Embedded Boundary Conditions for Thin Plates

Abstract eng:
An efficient procedure for embedding kinematic boundary conditions in thin plate bending, is based on a stabilized variational formulation, obtained by Nitsche's approach for enforcing boundary constraints. The absence of kinematic admissibility constraints allows the use of non-conforming meshes with non-interpolatory approximations, thereby providing added flexibility in addressing the higher continuity requirements typical of these problems. Work-conjugate pairs weakly enforce kinematic boundary conditions. The enforcement of tangential derivatives of deflections obviates the need for pointwise enforcement of corner values in the presence of corners. A single stabilization parameter is determined from a local generalized eigenvalue problem, guaranteeing coercivity of the discrete bilinear form. The accuracy of the approach is verified by representative computations with bicubic B-splines, exhibiting optimal rates of convergence and robust performance with respect to values of he stabilization parameter.

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