Modified shape functions for the three‐node plate bending element passing the patch test

A polynomial displacement basis for the three-node plate bending element (Zienkiewicz-triangle) is developed from a relaxed C1-continuity requirement called the interpolation test. The test provides a general convergence criterion for non-conforming shape functions and a practical guideline to select a proper displacement basis. The resulting simple displacement type element passes the patch test. Several reduced numerical integration schemes are discussed and numerical testing provides a comparison with the standard element formulated by Zienkiewicz.