Three-node Mindlin plate finite element with shear stress resultants derived from equilibrium equations

A new 9-DOF triangular plate finite element for linear-elastic analysis of very thin to thick plates with small deformations is presented. The element is based on Mindlin plate theory and has higher-order interpolations that are conceived to satisfy all differential equations, including the equilibrium ones based on which the shear stress resultants are derived. Numerical investigation revealed certain limitations of the initial formulation which were resolved with an alternative approach for the derivation of the higher-order terms in the rotational fields. This resulted in a close relation of the formulation to the established DKT element for thin plate scenarios. Numerical investigation shows that the presented element has a correct rank, passes the patch test, is shear locking free and high-performing. It also indicates its consistent performance in regard to different meshing or boundary conditions, all of which makes it highly suitable for practical engineering applications.