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An enhanced cell-based smoothed finite element method for the analysis of Reissner-Mindlin plate bending problems involving distorted mesh. (English) Zbl 1352.74452
Summary: An enhanced cell-based smoothed finite element method (FEM) is presented for the Reissner–Mindlin plate bending analysis. The smoothed curvature computed by a boundary integral along the boundaries of smoothing cells in original smoothed FEM is reformulated, and the relationship between the original approach and the present method in curvature smoothing is established. To improve the accuracy of shear strain in a distorted mesh, we span the shear strain space over the adjacent element. This is performed by employing an edge-based smoothing technique through a simple area-weighted smoothing procedure on MITC4 assumed shear strain field. A three-field variational principle is utilized to develop the mixed formulation. The resultant element formulation is further reduced to a displacement-based formulation via an assumed strain method defined by the edge-smoothing technique. As the result, a new formulation consisting of smoothed curvature and smoothed shear strain interpolated by the standard transverse displacement/rotation fields and smoothing operators can be shown to improve the solution accuracy in cell-based smoothed FEM for Reissner-Mindlin plate bending analysis. Several numerical examples are presented to demonstrate the accuracy of the proposed formulation.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74G60 Bifurcation and buckling
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