Article

A smoothed finite element method for plate analysis

University of Glasgow, Civil Engineering, Rankine building, G12 8LT, United Kingdom
Computer Methods in Applied Mechanics and Engineering (Impact Factor: 2.63). 02/2008; 197(13-16):1184-1203. DOI: 10.1016/j.cma.2007.10.008

ABSTRACT A quadrilateral element with smoothed curvatures for Mindlin–Reissner plates is proposed. The curvature at each point is obtained by a non-local approximation via a smoothing function. The bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements (smoothing cells). Numerical results show that the proposed element is robust, computational inexpensive and simultaneously very accurate and free of locking, even for very thin plates. The most promising feature of our elements is their insensitivity to mesh distortion.

Download full-text

Full-text

Available from: Stéphane Pierre Alain Bordas, Aug 06, 2015
0 Followers
 · 
109 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, a locking-free meshless local Petrov–Galerkin formulation is presented for shear flexible thick plates, which remains theoretically valid in the thin-plate limit. The kinematics of a three-dimensional solid is used, instead of the conventional plate assumption. The local symmetric weak form is derived for cylindrical shaped local sub-domains. The numerical characteristics of the local symmetric weak form, in the thin plate limit, are discussed. Based on this discussion, the shear locking is theoretically eliminated by changing the two dependent variables in the governing equations. The moving least square interpolation is utilized in the in-plane numerical discretization for all the three displacement components. In the thickness direction, on the other hand, a linear interpolation is used for in-plane displacements, while a hierarchical quadratic interpolation is utilized for the transverse displacement, in order to eliminate the thickness locking. Numerical examples in both the thin plate limit and the thick plate limit are presented, and the results are compared with available analytical solutions.
    Journal of Computational Physics 09/2005; 208(1):116-133. DOI:10.1016/j.jcp.2005.02.008 · 2.49 Impact Factor
  • International Journal for Numerical Methods in Engineering 01/1973; 6(3):333 - 343. DOI:10.1002/nme.1620060305 · 1.96 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: An improvement of a new technique for modelling cracks in the finite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous fields and the near tip asymptotic fields through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique.
    International Journal for Numerical Methods in Engineering 09/1999; 46(1):131-150. DOI:10.1002/(SICI)1097-0207(19990910)46:13.0.CO;2-J · 1.96 Impact Factor
Show more