4절점 응축 셸 요소를 이용한 복합재 적층 구조물의 전단응력 예측

  • Published : 2000.09.01


We propose an accurate and efficient estimation method of transverse shear stresses for analysis and design of laminated composite structures by 4-node quadrilateral degenerated shell elements. To get proper distributions of transverse shear stresses in each layer, we use 3-dimensional equilibrium equations instead of constitutive equations with shear correction factors which vary diversely according to the shapes of shell sections. Three dimensional equilibrium equations are integrated through the thickness direction with complete polynomial membrane stress fields, which are recovered by REP (Recovery by Equilibrium in Patches) recovery method. The 4-node quadrilateral degenerated shell element used in this paper has drilling degrees of freedom and shear stresses derived from assumed strain fields that are set up at natural coordinate systems. The numerical results demonstrate that the proposed estimation method attains reasonable accuracy and efficiency compared with other methods and FE analysis using 4-node degenerated shell elements.


Transverse Shear Stress;Laminated Compostie Structure;Degenerated Shell Element;REP Recovery Method


  1. Reddy, J. N., 1984, 'A Simple Higher-Order Theory for Laminated Composite plates', ASME Journal of Applied Mechanics, Vol. 51, pp. 745-752
  2. Kim, J. H. and Lee, B. C., 1998, 'A Four Node Degenerated Shell Element with Drilling Degrees of Freedom,' Structural Engineering and Mechanics, Vol. 6, pp. 912-938
  3. 김광수, 홍창선, 1982, '복합적층판의 Delamination해석,' 대한기계학회논문집, 제6권, 제2호, pp. 140-146
  4. Kant, T. and Manjunatha, B. S., 1994, 'On Accurate Estimation of Transverse Stresses in Multilayer Laminates,' Computer & Structures, Vol. 50, No. 3, pp. 351-365
  5. Engblom, J. J. and Ochoa, O. O., 1985, 'Through-the-thickness Stress Predictions for Laminated Plates of Advanced Composite Materials,' International Journal for Numerical Methods in Engineering, Vol. 21, pp. 1759-1776
  6. Boroomand, B. and Zienkiewicz, O. C., 1997, 'An Improved REP Recovery and the Effectivity Robustness Test,' International Journal for Numerical Methods in Engineering, Vol. 40, pp. 3247-3277<3247::AID-NME211>3.0.CO;2-Z
  7. Byun, C. and Kapania, R. K., 1992, 'Prediction of Interlaminar Stresses in Laminated Plates Using Global Orthogonal Interpolation Polynomials,' AIAA Journal, Vol. 30, No. 11, pp. 2740-2749
  8. Mao, S. T. and Pian, T. H. H., 1972, 'Finite Element solutions for Laminated Thick Plates,' Journal of Composite Materials, Vol. 6, pp. 304-311
  9. Jones, R. M., 1975, Mechanics of Composite Plates, McGrow-Hill
  10. Reddy, J. N., 1997, Mechanics of Laminated Composite Plates : Theory and Analysis, CRC Press
  11. Hsu, T. M. and Wang, J. T. S., 1970, 'A Theory of Laminated Cylindrical Shells Consisting of Layers of Orthotropic Laminate,' AIAA Journal, Vol. 8, No. 12, pp. 1041-2146
  12. Robbins, D. H. Jr. and Reddy, J. N., 1993, 'Modeling of Thick composites Using a Layerwise Laminate Theory,' International Journal for Numerical Methods in Engineering, Vol. 36, pp. 655-677
  13. Carrera, E., 1998, 'Evaluation of Layerwise Mixed Theories for Laminated Plates Analysis,' AIAA Journal, Vol. 36, No. 5, pp. 830-839
  14. Pagano, N. J., 1970, 'Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates,' Journal of Composite Materials, Vol. 4, pp. 20-34
  15. Whitney, J. M., 1969, 'The Effect of Transverse Shear Deformation on the Bending of Laminated Plates,' Journal of Composite Materials, Vol. 3, pp. 534-547
  16. Pagano, N. J. and Soni, S. R., 1983, 'Global-Local Laminate Variation Model,' international Journal of Solids and Structures, Vol. 19, No. 3, pp. 207-228
  17. Pagano, N. J., 1969, 'Exact Solutions for Composite Laminates in Cylindrical Bending,' Journal of Composite Materials, Vol. 3, pp. 398-411