Functions for patch test in finite element analysis of the Mindlin plate and the thin cylindrical shell

Current patch test for Mindlin plate element only satisfies the zero shear deformation condition.The patch test of non-zero constant shear for Mindlin plate problem cannot be performed.For shell element, the patch test does not even exist.Based on the theory of enhanced patch test proposed by Chen W J (2006),the authors proposed the enhanced patch test function for Mindlin plate and thin cylindrical shell elements.This enhanced patch test function can be used to assess the convergence of the Mindlin plate and cylindrical thin shell elements.