Studies of Refinement and Continuity in Isogeometric Structural Analysis (Preprint)
TEXAS UNIV AT AUSTIN INST FOR COMPUTING SCIENCE AND COMPUTER APPLICATIONS
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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.
- Theoretical Mathematics
- Numerical Mathematics