MultiPhysicsVault/.raw/ConceptsApplicationsFiniteElementAnalysis/ConceptsApplicationsFiniteElementAnalysis_064.md

Prismatic Solids," Report UC-SESM-70-21, Civil Engineering Department, University of California, Berkeley, 1970 (PB-196-462, N.T.I.S.).
10.9 O. C. Zienkiewicz and J. M. Too, "The Finite Prism in Analysis of Thick Simply Supported Bridge Boxes," Proc. Inst. Civil Engrs., Vol. 53, Part 2, 1972, pp. 147–172.
10.10 G. A. Greenbaum, L. D. Hofmeister, and D. A. Evenson, "Pure Moment Loading of Axisymmetric Finite Element Models," Int. J. Num. Meth. Engng., Vol. 5, No. 4, 1973, pp. 459–463.
10.11 K. J. Bathe and C. A. Almeida, "A Simple and Effective Pipe Elbow Element-Linear Analysis," J. Appl. Mech., Vol. 47, No. 1, 1980, pp. 93–100.
10.12 K. J. Han and P. L. Gould, "Line Node and Transitional Shell Element for Rotational Shells," Int. J. Num. Meth. Engng., Vol. 18, No. 6, 1982, pp. 879–895.
10.13 W. M. Chen and P. Tsai, "The Combined Use of Axisymmetric and Solid Elements for Three Dimensional Stress Analysis," Computers & Structures, Vol. 18, No. 4, 1984, pp. 689–694.

CHAPTER 11

11:1 S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd Ed., McGraw-Hill, New York, 1959.
11.2 F. J. Plantema, Sandwich Construction, John Wiley & Sons, New York, 1966.
11.3 J. M. Whitney and A. W. Leissa, "Analysis of Heterogeneous Anisotropic Plates," J. Appl. Mech., Vol. 36, No. 2, 1969, pp. 261-266.
11.4 M. M. Hrabok and T. M. Hrudey, "A Review and Catalog of Plate Bending Finite Elements," Computers & Structures, Vol. 19, No. 3, 1984, pp. 479–495.
11.5 R. H. Gallagher, Finite Element Analysis: Fundamentals, Prentice-Hall, Englewood Cliffs, NJ, 1975.
11.6 R. J. Melosh, “Basis for Derivation of Matrices for the Direct Stiffness Method,” AIAA Jnl., Vol. 1, No. 7, 1963, pp. 1631–1637 (discussion: Vol. 2, No. 2, 1964, p. 403; Vol. 2, No. 6, 1964, p. 1161; Vol. 3, No. 6, 1965, pp. 1215–1216).
11.7 Y. K. Cheung, Finite Strip Method in Structural Analysis, Pergamon Press, Oxford, England, 1976.
11.8 T. J. R. Hughes and M. Cohen, "The 'Heterosis' Finite Element for Plate Bending," Computers & Structures, Vol. 9, No. 5, 1978, pp. 445–450.
11.9 E. Hinton and H. C. Huang, "A Family of Quadrilateral Mindlin Plate Elements with Substitute Shear Strain Fields," Computers & Structures, Vol. 23, No. 3, 1986, pp. 409–431.
11.10 J. A. Stricklin et al., "A Rapidly Converging Triangular Plate Element," AIAA Jnl., Vol. 7, No. 1, 1969, pp. 180–181.
11.11 J. L. Batoz, K. J. Bathe, and L. W. Ho, “A Study of Three-Node Triangular Plate Bending Elements,” Int. J. Num. Meth. Engng., Vol. 15, No. 12, 1980, pp. 1771–1812.
11.12 J. L. Batoz, “An Explicit Formulation for an Efficient Triangular Plate Bending Element,” Int. J. Num. Meth. Engng., Vol. 18, No. 7, 1982, pp. 1077–1089.
11.13 C. Jeyachandrabose and J. Kirkhope, “An Alternative Formulation for the DKT Plate Bending Element,” Int. J. Num. Meth: Engng., Vol. 21, No. 7, 1985, pp. 1289–1293.
11.14 T. J. R. Hughes, M. Cohen, and M. Haroun, "Reduced and Selective Integration Techniques in the Finite Element Analysis of Plates," Nucl. Engng. Design, Vol. 46, No. 1, 1978, pp. 203-222.
11.15 M. P. Rossow, "Efficient C^0 Finite-Element Solutions of Simply Supported Plates of Polygonal Shape," J. Appl. Mech., Vol. 44, No. 2, 1977, pp. 347-349.
11.16 T. J. R. Hughes and T. E. Tezduyar, "Finite Elements Based on Mindlin Plate

