Article Sidebar

Submitted
August 10, 2023
Published
August 10, 2023
Download
PDF
Statistic
Read Counter : 51 Download : 43

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

Abstract

A globally and locally reliable strain recovery based a-posteriori error estimator for laminated composite plates is proposed in this study. An extensive check of the local and global quality of the proposed error estimator is carried out for the bending problem. Effect of material orientation, ply stacking sequence, boundary condition and loading profile is carried out for a square plate. It is found that this estimator is reliable for almost all the cases, and even predicts errors for the preasymptotic range reliably.

Keywords

Laminated Composite, Plates, Finite Element, Strain Recovery, A-posteriori Error

Article Details

How to Cite
Upadhyay, C., & Mohite, P. (2023). A Simple Strain Recovery based A-posteriori Error Estimator for Laminated Composite Plates. Journal of Aerospace Sciences and Technologies, 59(3), 212–222. https://doi.org/10.61653/joast.v59i3.2007.717
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Pandya, B.N., Mallikarjuna. and Kant, T., Technical Report, Aeronautics Research and Development Board, Ministry of Defence, Government of India.
  2. Research Grant Aero/RD-134/100/10/83-84/362.
  3. Kapania, R.K. and Raciti, S., "Recent Advances in Analysis of Laminated Beams and Plates, Part I: Shear Effects and Buckling", AIAA Journal, 1989, Vol. 27, No.7, pp. 923-934.
  4. Babuska, I. and Rheinboldt, W.C., "Error Estimates for Adaptive Finite Element Computations", SIAM J. Numer. Anal., 1978, Vol. 15, pp. 736-754.
  5. Babuska, I. and Rheinboldt, W.C., "A-posteriori Error Estimates for the Finite Element Method", Int. J.
  6. Numer. Methods Engg., 1978, Vol. 12, pp. 15971615.
  7. Kelly, D.W., Gago, J.P. de SR., Zienkiewicz, D.C.
  8. and Babuska, I., "A-posteriori Error Analysis and Adaptive Processes in the Finite Element Method: Part I - Error Analysis", Int. J. Numer. Methods Engg., 1983, Vol. 19, pp. 1593-1619.
  9. Kelly, D.W., "The Self-equilibration of Residuals and Complementary a-Posteriori Error Estimates in the Finite Element Method", Int. J. Numer. Methods Engg., 1984, Vol. 20, pp. 1491-1506.
  10. Bank, R,E. and Weiser, A., "Some a-Posteriori Error Estimators for Elliptic Partial Differential Equations", Math. Comp, 1985, Vol. 44, pp. 283-301.
  11. Zienkiewicz, O.C. and Zhu, J.Z., "A Simple Error Estimator and the Adaptive Procedure for Practical Engineering Analysis", Int. J. Numer. Methods Engg., 1987, Vol. 24, pp. 337-357.
  12. Rank, E. and Zienkiewicz, O.C., "A Simple Error Estimator in the Finite Element Method", Comm.
  13. Appl. Numer. Methods, 1987, Vol. 3, pp. 243-249.
  14. Zhu, J.Z. and Zienkiewicz, O.C., "Superconvergence Recovery Technique and a-Posteriori Error Estimators", Int. J. Numer. Methods Engg., 1990, Vol. 30, pp. 1321-1339.
  15. Cho, J.R. and Oden, J.T., "A-Priori Estimations of hp-finite Element Approximations for Hierarchical Models of Plate and Shell-like Structures", TICAM Report 95-15, November 16,1995.
  16. Oden, J.T. and Cho, J.R., "Adaptive hpq-finite Element Methods of Hierarchical Models for Plate and Shell-like Structures", TICAM Report 95-16, November 16, 1995.
