A simple p-adaptive refinement procedure for structural shape optimization

Finite Elements in Analysis and Design

Volumn 24, Issue 3, 1997, Pages 133-155

  Salagame, Raviprakash R ^a,b   Belegundu, Ashok D ^a  

^a The Center for Nanotechnology Education and Utilization   (United States)

^b IBM ALMADEN RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTICITY; ERRORS; ESTIMATION; NUMERICAL ANALYSIS; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; STRUCTURAL ANALYSIS;

ADAPTIVE REFINEMENT PROCEDURE; ERROR ESTIMATORS; POLYNOMIAL ESCALATION; STRUCTURAL SHAPE OPTIMIZATION;

FINITE ELEMENT METHOD;

EID: 0030736521     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-874X(96)00036-4     Document Type: Article

References (50)

1. B.A. Szabo, P.K. Basu and M.P. Rossow, Adaptive finite element analysis based on p-convergence, Proc. Symp. on Future Trends in Computerized Structural Analysis and Synthesis, Washington, DC, NASA Conf. Publication 2059, pp.43-50, 1978.
2. A.D. Belegundu and S.D. Rajan, A shape optimization approach based on natural design variables and shape functions, Comput. Methods Appl. Mech. Eng. 66, pp.87-106, 1988.
3. E.R.A. Oliveira, Optimization of finite element solutions, Proc. 3rd Conf. on Matrix Methods in Structural Mechanics, Wright-Patterson AFB, OH, October 1971.
4. J.T. Oden and L. Demkowicz, "Adaptive finite element methods for complex problems in solid and fluid mechanics", Computational Mechanics, IIT Bombay, 1985.
5. J.T. Oden and L. Demkowicz, "Survey of adaptive computational methods", in: J.T. Oden and A.K. Noor (eds.), State-of-the-art Surveys in Computational Mechanics ASME, New York, 1989.
6. A.K. Noor and I. Babuska, "Quality assessment and control of finite element solutions", Finite Elements in Analysis and Design 3, pp.1-26, 1987.
7. I. Babuska, J. Chandra and J.E. Flaherty (eds.), Adaptive Computational Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1983.
8. I. Babuska, O.G. Zienkiewicz, J. Gargo and E.R. de A. Oliveira (eds.), Accuracy Estimates and Adaptive Refinements in Finite Element Computations, Wiley, New York, 1986.
9. R.E. Ewing, A posteriori error estimation, in: J.T. Oden (ed.), Reliability in Computational Mechanics, North-Holland, Amsterdam, pp. 107-127, 1990.
10. J.T. Oden, L. Demkowicz, W. Rachowicz and T.A. Westerman, "Toward a universal h-p adaptive finite element strategy", part 2, A posteriori error estimation, Comput. Methods Appl. Mech. Eng. 77, pp. 113-180, 1989.
11. O.C. Zienkiewicz and J.Z. Zhu, "A simple error estimator and adaptive procedure for practical engineering analysis", Int. J. Numer. Methods Eng. 24, pp.337-357, 1987.
12. Y.C. Liu and H.A. Elmaraghy, "Assessment of discretized errors and adaptive refinement with quadrilateral finite elements", Int. J. Numer. Methods Eng. 33, pp.781-798, 1992.
13. J.Z. Zhu, E. Hinton and O.C. Zienkiewicz, "Adaptive finite element analysis with quadrilaterals", Comput. Struct. 40(5), pp.1097-1104,1991.
14. J.J. Rencis, T.J. Urekew, K.-Y. Jong, R. Kirk and P. Federico, "A posteriori error estimation for the finite element and boundary element methods", Comput. Struct. 37(1), pp.103-117, 1990.
15. L.F. Zeng and N.-E. Wiberg, "Adaptive h-p procedures for high accuracy finite element analysis of two-dimensional linear elastic problems", Comput. Struct. 42(6), pp.869-886, 1992.
16. I. Babuska and W.C. Rheinboldt, "A posteriori error estimates for the finite element method", Int. J. Numer. Methods Eng. 12, pp.1597-1615,1978.
17. D.W. Kelly, De.S.R. Gago, O.C. Zienkiewicz and I. Babuska, "A posteriori error analysis and adaptive processes in the finite element method: part I - error analysis, part II - adaptive mesh refinement", Int. J. Numer. Methods Eng. 19, pp.1593-1619, 1621-1656,1983.
18. R.J. Melosh and R.V. Marcal, "An energy basis for mesh refinement of solid continua", Int. J. Numer. Methods Eng. 11, pp.1083-1091,1977.
19. K. Eriksson and C. Johnson, "An adaptive finite element method for linear elliptic problems", Math. Comp. 50, pp.361-383, 1988.
20. I. Babuska, L. Planck and R. Rodriguez, "Basic problems of a posteriori error estimation", Comput. Methods Appl. Mech. Eng. 101, pp.97-112, 1992.
21. I. Babuska, L. Planck and R. Rodriguez, "Quality assessment of the a posteriori error estimation in finite elements", Finite Elements in Analysis and Design, 11, pp.285-306, 1992.
22. A.G. Paeno, Energy gradient technique for adaptive finite element analysis, 15th Annual Meeting of the Society of Engineering Science, Gainesville, Florida, 1978.
