In this study a framework that directly links a general tensor-based shell finite element to NURBS(Non-Uniform Rational B-Spline) geometric modeling is implemented. The geometrically exact shell element for analysis has been developed and the accuracy and efficiency were demonstrated in our previous work . Generally, in the CAD systems, surfaces are represented by NURBS which are industry standard tool for the representation and design of surface geometry. Here, NURBS blending functions are composed by two parameters in the parametric domain. A general tensor-based shell element also has a two-parameter representation in the surfaces, and all the computations of geometric quantities which are needed in shell finite element analysis such as normal vector and derivatives of the surface at a specific point on the surface can be performed in local surface patch. Because these quantities are calculated directly from the NURBS equations without any interpolation of nodal values, the geometry errors can be dramatically decreased. Naturally, the geometric modeling based on NURBS technology can be directly linked to the shell analysis [2,3,4].
SMLib(Solid Modeling library) is employed in our study to generate and manipulate NURBS surfaces for shell finite analysis. SMLib has an extensive set of routines that provide all aspects of implementing the NURBS technology[5,6]. The NURBS surfaces can be easily generated by interpolating or approximating given set of data points through SMLib. The type of parameterization, the number of control points, and the degrees of the surface, etc. can be chosen as we are pleased. Our developed framework can also import the surface data in IGES file format modeled in the commercial CAD systems and convert those surfaces into NURBS surfaces for the shell finite analysis. Through this process the proposed framework can analyze more general type of surfaces such as trimmed ones or blended ones as well as complex shaped ones.
Some well-known numerical examples are solved to verify validity and efficiency of the proposed linkage framework. The verifications for the trimmed surfaces with cutouts on their skins and the blended surfaces are performed in the integrated framework of NURBS and shell finite elements. The surfaces considered here are generated by interpolating set of data points through SMLib and discretized for the finite elements analysis. Especially, in case of the trimmed or blended surfaces, the surfaces are modeled in the CAD system and exported in IGES file format so that our developed program can import them for analysis.Through this process, the present linkage framework with the CAD surface modeling based on NURBS is integrated. The necessary information of the surfaces in the analysis routine is obtained from appropriate functions provided by SMLib.
1. M. Cho, H.Y. Roh, “Development of geometrically exact new shell element based on general curvilinear coordinates,” Int.J. Numer. Methods Engrg. 56 (2003) 81-115.
2. H.Y.Roh, M.Cho, “The application of geometrically exact shell elements to B-spline surfaces,” Computer Meth. Appled Mech and Engrg. 193 (2004) 2261-2299.
3. Park H, Kim K, Lee SC., “A method for approximate NURBS curve compatibility based on multiple curve refitting,” Computer-Aided Design 32(2000) 237-252.
4. H.Y.Roh, M.Cho, "Integration of geometric design and mechanical analysis using B-spline functions on surface," Int.J. Numer. Methods Engrg., 62(2005) 1927-1949.
5. Les Piegl, Wayne Tiller, The NURBS Book: Springer-Verlag, New York, NY Second Edition, 1997
6. SMLib™, NLib™, Solid Modeling Solutions, Inc. http://www.smlib.com/