대한기계학회논문집A (Transactions of the Korean Society of Mechanical Engineers A)

  • 제26권11호
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  • Pages.2312-2321
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  • 2002
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  • 1226-4873(pISSN)
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  • 2288-5226(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
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최소 제곱 무요소법을 이용한 선형 탄성 변형 해석

The Least-Squares Meshfree Method for Linear Elasticity

  • 권기찬 (한국과학기술원 기계공학과) ;
  • 박상훈 (기아자동차 승용차체설계 3팀) ;
  • 윤성기 (한국과학기술원 기계공학과)
  • 발행 : 2002.11.01
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초록

The first-order least-squares meshfree method for linear elasticity is presented. The conventional and the compatibility-imposed least-squares formulations are studied on the convergence behavior of the solution and the robustness to integration error. Since the least-squares formulation is a type of mixed formulation and induces positive-definite system matrix, by using shape functions of same order for both primal and dual variables, higher rate of convergence is obtained for dual variables than Galerkin formulation. Numerical examples also show that the presented formulations do not exhibit any volumetric locking for the incompressible materials.

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참고문헌

  1. Nayroles, B., Touzot, G. and VilIon, P., 1992, 'Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elements,' Comput. Mech., Vol. 10, pp. 307-318 https://doi.org/10.1007/BF00364252
  2. Belytschko, T., Lu, Y.Y and Gu, L., 1994, 'ElementFree Galerkin Methods,' Int. J. Numer. Meth. Engng., Vol. 37, pp. 229-256 https://doi.org/10.1002/nme.1620370205
  3. Liu, W.K., Jun, S. and Zhang, YF., 1995, 'Reproducing Kernel Particle Methods,' Int. J. Numer: Meth. Fluids, Vol. 20, pp. 1081-1106 https://doi.org/10.1002/fld.1650200824
  4. Duarte, C.A. and Oden, J.T., 1995, 'Hp Clouds - A Meshless Method to Solve Boundary-Value Problems,' Technical Report 95-05, TICAM, University of Texas at Austin
  5. Melenk, J.M. and Babuska, I., 1996, 'The Partition of Unity Finite Element Method: Basic Theory and Applications,' Camp. Meth. Appl. Meeh. Engng., Vol. 139, pp. 289-314 https://doi.org/10.1016/S0045-7825(96)01087-0
  6. Beissel, S. and Belytschko, T., 1996, 'Nodal Integration of the Element-free Galerkin Method,' Compo Meth. Appl. Mech. Engng., Vol. 139, pp. 49-74 https://doi.org/10.1016/S0045-7825(96)01079-1
  7. Nagashima, T., 1999, 'Node-by-node Meshless Approach and its Applications to Structural Analysis,' Int. J. Numer. Meth. Engng., Vol. 39, pp. 341-385 https://doi.org/10.1002/(SICI)1097-0207(19990930)46:3<341::AID-NME678>3.0.CO;2-T
  8. Onate, E., Zienkiewicz, O.C. and Taylor, R.L., 1996, 'A Finite Point Method in Computational Mechanics. Applications to Convective Transport and Fluid Flow,' Int. J. Numer. Meth. Engng., Vol. 39, pp. 3839-3866 https://doi.org/10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R
  9. Breitkopf, P., Touzot, G. and Villon, P., 2000, 'Double Grid Diffuse Collocation Method,' Comput. Mech., Vol. 25, pp. 199-206 https://doi.org/10.1007/s004660050469
  10. Chen, J.S., Wu, C.T., Yoon, S. and You, Y, 2001, 'A Stabilized Conforming Nodal Integration for Galerkin Mesh-free Methods,' Int. J. Numer. Meth. Engng., Vol. 50, pp. 435-466 https://doi.org/10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
  11. Atluri, S.N. and Zhu, T., 1998, 'A New Meshless Petrov-Galerkin (MLPG) Approach in Computational Mechanics,' Comput. Mech., Vol. 22, pp. 117-127 https://doi.org/10.1007/s004660050346
  12. Park, S.H. and Youn, S.K., 2001, 'The LeastSquares Meshfree Method,' Int. J. Numer. Meth. Fluids, Vol. 52, pp. 997-1012 https://doi.org/10.1002/nme.248
  13. Park, S.H. and Youn, S.K., 2001, 'Least-Squares Meshfree Methods and Integration Error,' Transactions of the KSME, A, Vol. 25, No. 10, pp. 1605-1612
  14. Dolbow, J. and Belytschko, T., 1999, 'Volumetric Locking in the Element Free Galerkin Method,' Int. J. Numer. Meth. Engng., Vol. 46, pp. 925-942 https://doi.org/10.1002/(SICI)1097-0207(19991030)46:6<925::AID-NME729>3.0.CO;2-Y
  15. Chen, J.S., Yoon, S., Wang, H.P. and Liu, W.K., 2000, 'An Improved Reproducing Kernel Particle Method for Nearly Incompressible Finite Elasticity,' Compo Meth. Appl. Mech. Engng., Vol. 181, pp. 117-145 https://doi.org/10.1016/S0045-7825(99)00067-5
  16. Jiang, B.N., 1998, The Least-Squares Finite Element Method - Theory and Applications in Computational Fluid Dynamics and Electromagnetics, Berlin, Spring-Verlag
  17. Lancaster, P. and Salkauskas, K., 1981, 'Surfaces Generated by Moving Least-Squares Methods,' Mathematics of Computation, Vol. 37, pp. 141-158 https://doi.org/10.2307/2007507
  18. Timoshenko, S.P. and Goodier, IN., 1987, Theory of Elasticity, 2nd Ed., New York, McGraw-Hill