Integration of Shell FEA with Geometric Modeling Based on NURBS Surface Representation

NURBS 곡면기반의 기하학적 모델링과 셀 유한요소해석의 연동

  • 최진복 (서울대학교 기계항공공학부) ;
  • 노희열 (삼성전자 주식회사) ;
  • 조맹효 (서울대학교 기계항공공학부)
  • Published : 2007.01.01


The linkage framework of geometric modeling based on NURBS(Non-Uniform Rational B-Spline) surface and shell finite analysis is developed in the present study. For this purpose, geometrically exact shell finite element is implemented. NURBS technology is employed to obtain the exact geometric quantities for the analysis. Especially, because NURBS is the most powerful and wide-spread method to represent general surfaces in the field of computer graphics and CAD(Computer Aided Design) industry, the direct computation of surface geometric quantities from the NURBS surface equation without approximation shows great potential for the integration between geometrically exact shell finite element and geometric modeling in the CAD systems. Some numerical examples are given to verify the performance and accuracy of the developed linkage framework. In additions, trimmed surfaces with some cutouts are considered for more practical applications.


Shell Finite Element Analysis;NURBS Surface;Integrated Design;Trimmed Surface


  1. Ahmad, S., Irons B.M. and Zienkiewicz O.C., 1970, 'Analysis of Thick and Shell Structures by Curved Finite Element,' International Journal for Numerical Methods in Engineering, Vol. 2, pp. 419-459
  2. Simo, J. C., Fox, D. D. and Rifai, S., 1989 'On a Stress Resultant Geometrically Exact Shell Model. Part II: The Linear Theory; Computational Aspects,' Computer Method in Applied Mechanics and Engineering, Vol. 73, pp. 53-92
  3. Cho, Manenghyo and Roh, Hee Yuel, 2003, 'Development of Geometrically Exact New Shell Elements Based on General Curvilinear Coordinates,' International Journal for Numerical Methods in Engineering, Vol. 56, No. 1, pp. 81-115
  4. Roh, H. Y. and Cho, M., 2004, 'The Application of Geometrically Exact Shell Elements to B-Spline Surfaces,' Computer Meth. Appled Mech and Engrg. 193, pp. 2261-2299
  5. Roh, Hee Yuel and Cho, Maenghyo, 2005, 'Integration of Geometric Design and Mechanical Analysis Using B-Spline Functions on Surface,' Int. J. Numer. Meth. Engng, Vol. 62, pp. 1927-1949
  6. Naghdi P. M.,1963, 'Foundations of Elastic Shell Theory. Progress in Solid Mechanics 4,' Edited by Sneddon, I. N. North-Holland
  7. Lee, K., Cho, C. M. and Lee S. W., 2002, A Geometrically Nonlinear Nine-Node Solid Shell Element Formulation with Reduced Sensitivity to Mesh Distortion CMES- Computer Modeling In Engineering & Sciences 3 (3): pp. 339-349
  8. Les Piegl nad Wayne Tiller., 1997, 'The NURBS Book,' Springer-Verlag, New York, NY Second Edition
  9. SMLib TM, NLib$^{TM}$, Solid Modeling Solutions, Inc.
  10. Bathe, K. Y and Dvorkin, E.M., 1986, A Formulation of General Shell Elements, the use of Mixed Interpolation of Tensorial Components. International Journal for Numerical Methods in Engineering; 22: pp. 697-722
  11. Love A. E., 1927, A Treatise on the Mathematical Theory of Elasticity, 4th Ed. Dover, New York
  12. Simo, J. C. and Fox, D. D., 1989, 'On a Stress Resultant Geometrically Exact Shell Model. Part I: Formulation and Optimal Parameterization,' Computer Method in Applied Mechanics and Engineering, Vol. 72, pp. 267-304
  13. Stander, N., Matzenmiller, A. and Ramm, E., 1989, 'An Assessment on Assumed Strain Methods in Finite Rotation Shell Analysis,' Engineering Computations, 3: pp. 58-66