Stochastic finite element method (FEM) and design of experiments for Pressure Vessel and Piping (PVP) decision making

American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP

Volumn 2006, Issue , 2006, Pages

  Fong, Jeffrey T ^a   Filliben, James J ^a   DeWit, Roland ^a   Bernstein, Barry ^b  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

^b Illinois Institute of Technology   (United States)

Author keywords

Anisotropie materials; Applied mechanics; Atomic force microscopy; Cantilevers; Design of experiments; Engineering statistics; Finite element method; Free vibrations; Natural frequencies; Reference benchmarks; Sensitivity analysis; Single crystal silicon

Indexed keywords

ATOMIC FORCE MICROSCOPY; CANTILEVER BEAMS; DECISION MAKING; DESIGN FOR TESTABILITY; FINITE ELEMENT METHOD; MECHANICS; NATURAL FREQUENCIES; PIPING SYSTEMS; SENSITIVITY ANALYSIS;

ANISOTROPIE MATERIALS; DESIGN OF EXPERIMENTS; ENGINEERING STATISTICS; FREE VIBRATIONS; REFERENCE BENCHMARKS; SINGLE CRYSTAL SILICON;

PRESSURE VESSEL CODES;

EID: 33751338083     PISSN: 0277027X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/PVP2006-ICPVT-11-93927     Document Type: Conference Paper

References (78)

