Dynamically Adaptive Finite Element Mesh Generation Schemes

  • Received : 2010.10.30
  • Accepted : 2010.11.29
  • Published : 2010.12.31

Abstract

The finite element method(FEM) is proven to be an effective approximate method of structural analysis if proper element types and meshes are chosen, and recently, the method is often applied to solve complex dynamic and nonlinear problems. A properly chosen element type and mesh yields reliable results for dynamic finite element structural analysis. However, dynamic behavior of a structure may include unpredictably large strains in some parts of the structure, and using the initial mesh throughout the duration of a dynamic analysis may include some elements to go through strains beyond the elements' reliable limits. Thus, the finite element mesh for a dynamic analysis must be dynamically adaptive, and considering the rapid process of analysis in real time, the dynamically adaptive finite element mesh generating schemes must be computationally efficient. In this paper, a computationally efficient dynamically adaptive finite element mesh generation scheme for dynamic analyses of structures is described. The concept of representative strain value is used for error estimates and the refinements of meshes use combinations of the h-method(node movement) and the r-method(element division). The shape coefficient for element mesh is used to correct overly distorted elements. The validity of the scheme is shown through a cantilever beam example under a concentrated load with varying values. The example shows reasonable accuracy and efficient computing time. Furthermore, the study shows the potential for the scheme's effective use in complex structural dynamic problems such as those under seismic or erratic wind loads.

Acknowledgement

Supported by : Hongik University

References

  1. Bathe, K.J., Wilson, E.L. (1976) Numerical Methods in Finite Element Analysis, Prentice Hall, Englewood Cliffs.
  2. Belytschko, T. (1974) Transient Analysis, Structural Mechanics, Computer Programs, Surveys, Assessments, and Availability, Edited by Pilkey, W., Saczalski, K. and Schaeffer, H. University of Virginia Press, Charlottesville, Virginia, pp.255-276.
  3. Belytschko, T., Hughes, J.R., Bathe, K.J. (1996) Finite Element Procedures, Prentice-Hall, Englewood Cliffs.
  4. Choi, C., Jung, H. (1998) Adaptive Mesh Generation for Dynamic Finite element Analysis, J. Korean Soc. of Civil Eng.(in Korean), 18(I-2), pp.203-220.
  5. Choi, C.K., Yu, W.J. (1998) Adaptive Finite Element Wind Analysis with Mesh Refinement and Recovery (in Korean), Wind and Structures, 1, pp.111-125. https://doi.org/10.12989/was.1998.1.1.111
  6. Cook, R.D., Malkus, D.S., Plesha, M.E. (1989) Concepts and Applications of Finite Element Analysis, 3rd Ed. John Wiley & Sons, New York.
  7. de Las Casas, E.B. (1988) R-H Mesh Improvement Algorithms for the Finite Element Method, Ph.D. Dissertation, Purdue University, West Lafayette.
  8. Heesom, D., Mahdjoubi, L. (2001) Effect of Grid Resolution and Terrain Characteristics on Data from DTM, J. Comp. in Civil Eng., ASCE, 15(2), pp.137-143. https://doi.org/10.1061/(ASCE)0887-3801(2001)15:2(137)
  9. Hwang, S.W. (1988) A Study on the r-h Method in the Finite Element Method, Master's Thesis(in Korean), Inha University, Inchon.
  10. Jeong, Y.C., Yoon, C. (2003) Representative Strain Value Based Adaptive Mesh Generation for Plane Stress, Hongik J. Science and Tech., 7, pp.71-86.
  11. Jeong, Y.C., Yoon, C., Hong, S. (2003) Adaptive Mesh Generation Scheme for Planar Problems using Representative Strain Values for Error(in Korean), Proc., Korean Soc. Comp. Structural Eng., 16 (2-31), pp.403-409.
  12. Ladeveze, P., Oden, J.T., Editors. (1998) Advances in Adaptive Computational Methods in Mechanics Studies in Applied Mechanics, 47, Elsevier, Oxford.
  13. MacLeod, I.A. (2002) The Education of Structural Analyst, Proc., Asranet Symp., Asranet, Dept. of Naval Architecture and Marine Eng., Univ. of Glasgow and Strathclyde, London.
  14. McFee, S., Giannacopoulos, D. (2001) Optimal Discretizations in Adaptive Finite Element Electromagnetics, Int. J. Numer. Meth. Eng., 52(9), pp.939-978. https://doi.org/10.1002/nme.240
  15. Newmark, N.M. (1959) A Method of Computation for Structural Dynamics, J. Eng. Mech. Division, American Society of Civil Engineers, 85(EM3), pp.67-94.
  16. Ohnimus, S., Stein, E., Walhorn, E. (2001) Local Error Estimates of FEM for Displacements and Stresses in Linear Elasticity by Solving Local Neumann Problems, Int. J. Numer. Meth. Eng., 52(7), pp.727-746. https://doi.org/10.1002/nme.228
  17. Rafiq, M.Y., Easterbrook, D.J. (2005) Using the Computer to Develop a Better Understanding in Teaching Structural Engineering Behavior to Undergraduates, J. Comp. in Civil Eng., 19(1), pp.34-44. https://doi.org/10.1061/(ASCE)0887-3801(2005)19:1(34)
  18. Stampfle, M., Hunt, K.J., Kalkkuhl, J. (2001) Efficient Simulation of Parameter-Dependent Vehicle Dynamics, Int. J. Numer. Meth. Eng., 52(11), pp.1273-1299. https://doi.org/10.1002/nme.254
  19. Reddy, J.N. (1993) An Introduction to the Finite Element Method, 2nd Ed., McGraw-Hill, New York.
  20. Yoon, C. (2005) Adaptive Mesh Generation for Dynamic Finite Element Analysis(in Korean), J. Korean Soc. Civil Eng., 25(6A), pp.989-998.
  21. Yoon, C. (2009) Computer Aided Teaching of Structural Engineering Using Adaptive Schemes in the Finite Element Method, J. Korean Soc. Hazard Mitigation., 9(1), pp.9-13.
  22. Zhu, J.Z., Zienkiewicz, O.C., Hinton, E., Wu, J. (1991) A New Approach to the Development of Automatic Quadrilateral Mesh Generation, Int. J. Numer. Meth. Eng., 32, pp.849-866. https://doi.org/10.1002/nme.1620320411
  23. Zienkiewicz, O.C., Taylor, R.L., Zhu, J.Z. (2005) The Finite Element Method: Its Basis and Fundamentals, 6th Ed. Elsevier Butterworth-Heinemann, Oxford.
  24. Zienkiewcz, O.C., Zhu, J.Z. (1987) A Simple Error Estimator and Adaptive Procedure for Practical Engineering Analysis, Int. J. Numer. Meth. Eng., 24, pp.337-357. https://doi.org/10.1002/nme.1620240206