Theory with Particular Reference to the Four-Node Bilinear Isoparametric Element," J. Appl. Mech., Vol. 48, No. 3, 1981, pp. 587–596.
11.17 J. Donea and L. G. Lamain, "A Modified Representation of Transverse Shear in C^0 Quadrilateral Plate Elements," Comp. Meth. Appl. Mech. Engng., Vol. 63, No. 2, 1987, pp. 183-207.

CHAPTER 12

12.1 F. Kikuchi and K. Tanizawa, "Accuracy and Locking-Free Property of the Beam Element Approximation for Arch Problems," Computers & Structures, Vol. 19, No. 1-2, 1984, pp. 103-110.
12.2 G. Prathap, "The Curved Beam/Deep Arch/Finite Ring Element Revisited," Int. J. Num. Meth. Engng., Vol. 21, No. 3, 1985, pp. 389–407.
12.3 H. R. Meck, "An Accurate Polynomial Displacement Function for Finite Ring Elements," Computers & Structures, Vol. 11, No. 4, 1980, pp. 265-269.
12.4 P. M. Mebane and J. A. Stricklin, "Implicit Rigid Body Motion in Curved Elements," AIAA Jnl., Vol. 9, No. 2, 1971, pp. 344–345.
12.5 G. Prathap and C. R. Babu, "An Isoparametric Quadratic Thick Curved Beam Element," Int. J. Num. Meth. Engng., Vol. 23, No. 9, 1986, pp. 1583–1600.
12.6 S. F. Pawsey and R. W. Clough, "Improved Numerical Integration of Thick Shell Finite Elements," Int. J. Num. Meth. Engng., Vol. 3, No. 4, 1971, pp. 575-586.
12.7 M. A. Crisfield, "Explicit Integration and the Isoparametric Arch and Shell Elements," Comm. in Appl. Num. Meth., Vol. 2, No. 2, 1986, pp. 181-187.
12.8 N. Carpenter, H. Stolarski, and T. Belytschko, "Improvements in 3-Node Triangular Shell Elements," Int. J. Num. Meth. Engng., Vol. 23, No. 9, 1986, pp. 1643–1667.
12.9 O. C. Zienkiewicz, The Finite Element Method, 3rd Ed., McGraw-Hill, London, 1977.
12.10 C. R. Babu and G. Prathap, "A Field-Consistent Two-Noded Axisymmetric Shell Element," Int. J. Num. Meth. Engng., Vol. 23, No. 7, 1986, pp. 1245–1261.
12.11 A. Tessler, "An Efficient, Conforming Axisymmetric Shell Element Including Transverse Shear and Rotary Inertia," Computers & Structures, Vol. 15, No. 5, 1982, pp. 567–574.
12.12 B. M. Irons and A. Razzaque, "Further Modification to Ahmad's Shell Element," Int. J. Num. Meth. Engng., Vol. 5, No. 4, 1973, pp. 588–589.
12.13 T. Belytschko et al., "Implementation and Application of a 9-Node Lagrange Shell Element With Spurious Mode Control," Computers & Structures, Vol. 20, No 1-3, 1985, pp. 121-128.
12.14 V. T. Nicholas and E. Citipitioglu, "A General Isoparametric Finite Element Program SDRC SUPERB," Computers & Structures, Vol. 7, No. 2, 1977, pp. 303–313
12.15 R. H. MacNeal and R. L. Harder, “A Proposed Standard Set of Problems to Tes Finite Element Accuracy,” Finite Elements in Analysis and Design, Vol. 1, No 1, 1985, pp. 3–20.
12.16 S. S. Murthy and R. H. Gallagher, "Patch Test Verification of a Triangular Thin Shell Element Based on Discrete Kirchhoff Theory," Comm. in Appl. Num. Meth. Vol. 3, No. 2, 1987, pp. 83–88.
12.17 H. Stolarski and T. Belytschko, "Membrane Locking and Reduced Integration for Curved Elements," J. Appl. Mech., Vol. 49, No. 1, 1982, pp. 172–176.