1. Post, D. E., and Votta, L. G., 2005, "Computational Science Demands a New Paradigm," Physics Today. Jan. 2005, pp. 3541(2005).
2. Ku, H. H., 1966, "Notes on the Use of Propagation of Error Formulas," J. Research of the National Bureau of Standards - C. Engineering and Instrumentation, Vol. 70C, No. 4, pp. 263-273 (1966).
3. ISO, 1993, Guide to the Expression of Uncertainty in Measurement, prepared by ISO Technical Advisory Group 4 (TAG 4), Working Group 3 (WG 3), Oct. 1993. ISO/TAG 4, sponsored by the BIPM (Bureau International des Poids et Mesures), IEC (International Electrotechnical Commission), IFCC (International Federation of Clinical Chemistry), ISO, IUPAC (Int. Union of Pure and Applied Chemistry), IUPAP (International Union of Pure and Applied Physics), and OIML (Int. Organization of Legal Metrology).
4. Hammer, C., 1967, "Statistical validation of mathematical computer routines," AFIPS Proc. Spring Joint Computer Conference (SJCC) (1967).
5. Cody, W. J., 1969, "Performance testing of function subroutines," AFTPS Proc. Spring Joint Computer Conference (SJCC). pp. 759-763 (1969).
6. Lozier, D. W., Maximon, L. C., and Sadowski, W. L., 1973, "Performance Testing of a FORTRAN Library of Mathematical Function Routines - A Case Study in the Application of Testing Techniques," J. Res. Natl. Bur. Stand., Vol. 77B, Nos. 3 & 4, pp. 101-110 (1973).
7. Lozier, D. W., 1983, "The Use of Floating-Point and Interval Arithmetic in the Computation of Error Bounds," IEEE Transactions on Computers, Vol. C-32, No. 4, pp. 411-417 (1983).
8. Rice, J. R., and Boisvert, R. F., 1985, Solving Elliptic Problems Using ELLPACK. Springer-Verlag (1985).
9. th AIAA Aerospace Ground Testing Conference, Colorado Spring, CO (1994).
10. Karniadakis, G E., 1995, "Toward a Numerical Error Bar in CFD," ASME Trans., J. Fluids Engineering. 117, pp. 7-9 (1995).
11. Dept. of Defense, 1996, POD Directive No. 5000.61: Modeling and Simulation (M&S) Verification, Validation, and Accreditation (W&A), Defense Modeling and Simulation Office, Office of the Director of Defense Research and Engineering (1996). www.dmso.mil/docslib
12. DOD, 1996, Verification, Validation, and Accreditation (VV&A) Recommended Practices Guide, Defense Modeling and Simulation Office, Office of the Director of Defense Research and Engineering, www.dmso.mil/docslib (1996)
13. Boisvert, R. F., ed., 1997, Quality of Numerical Software - Assessment and Enhancement. Proc. IFIP TC2/WG2.5 Working Conf. on the Quality of Numerical Software, Assessment and Enhancement, Oxford, U.K., 8-12 July 1996. Chapman & Hall (1997).
14. Cohen, M. L., Ralph, J. E., and Steffey, D. L., eds., 1998, Statistics, Testing, and Defense Acquisition: New Approaches and Methodological Improvements. National Academy Press, Washington, DC (1998).
15. Roache, P. J., 1998, "Verification of Codes and Calculations," AIAA Journal Vol. 36, No. 5, pp. 696-702 (1998).
16. Roache, P. J., 1998, Verification and Validation in Computational Science and Engineering. Hermosa Publishers, Albuquerque, NM (1998).
17. Croarkin, C., Pagan, P., Filliben, J. J., Gill, L., Guthrie, W., Lagergren, E., Liu, H. K., Rogers, J., Rust, B., Vangel, M., and Zhang, N. F., 2000, Statistical Reference Datasets (StRD), National Institute of Stand. And Technology, Gaithersburg, MD 20899. (http://www.itl.nist.gov/div898/strd/index. html)
18. st Century, Oct. 22-23, 2002, John Hopkins University/Applied Physics Laboratory, Laurel, MD, D. Pace & S. Stevenson, eds., Society for Modeling & Simulation Int'1 (2002).
19. st Century, 22-23 Oct. 2002, John Hopkins Univ./Appl. Phys. Lab., Laurel, Maryland, D. Pace & S. Stevenson, eds., published by Society for Modeling & Simulation International (2002).
20. th International Conf. and Workshop on Numerical Simulation of 3-D Sheet Metal Forming Processes - Verification of Simulation with Experiment, Jeju Islands, Korea, Oct. 21-25, 2002, Yang, D., Oh, S. I., Huh, H., and Kim, Y. H., eds., Vols. 1. pp. 313-318. Published by the Korean Adv Inst Sci & Tech., 373-1, Science Town, Taejon, 305-701, Korea (2002).
21. Lord, G J., and Wright, L., 2003, Uncertainty Evaluation in Continuous Modelling NPL Report CMSC 31/03 to the National Measurement System Policy Unit, U. K. Department of Trade and Industry, December 2003.
22. Fong, J. T., Filliben, J. J., Fields, R. J., deWit, R., and Bernstein, B., 2004, "A Reference Benchmark Approach to V & V of Computer Models of High-Consequence Engineering Systems," in Proc. NIST-DOD Workshop, Nov. 8-9, 2004, Gaithersburg, MD, J. T. Fong and R. deWit, eds., Vol. 2, Chap. 4, pp. 77-94.29. Published as a working document of NIST Math. & Comput. Sci. Div. (NIST_891_fong2004.11_V&V_Workshop_Report.pdf), and available upon request to fong(q)nist.gov.
