Different computer codes used in the book are presented. The cross-references to the sections, examples, and exercises are provided.


Computer Code Load Case Load Step Maximum Absolute Node Temp 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. M. Abramowitz and I. A. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, Appl. Math. Series 55, U.S. Govt. Printing Office, Washington, DC; reprinted by Dover, New York, 1968.Google Scholar
  2. E. E. Agur and J. Vlachopoulos, Heat transfer to molten polymer flow in tubes, J. Appl. Polm. Sci., 26 (1981), 765–773.CrossRefGoogle Scholar
  3. J. Ed Akin, Finite Element Analysis for Undergraduates, Academic Press, New York, 1986.Google Scholar
  4. O. Axelsson and V. A. Barker, Finite Element Solution of Boundary Value Problems, Academic Press, Orlando, FL, 1984.MATHGoogle Scholar
  5. G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1967.MATHGoogle Scholar
  6. R. Bellman, Introduction to Matrix Analysis, 2nd ed., McGraw-Hill, New York, 1970.MATHGoogle Scholar
  7. E. Bernhardt, G. Bertacchi, and A. Moroni, Modeling of flow in extruder dies—Fundamentals and Applications of the TMconcept-faBest finite element flow analysis, in Applications of Computer Modeling of Extrusion and Other Continuous Polymer Processes (Keith T. O’Brien, eds.), Oxford University Press, Munich, 1992.Google Scholar
  8. R. B. Bird, R. Armstrong and O. Hassager, Dynamics of Polymeric Fluids, Vol. 1. Fluid Mechanics, Wiley, New York, 1976.Google Scholar
  9. D. V. Boger, A. Cabelli, and A. L. Halmos, The behavior of a power-law fluid flowing through a sudden expansion, AIChE Journal, 21 (1975), 540–549.CrossRefGoogle Scholar
  10. E. K. Bruch, The Boundary Element Method for Groundwater Flow, Lecture Notes in Engg., vol. 70, Springer-Verlag, Berlin, 1991.Google Scholar
  11. R. L. Burden and J. Douglas Faires, Numerical Analysis, Academic Press, New York, 1997.Google Scholar
  12. C. R. Calladine, Plasticity For Engineers, Wiley, New York, 1985.Google Scholar
  13. B. Carnaham, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods, Wiley, New York, 1969.Google Scholar
  14. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed., Oxford University Press, New York, 1959.Google Scholar
  15. Y. A. Çe ngel, Heat Transfer, WCB McGraw-Hill, Boston, MA, 1998.Google Scholar
  16. R. P. Chhabra and J. F. Richardson, Non-Newtonian Flow in the Process Industriex— Fundamentals and Engineering Applications, Butterworth-Heinemann, London, 1999.Google Scholar
  17. R. W. Clough, The finite element method in plane stress analysis, Proc. 2nd ASCE Conf. Electronic Comput. (Sept. 1960), Pittsburgh, PA, 345-378.Google Scholar
  18. R. W. Clough, —, The finite element method after twenty-five years: A Personal View, Computers and Structures, 12 (1980), 361–370.MathSciNetMATHCrossRefGoogle Scholar
  19. J. J. Connor and C. A. Brebbia, Finite Element Techniques for Structural Engineers, Butterworth, London, 1973.Google Scholar
  20. J. J. Connor and C. A. Brebbia, —, Finite Element Techniques for Fluid Flow, Butterworth, London, 1976.Google Scholar
  21. R. Courant, Variational methods for the solution of problems of equilibrium and vibrations, Bull. Amer. Math. Soc, 49 (1943), 1–23.MathSciNetMATHCrossRefGoogle Scholar
  22. R. Courant, —, Differential and Integral Calculus, vol. 1, 2, Interscience, New York, 1964, 1965.Google Scholar
  23. R. Courant, — and D. Hilbert, Methods of Mathematical Physics, vol. 1, Interscience, New York, 1952.Google Scholar
  24. Y. H. Dai and Y. Yuan, Nonlinear Conjugate Gradient Methods, Shanghai Scientific and Technology Publisher, 1999.Google Scholar
  25. Y. H. Dai, —and Y. Yuan, A nonlinear conjugate gradient with a strong global convergence, SIAM J. Optim., 10 (2000), 177–182.Google Scholar
