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  • Linked interpolation and strain invariance in finite-element modelling of micropolar continuum : doctoral thesis
    Grbčić, Sara
    At the core of this thesis is an alternative continuum theory called the micropolar(Cosserat) continuum theory, developed in order to describe the phenomena whichthe classical continuum theory is not ... able to describe. In this theory, in addition tothe displacement eld, there also exists an independent microrotation eld and, inorder to completely describe such a material, six material parameters are needed.In the framework of the nite-element method, new nite elements based on the micropolar continuum theory in both linear and geometrically non-linear analysisare developed using the displacement-based approach.In the linear analysis, both two- and three-dimensional set-ups are analysed. In 2Dnew families of triangular and quadrilateral nite elements with linked interpolationof the kinematic elds are derived. In order to assure convergence of the derivednite elements, they are modied using the Petrov-Galerkin approximation. Theirperformance is compared against existing conventional micropolar nite elementson a number of micropolar benchmark problems. It is observed that the linkedinterpolation shows enhanced accuracy in the bending test when compared againstthe conventional Lagrange micropolar nite element.Next, the weak formulation is extended to 3D and a rst-order hexahedral niteelement enhanced with the incompatible modes is derived. The element performanceis assessed by comparing the numerical results against the available analytical solutionsfor various boundary value problems, which are shown to be signicant forthe experimental verication of the micropolar material parameters. It is concludedthat the proposed element is highly suitable for the validation of the methodologyto determine the micropolar material parameters.In the non-linear part, rst- and second-order geometrically nonlinear hexahedralnite elements with Lagrange interpolation are derived. In order to test theperformance of the presented nite elements, a pure-bending non-linear micropolaranalytical solution is derived. It is observed that the elements converge to thederived solution. The elements are tested on three additional examples where thepath-dependence and strain non-invariance phenomena are detected and assessedin the present context. A procedure to overcome the non-invariance anomaly isoutlined.
    Vrsta gradiva - disertacija ; neleposlovje za odrasle
    Založništvo in izdelava - Rijeka : [S. Grbčić], 2018
    Jezik - angleški
    COBISS.SI-ID - 8658529

Nobena knjižnica v sistemu COBISS.SI nima izvoda tega gradiva (gre za elektronski vir ali pa poleg tiskane verzije obstaja tudi elektronska).
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