DOI QR코드

DOI QR Code

Variational Formulation of Hybrid-Trefftz Plate Elements and Evaluation of Their Static Performance

하이브리드 트레프츠 평판 요소의 변분 수식화와 성능 평가

  • 추연석 (한국과학기술원 기계공학과) ;
  • 이병채 (한국과학기술원 기계공학과)
  • Published : 2003.02.01

Abstract

Hybrid-Trefftz plate bending elements are known to be robust and free of shear locking in the thin limit because of Internal displacements fields and linked boundary displacements. Also, their finite element approximation is very simple regardless to boundary shape since all element matrices can be calculated using only boundary integrals. In this study, new hybrid-Trefftz variational formulation based on the total potential energy principle of internal displacements and displacement consistency conditions at the boundary is derived. And flat shell elements are derived by combining hybrid-Trefftz bending stiffness and plane stress stiffness with drilling dofs.

Keywords

Hybrid-Trefftz Element;Plate Element;Flat Shell Element

References

  1. Reissner, E., 1945, 'The Effect of Shear Deformation on the Bending of Elastic Plates,' Journal of Applied Mechanics, ASME, Vol. 12, pp. 69-76
  2. Mindlin, R. D., 1951, 'Influence of Rotatory Inertia and Shear in Flexural Motion of Isotropic Elastic Plates,' Journal of Applied Mechanics, ASME, Vol. 18, pp. 31-38
  3. Zienkiewicz, O. C., 1993, 'Linked Interpolation for Reissner-Mindlin Plate Elements : Part II-A Simple Triangle,' International Journal of Numerical Methods in Engineering, Vol. 36, pp. 3057-3066 https://doi.org/10.1002/nme.1620361803
  4. Allman, D. J., 1984, 'A Compatible Triangular Element Including Vertex Rotations for Plane Elasticity Analysis,' Computers & Structures, Vol. 19, pp. 1-8 https://doi.org/10.1016/0045-7949(84)90197-4
  5. MacNeal, R. H. and Harder, R. L., 1988, 'A Refined Four-Node Membrane Element with Rotational Degrees of Freedom,' Computers & Structures, Vol. 28, pp. 75-84 https://doi.org/10.1016/0045-7949(88)90094-6
  6. J. Petrolito, 'Triangular thick plate elements based on a hybrid-Trefftz approach,' Computer & Structures, Vol. 60, pp. 883-894, 1996 https://doi.org/10.1016/0045-7949(95)00453-X
  7. MacNeal, R. H. and Harder, R. L., 1985, 'A Proposed Standard Set of Problems to Test Finite Element Accuracy,' Finite Elements in Analysis and Design 1, pp. 3-20 https://doi.org/10.1016/0168-874X(85)90003-4
  8. Morley, L. S. D., 1964, 'Bending of Clamped Rectilinear Plates,' The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 17, pp. 293-317 https://doi.org/10.1093/qjmam/17.3.293
  9. Zienkiewicz, O. C., 1993, 'Linked Interpolation for Reissner-Mindlin Plate Elements : Part I - A Simple Quadrilateral,' International Journal of Numerical Methods in Engineering, Vol. 36, pp. 3043-3056 https://doi.org/10.1002/nme.1620361802
  10. Jirousek, J., 1993, 'Variational Formulation of Two Complementary Hybrid-Trefftz FE Models,' Communication in Numerical Methods in Engineering, Vol. 9, pp. 837-845 https://doi.org/10.1002/cnm.1640091007
  11. J. Petrolito, 1990, 'Hybrid-Trefftz Quadrilateral Element for Thick Plate Analysis,' Computer Methods in Applied Mechanics and Engineering, Vol. 78, pp. 331-351 https://doi.org/10.1016/0045-7825(90)90005-7
  12. Jirousek, J., Wroblewsk, A. and Szybinski, B., 1995, 'A New 12 DOF Quadrilateral Element for Analysis of Thick Plates,' International Journal of Numerical Methods in Engineering, Vol. 38, pp. 2619-2638 https://doi.org/10.1002/nme.1620381508
  13. Jirousek, J. and Leon, N., 1977, 'A Powerful Finite Element for Plate Bending,' Computer Methods in Applied Mechanics and Engineering, Vol. 12, pp. 77-96 https://doi.org/10.1016/0045-7825(77)90052-4
  14. Jirousek, J. and Guex Lan, 1986, 'Hybrid-Trefftz Finite Element Model and Its Application to Plate Bending,' International Journal of Numerical Methods in Engineering, Vol. 23, pp. 651-693 https://doi.org/10.1002/nme.1620230410