  26. Y. H. Dai et al., Testing different nonlinear conjugate gradient methods, Research Report, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, 1998.Google Scholar
  27. —and Y. Yuan, A nonlinear conjugate gradient with a strong global convergence, SIAM J. of Optim., 10 (2000), 177–182.CrossRefGoogle Scholar
  28. A. J. Davies, The Finite Element Method, Clarendon Press, Oxford, 1980.MATHGoogle Scholar
  29. A. M. J. Davis and T.-Z. Mai, Steady pressure-driven non-Newtonian flow in a partially filled pipe, J. Non-Newtonian Fluid Mech., 41 (1991), 81–100.MATHCrossRefGoogle Scholar
  30. A. L. Deak and T. H. Pian, Applications of the smooth surface interpolation to finite element analysis, AIA Aerospace J. (Jan. 1967), 187–189.Google Scholar
  31. B. F. de Veubeke, Upper and lower bounds in matrix structural analysis, in Matrix Methods of Structural Analysis (B. F. de Veubeke, ed.), Pergamon, New York, 1964, pp. 165–201.Google Scholar
  32. P. England and J. Jackson, Active deformation of the continents, Ann. Rev. Earth Planet. Sci., 17 (1989), 197–226.CrossRefGoogle Scholar
  33. —and D. McKenzie, A thin viscous sheet model for continental deformation, Geophys. J. R. Astr. Soc, 70 (1983), 295–321.Google Scholar
  34. —and D. McKenzie, Correction to: A thin viscous sheet model for continental deformation, Geophys. J. R. Astr. Soc, 73 (1983), 523–532.CrossRefGoogle Scholar
  35. J. L. Fastook, The finite-element method for solving conservation equations in glaciology, Computational Science and Engineering, 1 (1993), 55–67.CrossRefGoogle Scholar
  36. B. A. Finlayson, The Method of Weighted Residuals and Variational Principles, Academic Press, New York, 1972.MATHGoogle Scholar
  37. A. F. Flores, J. C. Gottifredi, G.V. Morales, and O. D. Quiroga, Heat transfer to powerlaw fluids flowing in tubes and flat ducts with viscous heat generation, Chemical Engineering Science, 46 (1991), 1385–1392.CrossRefGoogle Scholar
  38. Fluent, Inc., Fidap Theory Manual, Fluent, Inc., 1998.Google Scholar
  39. K. O. Friedrichs, A finite difference scheme for the Neumann and the Dirichlet problems, NYO-9760, Courant Institute of Mathematical Science, New York University, New York, 1962.Google Scholar
  40. C. E. Froberg, Introduction to Numerical Analysis, Addison-Wesley, Reading, MA, 1969.Google Scholar
  41. P. Garrity, A finite element model for vortex-flow temperature separation of a compressible fluid, Final Homework Project Math 6230, University of New Orleans (Private Communication) (2000), 1–7.Google Scholar
  42. P. N. Godbole, S. Nakazawa, and O. C. Zienkiewicz, Blood flow analysis by the finite element method, International Conference on Finite Elements in Biomechanics, February 18-20, 1980.Google Scholar
  43. G. L. Goudreau and R. L. Taylor, Evaluation of numerical integration methods in elastodynamics, J. Computer Methods in Appl. Mech. Engg., 2 (1973), 69–97.MathSciNetMATHCrossRefGoogle Scholar
  44. J. Greenstadt, On the reduction of continuous problems to discrete form, IBM J. Res. Div. 3 (1959), 355–363.MathSciNetCrossRefGoogle Scholar
  45. P. C. Hammer, O. P. Marlowe, and A. H. Stroud, Numerical Integration over Simplexes and Cones, in Mathematical Tables and Aids to Computation, National Research Council, Washington, DC, vol. 10, 1956, pp. 130–137.MathSciNetMATHCrossRefGoogle Scholar
  46. J. Hersch, Equations differentielles et functions de cellules, C. R. Acad. Sci. Paris, 240 (1955), 1602–1604.MathSciNetMATHGoogle Scholar
  47. M. A. Hussain, S. Kar, and R.R. Puniyani, Relationship between power law coefficients and major blood constituents affecting the whole blood viscosity, Journal of BioSciences, 24 (1999), 329–337.CrossRefGoogle Scholar
