Effect of Superconvergent Stress Points for Solution Improvement and Error Estimation of Isogeometric Analysis of Axisymmetric Problems

علوم کاربردی و محاسباتی در مکانیک

Article 6, Volume 26, Issue 1 - Serial Number 11, March 2015, Pages 79-95   

Document Type: Original Article

DOI: 10.22067/fum-mech.v26i1.44703

Authors

Ahmad Ganjali^* ; B. Hassani

Abstract

A method for error estimation of isogeometric analysis of plane stress problems which is the based on stress recovery and using the super convergent properties of the Gauss points, has been already introduced. This paper is devoted to the development of the method and study of the effects of these supercovergent points on the solution improvement and error estimation of axisymmetric problems by the isogeometric analysis method. It is concluded that by using these optimal points for stress recovery and error estimation by isogeometric analysis a considerable improvement is attained.

Keywords

Isogeometric Analysis; Axisymmetric Problems; Error estimation; Stress Recovery

References

1. Kagan, P., Fischer, A. and Bar-Yoseph, P.Z., "New B-Spline finite element approach for geometrical design and mechanical analysis", Int. J. numer. Methods Engrg., Vol. 41, pp. 435-458, (1998).

2. Hollig, K., Reif, U. and Wipper, J., "Weighted extended B-Spline approximation of dirichlet problems", SIAM J. Numer. Anal., Vol. 39, 2, pp. 442-462, (2001).

3. Kagan, P., Fischer, A. and Bar-Yoseph, P.Z., "Mechanically based models: adaptive refinement for B-Spline finite element", Int. J. numer. Methods Engrg., Vol. 57, pp. 1145-1175, (2003).

4. Hughes, T.G.R., Cottrell, J.A. and Bazilevs, Y., "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Method Appl. Mech. Engrg, Vol. 194, pp. 4135–4195, (2005).

5. Hassani, B., Ganjali, A. and Tavakkoli, M., "An isogeometrical approach to error estimation and stress recovery", European Journal of Mechanics A/Solids, Vol. 31, pp. 101-109, (2011).

6. Cottrell, J.A., Hughes, T.J.R. and Bazilevs, Y., "Isogeometric Analysis: toward integration of CAD and FEA", Wiley, (2009).

7. Zienkiewicz, O.C., Taylor, R.L. and Zhu, J.Z., "The Finite Element Method", 6th edition, Elsevier Butterworth-Heinemann, (2005).

8. Rogers D.F., "An Introduction to NURBS", Morgan Kaufmann Publishers, (2001).

9. Piegl, L. and Tiller, W., "The NURBS Book", 2nd ed., Springer-Verlag, New York, (1997).

10. Hughes, T.J.R., Reali, A. and Sangalli, G., "Efficient quadrature for NURBS-based isogeometric analysis", Comput. Methods Appl. Mech. Engrg., Vol. 199, pp. 5-8: 301-313, (2010).

11. Barlow, J., "Optimal stress locations in finite element models", Int. J. Numer. Meth. Eng., Vol. 10, pp. 243–251, (1976).

12. Sadd, M.H., "ELASTICITY:Theory, Applications, and Numerics", Elsevier Butterworth–Heinemann, (2005).

13. Gratsch, T. and Bathe, KJ, "A posteriori error estimation techniques in practical finite element analysis", Computers and Structures, Vol. 83, pp. 235–265, (2005).

14. Timoshenko, S. and Woinowsky-Krieger, S., "Theory of Plates and Shells", 2nd ed., McGraw-Hill, (1959).