  17. Verfurth, R., "A-Posteriori Error Estimators for the Stokes Equation", Numer. Math., 1989, Vol. 55, pp. 309-325.
  18. Actis, R.L., Szabo, B.A. and Schwab, C., "Hierarchic Models for Laminated Plates and Shells", Comput.
  19. Methods Appl. Mech. Engg, 1999, Vol. 172, pp.
  20. -107.
  21. Mohite, P.M. and Upadhyay, C.S., "Local Quality of Smoothening Based A-Posteriori Error Estimators for Laminated Plates Under Transverse Loading", Computers and Structures, 2002, Vol. 80, pp. 14771488.
  22. Jones, R.M., "Mechanics of Composite Materials", Scripta Book Company, McGraw-Hill Kogakusha Ltd, New Delhi, 1975.
  23. AUGUST 2007 ERROR ESTIMATOR FOR LAMINATED COMPOSITE PLATES 221 17. Herakovich, C. T., "Mechanics of Fibrous Composites", John Wiley and Sons, Inc., New York, 1998.
  24. Gastaldi, L., "Uniform Interior Error Estimates for the Reissner-Mindlin Plate Model", Math. Comp., 1993, Vol. 61, No. 204, pp. 539-567.
  25. Babuska, I., Plank, L. and Rodriguez, R., "Quality Assessment of the A-Posteriori Error Estimation in Finite Elements", Finite Elements in Analysis and Design, 1992, Vol. 11, pp. 285-306.
  26. Babuska, I., Strouboulis, T. and Upadhyay, C.S., "A Model Study of the Quality of A-Posteriori Error Estimators for Linear Elliptic Problems. Error Estimation in the Interior of Patchwise Uniform Grids of Triangles", Comput. Methods Appl. Mech. Engg, 1994, Vol. 114, pp. 307-378.
  27. Babuska, I., Strouboulis, T., Upadhyay, C.S., Gangaraj, S.K. and Copps, K., "Validation of A-Posteriori Error Estimators by Numerical Approach", Int. J.
  28. Numer. Methods Engg, 1994, Vol. 37 pp. 10731123.
  29. Babuska, I., Strouboulis, T., Gangaraj, S.K. and Upadhyay, C.S., "Validation of Recipes for the Recovery of Stresses and Derivatives by a Computerbased Approach", Mathl. Comput. Modelling, 1994, Vol. 20, pp. 45-89.
  30. Upadhyay, C.S., "Computer-based Analysis of Error Estimation and Superconvergence in Finite Element Computations", Ph. D. Dissertation at Texas Aand M University, Texas. May 1997.
  31. Zienkiewicz, O.C. and Zhu, J.Z., "Error Estimates
  32. and Adaptive Refinement for Plate Bending Problems",
  33. Int. J. Numer. Methods Engg, 1989, Vol. 28,
  34. pp. 2839-2853.
  35. Yunus, S.M., Pawlak, T.P. and Wheeler, M.J., "Application
  36. of the Zienkiewicz-Zhu Error Estimator for
  37. Plate and Shell Analysis", Int. J. Numer. Methods
  38. Engg, 1990, Vol. 29, pp. 1281-1298.
  39. Pitkaranta, J. and Suri, M., "Design Principles and
  40. Error Analysis for Reduced-shear Plate-bending Finite
  41. Elements", Numer. Math., 1996, Vol. 75, No. 75,
  42. pp. 223-266.
  43. Babuska, I. and Li., "The h-p Version of the Finite
  44. Element Method in the Plate Modelling Problem",
  45. Comm. Appl. Numer. Methods, 1992, Vol. 8, pp.
  46. -26.
  47. Suri, M., Babuska, I. and Schwab, C., "Locking
  48. Effects in the Finite Element Approximation of Plate
  49. Models", Mathematics of Computation, 1995, Vol.
  50. , No. 210, pp. 461-482.
  51. Reddy, Y .S.N. and Reddy, J.N., "Linear and Nonlinear
  52. Failure Analysis of Composite Laminates with
  53. Transverse Shear", Composites Science and Technology,
  54. , Vol. 44, pp. 227-255.