  48. M. Iga and J. N. Reddy, Penalty finite element analysis of free surface flows of power-law fluids. The mathematics of finite elements and applications, VI, Uxbridge (1987), Academic Press, London, 423–433(1988), 76-80.Google Scholar
  49. E. Isaacson and H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966.MATHGoogle Scholar
  50. W. Janna, Introduction to Fluid Mechanics, PWS, Boston, 1993.Google Scholar
  51. —, Design of Fluid Thermal Systems, PWS, Boston, 1993.Google Scholar
  52. R. E. Jones, A generalization of the direct-stiffness method of structural analysis, AIAA J., 2 (1964), 821–826.MATHCrossRefGoogle Scholar
  53. S. Kakaç and Y. Yener, Heat Conduction, 3rd ed., Taylor and Francis, Washington, D. C., 1993.Google Scholar
  54. L. V. Kantorovich and V. L. Krylov, Approximate Methods of Higher Analysis, Interscience, New York, 1958.MATHGoogle Scholar
  55. H. Kardestuncer and D. H. Norrie (eds.), Finite Element Handbook, McGraw-Hill, New York, 1987.MATHGoogle Scholar
  56. W. M. Khairy, Partially filled pipe flow, Final Homework Project Math 6230, University of New Orleans (Private Communication) (April 1998), 1–29.Google Scholar
  57. —, Flow past a cylinder in viscous flow, Final Exam Project Math 6230, University of New Orleans (Private Communication) (May 1998), 1–91.Google Scholar
  58. K. Khellaf and G. Lauriat, A new analytical solution for heat transfer in the entrance region of ducts: Hydrodynamically developed flows of power-law fluids with constant wall temperature, Int. J. Heat Mass Transfer, 40 (1996), 3443–3447.CrossRefGoogle Scholar
  59. R. D. Krieg, Unconditional stability in numerical time integration methods, Trans. ASME, J. Appl. Mech. 40 (1973), 417–421.MATHCrossRefGoogle Scholar
  60. N. M. Newmark, A method of computation for structural dynamics, J. Engg. Mech. Division, ASCE 85 (1959), 67–94.Google Scholar
  61. M. Kŕi žek and P. Neittaanmäki, Finite Element Approximation of Variational Problems and Applications, Longman Scientific & Tecnical, Harlow, U.K., 1990.Google Scholar
  62. A. Kumar and M. Bhattacharya, Numerical analysis of aseptic processing of a non-Newtonian liquid food in a tubular heat exchanger, Chem. Eng. Comm., 103 (1991), 27–51.CrossRefGoogle Scholar
  63. P. K. Kythe, An Introduction to Boundary Element Methods, CRC Press, Boca Raton, FL, 1995.MATHGoogle Scholar
  64. —, Fundamental Solutions for Differential Operators and Applications, Birkhäuser, Boston, 1996.MATHCrossRefGoogle Scholar
  65. —, P. Puri, and M. R. Schäferkotter, Partial Differential Equations and Boundary Value Problems with Mathematica, CRC Press, Boca Raton, 2002.Google Scholar
  66. J. E. Lay, An experimental and analytical study of vortex-flow temperature separation by superposition of spiral and axial flow, Part 2, ASME J. Heat Transfer, 81 (1959), 213–222.Google Scholar
  67. N. N. Lebedev, I. P. Skalskaya, and Y. S. Uflyand, Worked Problems in Applied Mathematics, Dover, New York, 1965.Google Scholar
  68. L. Lefton and D. Wei, Finite element solutions for pressure driven flow of power law fluid in pipes of noncircular cross section, private communication, presented at Soc. of Engg., 32nd Annual Tech. Meeting, SES′95, New Orleans, LA, 29 Oct–2 Nov., 1995.Google Scholar
  69. M. J. Lighthill, Mathematical Biofluiddynamics, SIAM, Philadelphia, PA, 1975.MATHCrossRefGoogle Scholar
  70. T. J. Liu, H. M. Lin, and C. N. Hong, Comparison of two numerical methods for the solution of non-Newtonian flow in ducts, Int. J. Numer. Methods Fluids, 8 (1988), 845–861.MATHCrossRefGoogle Scholar
  71. —, S. Wen, and J. Tsou, Three-dimensional finite element analysis of polymeric fluid flow in an extrusion die. Part I: Entrance effect, Polymer Engineering Science, 34 (1994), 827–834.CrossRefGoogle Scholar
  72. D. L. Logan, A First Course in the Finite Element Method, PWS, Boston, 1997.Google Scholar