CHAPTER 13

13.1 R. W. Clough and J. Penzien, Dynamics of Structures, McGraw-Hill, New York, 1975.

13.2 R. R. Craig, Jr., Structural Dynamics, John Wiley & Sons, New York, 1981.
13.3 J. W. S. Rayleigh, Theory of Sound, 2nd Ed., Vols. I and II, Dover Publications, New York, 1945 (originally published in 1894).
13.4 J. S. Archer, "Consistent Matrix Formulations for Structural Analysis Using Finite Element Techniques," AIAA Jnl., Vol. 3, No. 10, 1965, pp. 1910–1918.
13.5 E. Hinton, T. Rock, and O. C. Zienkiewicz, "A Note on Mass Lumping and Related Processes in the Finite Element Method," Earthquake Engng. Struct. Dynamics, Vol. 4, No. 3, 1976, pp. 245–249.
13.6. K. S. Surana, "Lumped Mass Matrices with Non-Zero Inertia for General Shell and Axisymmetric Shell Elements," Int. J. Num. Meth. Engng., Vol. 12, No. 11, 1978, pp. 1635–1650.
13.7 D. S. Malkus and M. E. Plesha, “Zero and Negative Masses in Finite Element Vibration and Transient Analysis,” Comp. Meth. Appl. Mech. Engng., Vol. 59, No. 3, 1986, pp. 281–306.
13.8 D. S. Malkus, M. E. Plesha, and M. R. Liu, “Reversed Stability Conditions in Transient Finite Element Analysis,” Comp. Meth. Appl. Mech. Engng., Vol. 68, No. 1, 1988, pp. 97–114.
13.9 G. J. Fix, "Effects of Quadrature Errors in Finite Element Approximation of Steady State Eigenvalue and Parabolic Problems," in Mathematical Foundations of the Finite Element Method, I. Babuska and A. K. Aziz, eds., Academic Press, New York, 1972, pp. 525-556.
13.10 Z. Kopal, Numerical Analysis, John Wiley & Sons, New York, 1955.
13.11 S. H. Crandall, Engineering Analysis, McGraw-Hill, New York, 1956.
13.12 E. Isaacson and H. B. Keller, Analysis of Numerical Methods, John Wiley & Sons, New York, 1966.
3.13 E. Dokumaci, "A Critical Examination of Discrete Models in Vibration Problems of Continuous Systems," J. Sound Vibration, Vol. 53, No. 2, 1977, pp. 153–164.
3.14 T. Belytschko, "A Survey of Numerical Methods and Computer Programs for Dynamic Structural Analysis, Nucl. Engng. Design, Vol. 37, No. 1, 1976, pp. 23-34.
3.15 R. H. MacNeal, ed., The NASTRAN Theoretical Manual (Level 16.0), NASA-SP-221(03), march 1976 (N79-27531, N.T.I.S.).
3.16 T. Belytschko and W. L. Mindle, "The Treatment of Damping in Transient Computations," in Damping Applications for Vibration Control, P. J. Torvik, ed., ASME AMD, Vol. 38, 1980, pp. 123–132.
3.17 M. E. Plesha, "Mixed Time Integration for the Transient Analysis of Jointed Media," Int. J. Num. An. Meth. Geomech., Vol. 10, No. 1, 1986, pp. 91-110.
3.18 K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1982.
3.19 L. Fox, An Introduction to Numerical Linear Algebra, Oxford University Press, New York, 1965.
3.20 W. C. Hurty and M. F. Rubinstein, Dynamics of Structures, Prentice-Hall, Englewood Cliffs, NJ, 1964.
3.21 O. C. Zienkiewicz, R. W. Lewis, and K. G. Stagg, Numerical Methods in Offshore Engineering, John Wiley & Sons, Chichester, England, 1978.
3.22 N. R. Maddox, "On the Number of Modes Necessary for Accurate Response and Resulting Forces in Dynamic Analysis," J. Appl. Mech., Vol. 42, No. 2, 1975, pp. 516–517.
3.23 O. E. Hansteen and K. Bell, "On the Accuracy of Mode Superposition Analysis in Structural Dynamics," Earthquake Engng. Struct. Dynamics, Vol. 7, No. 5, 1979, pp. 405–411.
3.24 R. E. Cornwell, R. R. Craig, Jr., and C. P. Johnson, “On the Application of the Mode-Acceleration Method to Structural Engineering Problems,” Earthquake Engng. Struct. Dynamics, Vol. 11, No. 5, 1983, pp. 679–688.
3.25 E. L. Wilson, M. Y. Yuan, and J. M. Dickens, "Dynamic Analysis by Direct Superposition of Ritz Vectors," Earthquake Engng. Struct. Dynamics, Vol. 10, No. 6, 1982, pp. 813–821.

