Studies of refinement and continuity in isogeometric structural analysis

• Published in: Computer methods in applied mechanics and engineering Vol. 196; no. 41; pp. 4160 - 4183
• Main Authors: Cottrell, J.A., Hughes, T.J.R., Reali, A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2007; Elsevier
• Subjects: Computational techniques; Continuity; Exact sciences and technology; Finite element analysis; Fundamental areas of phenomenology (including applications); Isogeometric analysis; k-Method; Mathematical methods in physics; p-Method; Physics; Refinement; Shells; Singularities; Smoothness; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Structural eigenvalue problems; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Isogeometric analysis; k-Method; Structural eigenvalue problems; Singularities; p-Method; Refinement; Shells; Continuity; Finite element analysis; Smoothness; Singularity; Vibration; Refinement method; Modeling; Geometrical model; Finite element method; Shell; Boundary value problem; Non uniform rational B spline; Eigenvalue problem; Potential method; Mesh generation; Structural analysis
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2007.04.007

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 C 0 -continuous “ p-method,” whereas a judicious insertion of C 0 -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 C 0 -continuous finite elements and therefore further studies are warranted.