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  • 1.
    Monfared, M. M.
    et al.
    University of Zanjan, Iran.
    Ayatollahi, M.
    University of Zanjan, Iran.
    Mousavi, Mahmoud
    Aalto University, Finland.
    The mixed-mode analysis of a functionally graded orthotropic half-plane weakened by multiple curved cracks2016In: Archive of applied mechanics (1991), ISSN 0939-1533, E-ISSN 1432-0681, Vol. 86, no 4, p. 713-728Article in journal (Refereed)
    Abstract [en]

    The problem of functionally graded orthotropic half-plane with climb and glide edge dislocations is solved. Dislocations are used as the building blocks of defects to model cracks of modes I and II. Following a dislocation-based approach, the problem is reduced to a system of singular integral equations for dislocation density functions on the surfaces of smooth cracks. These integral equations enforce the crack-face boundary conditions and are solved numerically for the dislocation density. The numerical results include the stress intensity factors for several different cases of crack configurations and arrangements.

  • 2.
    Mousavi, Mahmoud
    et al.
    Aalto University, Finland.
    Paavola, Juha
    Aalto University, Finland.
    Analysis of plate in second strain gradient elasticity2014In: Archive of applied mechanics (1991), ISSN 0939-1533, E-ISSN 1432-0681, Vol. 84, no 8, p. 1135-1143Article in journal (Refereed)
  • 3.
    Yaghoubi, Saba Tahaei
    et al.
    Aalto University, Finland.
    Mousavi, Mahmoud
    Aalto University, Finland.
    Paavola, Juha
    Aalto University, Finland.
    Strain and velocity gradient theory for higher-order shear deformable beams2015In: Archive of applied mechanics (1991), ISSN 0939-1533, E-ISSN 1432-0681, Vol. 85, no 7, p. 877-892Article in journal (Refereed)
    Abstract [en]

    The strain and velocity gradient framework is formulated for the third-order shear deformable beam theory. A variational approach is applied to determine the governing equations together with initial and boundary conditions. Within the gradient framework, the strain energy is generalized to include strain as well as strain gradient. Furthermore, the kinetic energy is also generalized to include velocity and the velocity gradient. Such approach results in the introduction of the static and kinetic internal length scales. For dynamic analysis of beams, most of the gradient theories do not take the velocity gradient into account. The model developed in this paper depicts the influence of the velocity gradient on the governing equations and initial and boundary conditions of the third-order shear deformable theory. Through the assumption of the velocity gradients, kinematic quantities are distinguished on the microscale and on the macroscale. Finally, Timoshenko and Euler–Bernoulli beam theories are also presented by simplifying the third-order theory.

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