13.26 V. N. Shah, G. J. Bohm, and A. N. Nahavandi, "Modal Superposition Method for Computationally Economical Nonlinear Structural Analysis," J. Pressure Vessel Tech., ASME, Vol. 101, No. 2, 1979, pp. 134–141.
13.27 J. A. Stricklin and W. E. Haisler, "Formulations and Solution Procedures for Nonlinear Structural Analysis," Computers & Structures, Vol. 7, No. 1, 1977, pp. 125–136.
13.28 K. J. Bathe and E. L. Wilson, Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1976.
13.29 R. J. Guyan, "Reduction of Stiffness and Mass Matrices," AIAA Jnl., Vol. 3, No. 2, 1965, p. 380.
13.30 I. U. Ojalvo, "Computer Methods for Determining Vibration Modes of Complex Structures," Shock and Vibration Digest, Vol. 5, No. 5, May, 1983, pp. 3–10.
13.31 C. A. Felippa, "Refined Finite Element Analysis of Linear and Nonlinear Two-Dimensional Structures," Ph.D. dissertation, University of California, Berkeley, 1966 (also available as PB-178-418 and PB-178-419, N.T.I.S.; computer programs in the latter).
13.32 J. D. Sowers, "Condensation of Free Body Mass Matrices Using Flexibility Coefficients," AIAA Jnl., Vol. 16, No. 3, 1978, pp. 272-273.
13.33 M. Geradin, "Error Bounds for Eigenvalue Analysis by Elimination of Variables," J. Sound Vibration, Vol. 19, No. 2, 1971, pp. 111-132.
13.34 R. L. Kidder, "Reduction of Structural Frequency Equations," AIAA Jnl., Vol. 11, No. 6, 1973, p. 892 (discussion and closure: Vol. 13, No. 5, 1975, pp. 701–703).
13.35 V. B. Watwood, T. Y. Chow, Z. Zudans, and W. H. Miller, "Combined Analysis and Evaluation of Piping Systems Using the Computer," Nucl. Engng. Design, Vol. 27, No. 3, 1974, pp. 334–342.
13.36 R. D. Henshell and J. H. Ong, "Automatic Masters for Eigenvalue Economization," Earthquake Engng. Struct. Dynamics, Vol. 3, No. 4, 1975, pp. 375–383.
13.37 R. G. Anderson, B. M. Irons, and O. C. Zienkiewicz, "Vibration and Stability of Plates Using Finite Elements," Int. J. Solids Structures, Vol. 4, No. 10, 1968, pp. 1031–1055.
13.38 K. W. Matta, "Selection of Degrees of Freedom for Dynamic Analysis," J. Pressure Vessel Tech., Vol. 109, No. 1, 1987, pp. 65–69.
13.39 W. C. Hurty, "Dynamic Analysis of Structural Systems Using Component Modes," AIAA Jnl., Vol. 3, No. 4, 1965, pp. 678–685.
13.40 R. R. Craig, Jr., "A Review of Time-Domain and Frequency Domain Component Mode Synthesis Methods," Int. J. Analytical and Experimental Modal Analysis, Vol. 2, No. 2, 1987, pp. 59–72.
13.41 R. H. MacNeal, "A Hybrid Method of Component Mode Synthesis," Computers & Structures, Vol. 1, No. 4, 1971, pp. 581–601.
13.42 S. Rubin, "An Improved Component-Mode Representation," AIAA/ASME/SAE 15th Structures, Structural Dynamics and Materials Conference, Las Vegas, Nevada, 1974, pp. 17-19.
13.43 R. R. Craig, Jr. and M. C. C. Bampton, "Coupling of Substructures for Dynamic Analysis," AIAA Jnl., Vol. 6, No. 7, 1968, pp. 1313–1319.
13.44 V. N. Shah and M. Raymund, "Analytical Selection of Masters for the Reduced Eigenvalue Problem," Int. J. Num. Meth. Engng., Vol. 18, No. 1, pp. 89–98, 1982.
13.45 M. Paz, Structural Dynamics: Theory and Computation, 2nd ed., Van Nostrand Reinhold, New York, 1984.
13.46 T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987.
13.47 R. D. Richtmyer and K. W. Morton, Difference Methods for Initial Value Problems, Interscience, New York, 1967.
13.48 T. J. R. Hughes and T. Belytschko, "A Précis of Developments in Computational Methods for Transient Analysis," J. Appl. Mech., Vol. 50, No. 4b, 1983, pp. 1033–1041.