23. Fong, J. T., 2005, "AB C of Engineering Statistics and a Reference Benchmark Approach to Verification and Validation (V & V) of Multi-Physics Simulations of High-Consequence Engineering Systems," Proc. Symp. on "Applied Mechanics and Multi-Physics Simulations of High-Consequence Engineering Systems." Stanford University, CA, April 18, 2005, pp. 169-216. Stanford University Division of Mechanics and Computation, Dept of Mechanical Engineering, Stanford, CA 94305-4040 (2005).
24. Box, G. E., Hunter, W. G., and Hunter, J. S., 1978, Statistics for Experimenters: An Introduction to Design, Data Analysis, and Modeling Building. Wiley (1978).
25. Liu, H. K., and Zhang, N. F., 2002, "Bayesian Approach to Combining Results from Multiple Methods," Proc. Amer. Stat. Assoc., pp. 158-163 (2002).
26. ASME, 1969, Stochastic Processes in Dynamical Problems. Proc. Symp. co-sponsored by Shock and Vibration Committee of ASME Applied Mechanics Division and ASME Automatic Control Division, and held at Los Angeles, CA, on Nov. 19, 1969. New York: Amer. Soc. Mechanical Engineers (1969).
27. rd International Conference on Structural Safety and Reliability. Amsterdam, Elsevier, pp. 395-408.
28. Vanmarcke, E., and Grigoriu, M., 1983, "Stochastic finite element analysis of simple beams," J. Eng. Mech. Div. of ASCE, 109, pp. 1203-1214.
29. Liu, W. K., Belytschko, T., and Mani. A., 1986, "Random Field Finite Elements," Int. J. Numerical Methods in Engrg., 23, pp. 1831-1845.
30. Benaroya, H., and Rehak, M.,1988, "Finite element methods in probabilistic structural analysis: A selected review," Appl. Mech. Review, 41(5), pp. 201-213.
31. Shinozuka, M., and Yamazaki, F., 1988, "Stochastic finite element analysis: An introduction," Stochastic Structural Dynamics. Progress in Theory and Applications, S. T. Ariaratnm, G. I. Schueller, and I. Eishakoff, eds., Elsevier Appl. Sci., pp. 241-291.
32. Ghanem, R. G., and Spanos, P. D., 1991, Stochastic Finite Elements: A Spectral Approach, revised edition of an original version published in 1991 by Springer-Verlag. Dover (2003).
33. Matthies, H. G., and Bucher, C., 1999, "Finite elements for stochastic media problems," Comput. Methods Appl. Mechanics and Engrg., 168, pp. 3-17.
34. Ghanem, R., 1999, "Ingredients for a general purpose stochastic finite elements implementation," Comput. Methods Appl. Mechanics and Engineering. 168, pp. 19-34.
35. Ostoja-Starzewski, M., and Wang, X., 1999, "Stochastic finite elements as a bridge between random material microstructure and global response," Comput. Methods Appl. Mechanics and Engrg., 168, pp. 35-49.
36. Haldar, A., and Mahadevan, S., 2000, Reliability Assessment Using Stochastic Finite Element Analysis. Wiley (2000)
37. Rao, B. N., and Rahman, S., 2000, "An Efficient Messless Method for Fracture Analysis of Cracks," Computational Mechanics, Vol. 26, pp. 398408 (2000).
38. Anders, M., and Hori, M., 2001, "Three-dimensional stochastic finite element method for elasto-plastic bodies," Int. J. for Numerical Methods in Engrg., 51, pp. 449-478.
39. Rahman, S., and Rao, B. N., 2001, "A Perturbation Method for Stochastic Meshless Analysis in Elastostatics," Int. J. Num. Meth. Eng., Vol. 50, No. 8, pp. 1969-1991 (2001).
40. Elishakoff, I., and Ren, Y., 2003, Finite Element Methods for Structures with Large Stochastic Variations. Oxford University Press (2003).
41. Babuska, I., Tempone, R., and Zouraris, G. E., 2004, "Galerkin Finite Element Approximations for Stochastic Elliptic Partial Differential Equations," SIAM J. Numer. Anal., 42(2), pp. 800-825.
42. Hlavacek, I., Chleboun, J., and Babuska, I., 2004, Uncertain Input Data Problem and the Worst Scenario Method. Elsevier (2004).
43. Rahman, S., and Xu, H., 2005, "A Meshless Method for Computational Stochastic Mechanics," Int. J. Compu. Meth. Eng. Sci. Mech.: Vol. 6, pp. 41-58 (2005).
44. Fong, J. T., 2005, "ABC of Statistics for Verification and Validation (V & V) of Simulations of High-Consequence Engineering Systems," Proc. 2005 ASME Pressure Vessels and Piping Division Conference, July 17-21, 2005, Denver, CO., Paper PVP2005-MF-13-1 (2005).
45. Fong, J. T., Filliben, J. J., deWit, R., Fields, R. J., Bernstein, B., and Marcal, P. V., 2006, "Uncertainty in Finite Element Modeling and Failure Analysis: A Metrology-Based Approach," ASME Trans., J. Press. Vess. Tech., Vol. 128, pp. 140-147 (2006).
46. ABAQUS, 2005, ABAOUS User's Manual. Version 6.5-5. ABAQUS, Inc., 1080 Main St., Pawtucket, Rhode Island 02860-4847 (2005).
47. ANSYS, 2005, ANSYS User's Manual. Release 10.0. ANSYS, Inc., 275 Technology Dr., Cannonsburg, PA 15317 (2005).
