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  • 1.
    Tahaei Yaghoubi, Saba
    et al.
    Aalto University, Finland.
    Balobanov, Viacheslav
    Aalto University, Finland.
    Mousavi, Mahmoud
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Niiranen, Jarkko
    Aalto University, Finland.
    Variational formulations and isogeometric analysis for the dynamics ofanisotropic gradient-elastic Euler-Bernoulli and shear-deformable beams2018In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 69, p. 113-123Article in journal (Refereed)
    Abstract [en]

    A strain and velocity gradient framework is formulated for centrosymmetric anisotropic Euler-Bernoulli and third-order shear-deformable (TSD) beam models, reducible to Timoshenko beams. The governing equations and boundary conditions are obtained by using variational approach. The strain energy is generalized to include strain gradients and the tensor of anisotropic static length scale parameters. The kinetic energy includes velocity gradients and a tensor of anisotropic length scale parameters and hence the static and kinetic quantities of centrosymmetric anisotropic materials are distinguished in micro- and macroscales. Furthermore, the external work is written in the corresponding general form. Free vibration of simply supported centrosymmetric anisotropic TSD beams is studied by using analytical solution as well as an isogeometric numerical method verified with respect to convergence.

  • 2.
    Tofique, Muhammad Waqas
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Hallbäck, Nils
    Karlstad University, Faculty of Technology and Science, Materials Science. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Development of the distributed dislocation dipole technique for the analysis of closure of complex fractures involving kinks and branches2018In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 69, p. 168-178Article in journal (Refereed)
    Abstract [en]

    This paper presents the development of the distributed dislocation dipole technique (DDDT) for the analysis of straight, kinked and branched cracks where parts of the cracks may close during loading. The method has been developed for plane problems. Crack cases in which closure occurs are analyzed by reformulating the Buecicner's principle, taking into account the contact stresses at the contacting portions of the crack surfaces. Stress intensity factors corresponding to opening and the in-plane sliding mode of deformation at the crack tips are computed. Several test cases involving straight, kinked and/or branched cracks where parts of the cracks undergoes crack surface closure when subjected to the outer loading are analyzed. The results obtained from the DDDT are compared to those obtained from a Finite Element Method (FEM) analysis of the same crack cases. This comparison shows that the computation of stress intensity factors for the cases involving crack surface closure are less accurate than those for fully open crack cases. However, for the cases under consideration, the stress intensity factors were still computed with a maximum difference of approximately 2 per cent compared to the FEM calculations if Jacobi polynomial expansions of at least the twelfth order were used to represent the crack surface opening and sliding displacements. In most cases under consideration, sixth order Jacobi polynomial expansions were sufficient to obtain results within that margin of deviation.

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