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  • The influence of compatibility equations of non-linear elasticity on convergence for spectral method solutions [Elektronski vir]
    Flajs, Rado, gradbeništvo
    In structural mechanics the stresses are of a primary interest. Due to the required regularity of the approximation it is ofteninconvenient to obtain the stresses from the displacement methods. Mixed ... and hybrid methods are thus proposed to avoid thisobstacle. The compatibility conditions should be fulfilled in order to obtain a unique solution. In this paper the compatibility equations of non-linear elasticity are considered. Despite its very long history, this issuehas not been satisfactorily resolved for non-simply-connected bodies until recently. Its well known however, that thecompatibility conditions are linearly dependent.The aim of the present contribution is to include the spectral methods [2] in order to improve the finite element solution procedure for the reversible elastodynamics problem, formulated for a large strain deformation with the deformation gradient tensor as one of the basic unknowns. In the case of the small strains the components of the deformation gradient tensorare of different magnitude. The main contribution is the derivation of the solution strategy in order to take this information into account. Applying this strategy to the implicit time integration method the exponent decrease of the condition numbersof the iteration matrices was achieved. Consequently the accuracy of the calculations should increase and the convergencefor spectral method solutions should considerably improve. The theoretical findings are confirmed by a selected numerical example from structural mechanics.
    Source: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), November 2019 [Elektronski vir] (Vol. 19, iss. 9. nov., 2020, Str. 1-2)
    Type of material - conference contribution ; adult, serious
    Publish date - 2020
    Language - english
    COBISS.SI-ID - 60083459

    Link(s):

    https://onlinelibrary.wiley.com/doi/epdf/10.1002/pamm.202000303
    DOI

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