13.49 T. Belytschko and T. J. R. Hughes, eds., Computational Methods for Transient Analysis, North Holland, Amsterdam, 1983.
13.50 R. Courant, K. O. Friedrichs, and H. Lewy, “Uber die partiellen Differenzengleichungen der mathematischen Physik,” Math. Ann., Vol. 100, 1928, pp. 32–74. (Translated by P. Fox: “On the Partial Differential Equations of Mathematical Physics,” New York University, Courant Institute of Mathematical Sciences, Report NYO-7689, 1956.)
13.51 M. E. Plesha, "Eigenvalue Estimation for Dynamic Contact Problems," J. of Engng. Mech., Vol. 113, No. 3, 1987, pp. 457-462.
13.52 D. D. Flanagan and T. Belytschko, "A Uniform Strain Hexahedron and Quadrilateral with Orthogonal Hourglass Control," Int. J. Num. Meth. Engng., Vol. 17, No. 5, 1981, pp. 679–706. (Also see Errata, Vol. 19, No. 3, 1983, pp. 467–468.)
13.53 T. Belytschko, J. S. J. Ong, W. K. Liu, and J. M. Kennedy, "Hourglass Control in Linear and Nonlinear Problems," Comp. Meth. Appl. Mech. Engng., Vol. 43, No. 3, 1984, pp. 251–276.
13.54 W. K. Liu and T. Belytschko, "Efficient Linear and Nonlinear Heat Conduction with a Quadrilateral Element," Int. J. Num. Meth. Engng., Vol. 20, No. 5, 1984, pp. 931–948.
13.55 J. C. Houbolt, "A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft," J. Aero. Sci., Vol. 17, No. 9, 1950, pp. 540–550.
13.56 N. M. Newmark, “A Method of Computation for Structural Dynamics,” J. Engng. Mech. Div., Proc. ASCE, Vol. 85, No. EM3, 1959, pp. 67–94.
13,57 E. L. Wilson, “A Computer Program for the Dynamic Stress Analysis of Underground Structures,” SESM Report No. 68-1, Division of Structural Engineering and Structural Mechanics, University of California, Berkeley, 1968.
13.58 H. M. Hilber, T. J. R. Hughes, and R. L. Taylor, “Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics,” Earthquake Engng. Struct. Dynamics, Vol. 5, No. 3, 1977, pp. 283–292.
13.59 T. Belytschko and R. Mullen, “Mesh Partitions of Explicit-Implicit Time Integration,” in Formulation and Computational Algorithms in Finite Element Analysis, K. J. Bathe, J. T. Oden, and W. Wunderlich, eds., MIT Press, Cambridge, MA, 1977, pp. 673–690.
13.60 T. Belytschko and R. Mullen, "Stability of Explicit-Implicit Mesh Partitions in Time Integration," Int. J. Num. Meth. Engng., Vol. 12, No. 10, 1978, pp. 1575–1586.
13.61 T. J. R. Hughes and W. K. Liu, "Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory," J. Appl. Mech., Vol. 45, No. 2, 1978, pp. 371-374.
13.62 T. J. R. Hughes and W. K. Liu, "Implicit-Explicit Finite Elements in Transient Analysis: Implementation and Numerical Examples," J. Appl. Mech., Vol. 45, No. 2, 1978, pp. 375–378.
13.63 T. J. R. Hughes, K. S. Pister, and R. L. Taylor, "Implicit-Explicit Finite Elements in Nonlinear Transient Analysis," Comp. Meth. Appl. Mech. Engng., Vol. 17/18, Part I, 1979, pp. 159–182.
13.64 T. J. R. Hughes, W. K. Liu, and A. Brooks, "Finite Element Analysis of Incompressible Viscous Flows by the Penalty Function Formulation," J. of Comp. Phys., Vol. 30, No. 1, 1979, pp. 1-60.
13.65 M. Ortiz, P. M. Pinsky, and R. L. Taylor, "Unconditionally Stable Element-by-Element Algorithms for Dynamic Problems," Comp. Meth. Appl. Mech. Engng., Vol. 36, No. 2, 1983, pp. 223-239.
13.66 T. J. R. Hughes, I. Levit, and J. Winget, “Unconditionally Stable Element-by-Element Implicit Algorithm for Heat Conduction Analysis,” J. of Engng. Mech., Vol. 109, No. 2, 1983, pp. 576–585.
13.67 T. J. R. Hughes, I. Levit, and J. Winget, "An Element-by-Element Solution Algorithm for Problems of Structural and Solid Mechanics," Comp. Meth. Appl. Mech. Engng., Vol. 36, No. 2, 1983, pp. 241–254.
13.68 I. Fried and D. S. Malkus, "Finite Element Mass Matrix Lumping by Numerical