  73. B.C. Lychet and R. B. Bird, The Graetz-Nusselt problem for a power-law non-newtonian fluid, Chemical Engineering Science, 6 (1956), 35–41.CrossRefGoogle Scholar
  74. J. McMahon, Lower bounds for the electrostatic capacity of a cube, Proc. Royal Irish Acad., 55(A) (1953), 133–167.MathSciNetGoogle Scholar
  75. R. J. Melosh, Basis for the derivation of matrices for the direct stiffness method, AIAA J., 1 (1963), 1631–1637.CrossRefGoogle Scholar
  76. S. G. Nash and A. Sofer, Linear and Nonlinear Programming, McGraw-Hill, 1996.Google Scholar
  77. M. Petyt, Introduction to Finite Element Vibration Analysis, Cambridge University Press, Cambridge, 1998.Google Scholar
  78. E. Polak and G. Ribière, Note sur la convergence de directions conjugées, Rev. Francaise Infomat Recherche Opertionelle, 3e Année, 16 (1969), 35–43.Google Scholar
  79. P. Ya. Polubarinova-Kochina, Theory of Groundwater Movement, Translated from Russian by J. M. R. de Wiest, Princeton Univ. Press, Princton, NJ, 1962.Google Scholar
  80. G. Pólya, Sur une interpretation de la methode des differences finies qui peut fournir des bornes superieures ou inferieures, C. R. Acad. Sci. Paris, 235 (1952), 995–997.MathSciNetMATHGoogle Scholar
  81. —, Estimates for Eigenvalues, in Studies in Mathematics and Mechanics Presented to Richard von Mises, Academic Press, New York, 1954, pp. 200–207.Google Scholar
  82. B. T. Polyak, The conjugate gradient method in extremem problems, USSR Comp. Math. and Math. Phys., 9 (1969), 94–112.CrossRefGoogle Scholar
  83. W. Prager and J. L. Synge, Approximations in elasticity based on the concept of function space, Quart. Appl. Math., 5 (1947), 241–269.MathSciNetMATHGoogle Scholar
  84. C. T. Reddy and D. J. Shippy, Alternative integration formulae for triangular finite elements, Intern. J. Numer. Methods in Engg., 17 (1981), 133–139.MathSciNetMATHCrossRefGoogle Scholar
  85. J. N. Reddy, An Introduction to the Finite Element Method, McGraw-Hill, New York, 1984; 2nd ed., McGraw-Hill, New York, 1993.Google Scholar
  86. V. Sahai, Effects of upwinding on the solution of a 1-D advection-diffusion problem, Lawrence Livermore National Laboratory, Report UCRL-ID-109126 (December 1991), 1–15.Google Scholar
  87. I. J. Schoenberg, Contributions to the problem of approximation of equidistant data by analytic functions: Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae, Quart. Appl. Math., 4 (1948), 45–99.MathSciNetGoogle Scholar
  88. L. J. Segerlind, Applied Finite Element Analysis, 2nd ed., Wiley, New York, 1984.Google Scholar
  89. J. F. Shackelford, Introduction to Materials Science for Engineers, 5th ed., Prentice-Hall, 2000.Google Scholar
  90. V. P. Shih, C. C. Huang, and S.Y. Tsay, Extended leveque solution for laminar heat transfer to power-Law fluids in pipes with wall slip, Int. J. Heat Mass Transfer, 38 (1995), 403–408.MATHCrossRefGoogle Scholar
  91. I. S. Sokolnikoff, Mathematical Theory of Elasticity, McGraw-Hill, New York, 1956.MATHGoogle Scholar
  92. L. J. Sonder and P. C. England, Vertical averages of rheology of the continental lithosphere,, Earth Planet. Sci. Lett., 77 (1986), 81–90.CrossRefGoogle Scholar
  93. E. M. Sparrow and R. D. Cess, Radiation Heat Transfer, Augmented Edition, McGraw-Hill-Hemisphere, New York, 1978.Google Scholar
  94. J. F. Steffe, Rheological Methods in Food Process Engineering, Freeman Press, San Francisco, CA, 1992.Google Scholar
  95. K. Stephan, S. Lin, M. Durst, F. Huang, and D. Seher, A similarity relation for energy separation in a vortex tube, Int. J. Heat Mass Transfer, 27 (1984), 911–920.CrossRefGoogle Scholar
  96. J. L. Synge, Triangulation in the hypercircle method for plane problems, Proc. Royal Irish Acad., 54(A) (1952), 341–367.MathSciNetGoogle Scholar
