Finite element implementation of gradient elasticity theory on thin and thick plates

In this paper, static analysis of thin and thick plate bending problems with stress singularities is performed using gradient elasticity theory, and the obtained results are compared with each other and also for different boundary conditions. Two different rectangular finite elements having three degrees of freedom per node are used in the finite element implementation where the formulations of the finite elements are based on the Kirchhoff and Reissner–Mindlin plate theories. It is demonstrated through several examples that the stress singularities at sharp crack tips and under point loads of the plates are removed when using gradient elasticity. Convergence studies are also carried out to indicate the effectiveness of the implementations.