23. O.C. Zienkiewicz, De.S.R. Gago and D.W. Kelly, The hierarchical concept in finite element analysis, Comput. Struct. 16(1-4), pp.53-65, 1983.
24. I. Babuska and M. Suri, "The p- and h-p versions of the finite element method - an overview", Comput. Methods Appl. Mech. Eng. 80, pp.5-26, 1990.
25. I. Babuska and B. Szabo, "On the rates of convergence of the finite element method", Int. J. Numer. Methods Eng. 18, pp.323-341, 1982.
26. B.A. Szabo, "Mesh design for the p-version of the finite element method", Comput. Methods Appl. Mech. Eng. 55, pp.181-197, 1986.
27. J.T. Oden, L. Demkowicz, W. Rachowicz and O. Hardy, "Toward a universal h-p adaptive finite element strategy, part I: constrained approximation and data structure", Comput. Methods Appl. Mech. Eng. 77, pp.79-112, 1989.
28. I. Babuska and E. Rank, "An expert-system-like feedback approach in hp-version of the finite element method", Finite Elements in Analysis and Design 3, pp.127-147, 1987.
29. W.W. Tworzydlo and J.T. Oden, "Knowledge-based methods and smart algorithms in computational mechanics", Eng. Fract. Mech. 50(5-6), pp.759-800, 1995.
30. J.T. Oden and P. Abani, "A parallel adaptive strategy for hp finite element computations", Comput. Methods Appl. Mech. Eng. 121, pp.449-470, 1995.
31. P. Carnevali, R.B. Morris, Y. Tsuji and G. Taylor, "New basis functions and computational procedures for p-version finite element analysis", Int. J. Numer. Methods Eng. 36, pp.3759-3779,1993.
32. R.B. Morris, Y. Tsuji and P. Carnevali, "Adaptive solution strategy for solving large systems of p-type finite element equations", Int. J. Numer. Methods Eng. 33, pp.2059-2071,1992.
33. B.A. Szabo, "Implementation of a finite element software systems with h and p extension capabilities", Finite Elements in Analysis and Design 2, pp.177-194, 1986.
34. J.A. Stricklin, W.S. Ho, E.Q. Richardson and W.E. Haisler, "On isoparametric vs linear strain triangular elements", Int. J. Numer. Methods Eng. 11, pp.1041-1055,1977.
35. R.T. Haftka and R.V. Grandhi, "Structural shape optimization - a survey", Comput. Methods Appl. Mech. Eng. 57, pp.91-106, 1986.
36. Y. Ding, "Shape optimization of structures: a literature survey", Comput. Struct. 24(6), pp.985-1004,1986.
37. N. Kikuchi, K.Y. Chung, T. Torigaki and J.E. Taylor, "Adaptive finite element methods for shape optimization of linearly elastic structures", Comput. Methods Appl. Mech. Eng. 57, pp.67-89, 1986.
38. S.D. Rajan, J. Budiman and L. Gani, "Topologically based adaptive mesh generator for shape optimal design", Proc. 32nd AIAA/ASCE/ASME/AHS SDM Conf., Baltimore, MD, Part 1, pp.653-663, 1991.
39. S. Kodiyalam and V.N. Parthasarathy, "Optimized/adapted finite elements for structural shape optimization", Finite Elements in Analysis and Design 12, pp.1-11, 1992.
40. K.H. Chang and K.K. Choi, "An error analysis and mesh adaptation method for shape optimal design of structural components", Comput. Struct. 44(6), pp.1275-1289,1992.
41. G. Bugeda and J. Oliver, "A general methodology for structural shape optimization problems using automatic adaptive remeshing", Int. J. Numer. Methods Eng. 36, pp.3161-3185,1993.
42. J.E. Schiermeier and B.A. Szabo, "Interactive design based on the p-version of the finite element method", Finite Elements in Analysis and Design, 3, pp.93-107, 1987.
43. Y.K. Shyy, C. Fleury and K. Izadpanah, "Shape Optimal Design using Higher order Elements", Comput. Methods Appl. Mech. Eng. 71, pp.99-116, 1988.
44. R. King and P. Thanedar, "Shape optimization using adaptive higher order finite elements", 33 AIAA/ASME/ ASCE/AHS/ASC Structures Structural Dynamics and Materials Conf. 5, Dallas, TX, pp.2700-2707,1992.
45. S. Kodiyalam and P. Thanedar, "Some practical aspects of shape optimization and its influence on intermediate mesh refinement", Finite Elements in Analysis and Design, 15, pp.125-133, 1993.
46. R.R. Salagame and A.D. Belegundu, "Shape optimization with p-adaptivity", Proc. 5th AIAA/USAF/NASA/ISSMO Symp. on Multidisciplinary Analysis and Optimization, Panama City, FL, 1994.
47. R.R. Salagame and A.D. Belegundu, "Shape optimization with p-adaptivity", AIAA J. 33(12), pp.2399-2405,1995.
48. S. Zhang and A.D. Belegundu, "Mesh distortion control in shape optimization", AIAA J. 31(7), pp.1360-1362, 1993.
49. J.A. Bennet and M.E. Botkin, "Structural shape optimization with geometric description and adaptive mesh refinement", AIAA J. 23(3), pp.458-464, 1985.
50. A. Francavilla, C.V. Ramakrishnan, O.C. Zienkiewicz, "Optimization of Shape to Minimize Stress Concentration", J. Strain Anal. 10(2), pp.63-70, 1975.