Embedded boundary conditions for shear-deformable plate bending

Abstract

An efficient procedure for embedding kinematic boundary conditions of shear-deformable plate bending is based on stabilized variational formulations, obtained by Nitsche’s approach for enforcing surface constraints. Effective use of the plate thickness as scaling in the rotational constraint terms leads to a uniform problem statement with a single stabilization parameter. An alternative form of the plate kinematics precludes the vulnerability of computation based on the standard Reissner–Mindlin formulation to shear locking, yet raises other challenges in the form of higher-order regularity and unconventional boundary conditions. The embedded boundary Nitsche approach provides a framework that easily accommodates these features. The accuracy of the approach for both plate formulations is verified by representative computations with bicubic B-splines, exhibiting optimal rates of convergence, and robust performance with respect to values of the parameters.