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A stabilized smoothed finite element method for free vibration analysis of Mindlin-Reissner plates. (English) Zbl 1172.74047
Summary: We perform a free vibration analysis of Mindlin-Reissner plates using the stabilized smoothed finite element method. The bending strains of the MITC4 and STAB elements are incorporated with a cell-wise smoothing operation to give new proposed elements, the mixed interpolation and smoothed curvature (MISC$$k$$) and SMISC$$k$$ elements. The corresponding bending stiffness matrix is computed along the boundaries of the smoothing elements (smoothing cells). Note that shearing strains and the shearing stiffness matrix of the proposed elements are the same as for the original MITC4 and STAB elements. It is confirmed by numerical tests that the present method is free of shear locking and has marginal improvements compared with the original elements.

MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74H45 Vibrations in dynamical problems in solid mechanics 74K20 Plates
Mfree2D
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