A New Shear Locking-Free Quadrilateral Plate Element for Free Vibration and Eigen-Buckling Analysis
A new plate element has been formulated by simply adding one degree of freedom for each node on the basis of the classical ACM element, based on a modified first-order shear deformation plate theory, which assumes that the plate deflection has bending and shearing components, with two rotations defined by differentiations of bending deflections. This new element, with 16 degrees of freedom, exhibits no locking effect, and is appropriate for both thin and thick plates.
To assess the performance of the newly developed plate element, it has been applied to the prediction of natural frequencies and critical bucking loads of square plates with various thickness ratios and boundary conditions. Comparisons with available analytical and numerical solutions in open publication show that the new element leads to highly accurate solutions in free vibration and eigen-buckling analysis with good convergence, and can be competitive with existing plate elements.