Studies of refinement and continuity in isogeometric structural analysis

We investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework. We consider two simple one-dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate NURBS solids. We also develop a local refinement strategy that we utilize in one of the shell analyses. We find that increased smoothness, that is, the “k-method,” leads to a significant increase in accuracy for the problems of structural vibrations over the classical C0-continuous “p-method,” whereas a judicious insertion of C0-continuous surfaces about singularities in a mesh otherwise generated by the k-method, usually outperforms a mesh in which all basis functions attain their maximum level of smoothness. We conclude that the potential for the k-method is high, but smoothness is an issue that is not well understood due to the historical dominance of C0-continuous finite elements and therefore further studies are warranted.