48. LSTC, 2003, LS-DYNA Keyword User's Manual Version 970, April 2003, Livermore Software Technology Corp., Livermore, CA (2003).
49. rd ed., Mathematica Version 3. Wolfram Media / Cambridge University Press (1996).
50. TrueGrid, 2001, TrueGrid User's Manual. Version 2.1.0, Vols. 1 & 2, Dec. 26, 2001, XYZ Scientific Applications, Inc., 1324 Concannon Blvd, Livermore, CA (2001).
51. Filliben, J. J., and Heckert, N. A., 2002, DATAPLOT: A Statistical Data Anal. Software System, a public domain software released by NIST, Gaithersburg, MD 20899, http://www.itl.nist.gov/div898/software/dataplot.html.
52. Lekhnitskii, S. G., 1981, Theory of Elasticity of an Anisotropie Body, translated from the revised 1977 Russian edition. Moscow: MIR Publishers (1981).
53. th ed., first American printing, 1944. New York: Dover Publications (1944).
54. nd ed. McGraw-Hill (1951).
55. rd ed. D. Van Nostrand (1955)
56. Petyt, M., 1998, Introduction to finite element vibration analysis, paperback ed Cambridge University Press (1998).
57. Hughes, T. J. R., 2000, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, revised edition of an original version published in 1987 by Prentice-Hall entitled "The Finite Element Method." Dover (2000).
58. th ed., Vol. 1, The Basis, Butterworth-Heinemann (2000).
59. nd ed. (Revised). Berkeley, CA 94704: Computers and Structures, Inc. (2003).
60. Nye, J. F., 1957, Physical Properties of Crystals: Their Representation by Tensors and Matrices, Chapter VIII (pp. 131-149) and Appendix B (pp. 276-288). Oxford University Press (1957).
61. rd Revised Edition. Pergamon (1980).
62. Draper, N. R., and Smith, H., 1966, Applied Regression Analysis. Wiley (1966).
63. Nelson, P. R., Coffin, M., and Copeland, K. A. F., 2003, Introductory Statistics for Engineering Experimentation. Elsevier Academic Press (2003).
64. Rabe, U., Janser, K., and Arnold, W., 1996, "Vibrations of free and surface-coupled atomic force microscope cantilevers: Theory and experiment," Rev. Sci. Instrum., 67 (9), 3281-3293 (1996).
65. Kester, E., Rabe, U., Presmanes, L., Tailhades, Ph., and Arnold, W., 2000, "Measurement of Young's modulus of nanocrystalline ferrites with spinel structures by atomic force acoustic microscopy," J. Phys. Chem. Solids, 61, 1275-1284 (2000).
66. Hurley, D. C., Shen, K., Jennett, N. M., and Turner, J. A., 2003, "Atomic force acoustic microscopy methods to determine thin-film elastic properties," J. Appl. Phys., 94(4), 2347-2354 (2003).
67. Hurley, D. C., 2004, "Summary of Finite Element Analysis (FEA) work for AFAM completed at NIST, Boulder, CO, as of Dec. 23, 2004," private communication via email to J. Fong (2004).
68. McSkimin, H. J., and Andreatch, P., Jr., 1964, "Elastic Moduli of Silicon vs. Hydrostatic Pressure at 25.0 C and -195.8 C" I Appl. Phys., 35(7) 2161-2165 (1964).
69. Wortman, J. J., and Evans, R. A., 1965, "Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon and Germanium," J. Appl. Phys., 36(1), 153-156 (1965).
70. Hall, J. J., 1967. Phys. Rev., 161. p. 756 (1967).
71. George, A., 1999, "Section 3.2: Elastic constants and moduli of diamond cubic Si," in Properties of Crystalline Silicon. R. Hull, ed., published by INSPEC, The Institution of Electrical Engineers, London, U.K. (1999).
72. Okada, Y., 1999, "Section 3.1: Diamond cubic Si: structure, lattice parameter and density," in Properties of Crystalline Silicon. R. Hull, ed., published by INSPEC, The Institution of Electrical Engineers, London, U.K. (1999).
73. Ono, N., Kitamura, K., Nakajima, K., and Shimanuki, Y., 2000, "Measurement of Young's Modulus of Silicon Single Crystal at High Temperature and Its Dependency on Boron Concentration Using the Flexural 'Vibration Method," Japan J. Appl. Phys., 39, Part 1, No. 2A, pp.368-371 (2000).
74. de Wit, R., 2003, "Determination of the Single Crystal Elastic Constants by Diffraction from a Cubic Polycrystal," NISTIR 6944, National Institute of Standards and Technology, Gaithersburg, MD, 20899, January 2003, 14 pp.
75. Fong, J. T., Filliben, J. J., Heckert, N. A., de Wit, R., and Bernstein, B., 2006, "A Reference Benchmark and Design of Experiment Approach to Verification of Solutions of a Free Vibration Problem in Anisotropie Elasticity by Multiple Finite Element Methods," manuscript to be submitted to a technical journal.
76. th ed., pp. 583-608. Prentice-Hall (2002).
77. Ballio, G, and Mazzolani, F. M. 1983, "Chap. 7. Connections," in Theory and Design of Steel Structures, pp. 213-304. Chapman and Hall (1983).
78. Oden, J. T. (Chair), et al, 2006, "Simulation-Based Engineering Science (SEES): Revolutionizing Engineering Science through Simulation," Report of the NSF Blue Ribbon Panel on SEES. Feb. 2006 hllp://www.iccs.ulcxas. udu/cvents/SBES_Final_Rcport.pdf