  97. J. L. Synge, —, The Hypercircle in Mathematical Physics, Cambridge University Press, New York, 1957.MATHGoogle Scholar
  98. B. Szabó and I. Babuska, Finite Element Analysis, Wiley, New York, 1991.MATHGoogle Scholar
  99. C. Taylor and T. G. Hughes, Finite Element Programming of the Navier-Stokes Equations, Pineridge Press Limited, Swansea, UK, 1981.MATHGoogle Scholar
  100. S. P. Timoshenko and N. Godier, Theory of Elasticity, McGraw-Hill, New York, 1951.MATHGoogle Scholar
  101. S. P. Timoshenko —, D.H. Young, and W. Weaver, Jr., Vibration Problems in Engineering, Wiley, New York, 1974.Google Scholar
  102. P. Tong and J. N. Rossettos, Finite-Element Method, The MIT Press, Cambridge, MA, 1977.Google Scholar
  103. D. Touati-Ahmed and C. Storey, Efficient hybrid conjugate gradient techniques, J. Optimization Theory Appl., 64 (1990), 379–397.MathSciNetMATHCrossRefGoogle Scholar
  104. A. C. Ugural, Stresses in Plates and Shells, McGraw-Hill, New York, 1981.Google Scholar
  105. J. V. Uspensky, Theory of Equations, McGraw-Hill, 1948.Google Scholar
  106. K. Washizu, Variational Methods in Elasticity and Plasticity, 2nd ed., Pergamon Press, New York, 1975.MATHGoogle Scholar
  107. W. Weaver, Jr. and P. R. Johnston, Finite Elements for Structural Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1984.MATHGoogle Scholar
  108. D. Wei, Penalty approximations to the stationary power-law Navier-Stokes problem, Numer. Funct. Anal. Optim., 22 (2001), 749–765.MathSciNetMATHCrossRefGoogle Scholar
  109. —, Existence and uniqueness of solutions to the stationary power-law Navier-Stokes problem in bounded convex domains, Proceedings of Dynamic Systems and Applications III (2001), 611–618.Google Scholar
  110. —and Z. Zhang, Decay estimates of heat transfer to molten polymer flow in pipes with visous dissipation, Electronic Journal of Differential Equations. 2001 (2001), 1–14.MathSciNetGoogle Scholar
  111. —and L. Lefton, A penalty method for approximations of the stationary power-law Stokes problem, Electron. J. Diff. Eqns., 2001 (2001), 1–12.Google Scholar
  112. —and H. Luo, Finite element solutions of heat transfer in molten polymer flow in tubes with viscous dissipation, International Journal of Heat and Mass Transfer 46 (2003), 3097–3108.MATHCrossRefGoogle Scholar
  113. —and L. Lefton, Penalty finite element solutions of the stationary power-law Stokes problem, to appear in, J. of Numer. Math.Google Scholar
  114. H. F. Weinberger, Upper and lower bounds for eigenvalues by finite difference methods, Commun. Pure Appl. Math., 9 (1956), 613–623.MathSciNetMATHCrossRefGoogle Scholar
  115. H. F. Weinberger, —, Lower bounds for higher eigenvalues by finite difference methods, Pacific J. Math., 8 (1958), 339–368.MathSciNetMATHGoogle Scholar
  116. G. N. White, Difference equations for plane thermal elasticity, LAMS-2745, Los Alamos Scientific Laboratories, Los Alamos, NM, 1962.Google Scholar
  117. J. R. Whiteman, A Bibliography for Finite Elements, Academic Press, New York, 1975.MATHGoogle Scholar
  118. W. Wilkinson, Non-Newtonian Fluids, Pergamon Press, New York, 1960.Google Scholar
  119. J. C. Wu and J. F. Thompson, Numerical solutions of time dependent incompressible Navier-Stokes equation using integro-differential formulation, Comput. Fluids, 1 (1973), 197–215.MATHCrossRefGoogle Scholar
  120. O. C. Zienkiewicz and Y. K. Cheung, Finite elements in the solution of field problems, The Engineer, 220 (1965), 507–510.Google Scholar
  121. O. C. Zienkiewicz —and R. L. Taylor, The Finite Element Method, Vol. 1: Linear Problems, McGraw-Hill, New York, 1989.Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Prem K. Kythe
    • 1
  • Dongming Wei
    • 1
  1. 1.Department of MathematicsUniversity of New OrleansNew OrleansUSA

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