Abstract
A four-noded rectangular element of the Mindlin displacement model is presented for thin plate bending and buckling analysis. By use of discrete Kirchhoff (DK) constraints the element properties are derived according to an eight-node interpolatory pattern specified to consist of bilinear Lagrangian and Serendipity bubble functions. A new DK shear constraint is proposed for the purpose of achieving exact satisfaction of the real Kirchhoff conditions in thin plate limit at 2 × 2 Gauss points. The element with quadratic accuracy is shown to satisfy the basic requirement of convergence under energy-orthogonal criteria. In addition to the analysis of single element bending properties, buckling investigations are performed to test the element geometric properties involving the DK constraints. Numerical results for buckling loads of square and rectangular plates with various edge conditions under compression are reported with very good convergence characteristics towards theoretical predictions.
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