in a stability analysis, tangent stiffness and geometric stiffness matrices are introduced into an eigenvalue problem used to determine possible bifurcation points. The common basis for these types of problems is that the matrix equation describing the problem contains two real, symmetric and sparse matrices.
    Original languageEnglish
    Place of PublicationAalborg
    PublisherDept. of Building Technology and Structural Engineering, Aalborg University
    Number of pages149
    Publication statusPublished - 1996
    SeriesEngineering Mechanics
    NumberSpecial Report No. 3
    VolumeR9606
    ISSN1395-7953

    Bibliographical note

    PDF for print: 154 pp

    Keywords

    • Effiecient Algorithms
    • Matrix Systems
    • Positive Matrices
    • Sparse Matrices
    • Structural Analysis
    • Lanczos-QR Technique

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