Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates

Sixth-order boundary value problems of a one-parameter gradient-elastic Kirchhoff plate model are formulated in a weak form within an H3 Sobolev space setting with the corresponding equilibrium equations and general boundary conditions. The corresponding conforming Galerkin method is proposed with error estimates for discretizations satisfying C2 continuity requirements. Continuity, coercivity and consistency of the corresponding bilinear form are utilized for proving the theoretical results. Numerical computations with conforming isogeometric discretizations of Cp−1-continuous NURBS basis functions of order p≥3 confirm the theoretical results and illustrate the features of the problem for both statics and free vibrations. In particular, the effects of the additional boundary conditions and parameter-dependent boundary layers corresponding to the gradient elasticity theory are addressed by the numerical examples.