A simple four-node quadrilateral finite element for plates

A simple and accurate four-node quadrilateral finite element based on the Mindlin plate theory and Kirchhoff constraints is presented for general thin plate bending applications. The derivation of the element stiffness properties is straightforward, starting with a specified eight-node interpolation; usual discrete Kirchhoff (DK) constraints are employed to constrain out the four midside nodes of the element. The present resulting DK element passes patch tests with elements of arbitrary and even highly distorted mesh types. Numerical studies of the element convergence behaviours are undertaken for various plate bending problems so far investigated. It is indicated from comparative examples that fairly good convergence characteristics have been achieved.