Integration With No Convergence Rate Loss," Int. J. Solids Structures, Vol. 11, No. 4, 1975, pp. 461–466.
13.69 G. M. Hulbert and T. J. R. Hughes, “An Error Analysis of Truncated Starting Conditions in Step-by-Step Time Integration: Consequences for Structural Dynamics,” Earthquake Engng. Struct. Dynamics, Vol. 15, No. 7, 1987, pp. 901–910.
13.70 R. A. Brockman, "Dynamics of the Bilinear Mindlin Plate Element," Int. J. Num. Meth. Engng., Vol. 24, No. 12, 1987, pp. 2343–2356.

CHAPTER 14

14.1 S. C. Chang and J. J. Chen, "Effectiveness of Linear Bifurcation Analysis for Predicting the Nonlinear Stability Limits of Structures," Int. J. Num. Meth. Engng., Vol. 23, No. 5, 1986, pp. 831–846.
14.2 R. H. Gallagher and J. Padlog, "Discrete Element Approach to Structural Stability Analysis," AIAA Jnl., Vol. 1, No. 6, 1963, pp. 1437-1439.
14.3 E. Chwalla, "Second Order Theory," in Handbook of Engineering Mechanics, W. Flügge, ed., McGraw-Hill, New York, 1962.
14.4 S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, 2nd Ed., McGraw-Hill, New York, 1961.
14.5 J. S. Przemieniecki, "Discrete-Element Methods for Stability Analysis," Aeronautical J., Vol. 72, No. 12, 1968, pp. 1077–1086.
14.6 R. A. Tinawi, "Anisotropic Tapered Elements Using Displacement Models," Int. J. Num. Meth. Engng., Vol. 4, No. 4, 1972, pp. 475-489.
14.7 R. D. Cook, "Finite Element Buckling Analysis of Homogeneous and Sandwich Plates," Int. J. Num. Meth. Engng., Vol. 9, No. 1, 1975, pp. 39–50.
14.8 R. S. Barsoum and R. H. Gallagher, "Finite Element Analysis of Torsional and Torsional-Flexural Stability Problems," Int. J. Num. Meth. Engng., Vol. 2, No. 3, 1970, pp. 335–352.
14.9 R. H. Gallagher and C. H. Lee, "Matrix Dynamic and Instability Analysis with Nonuniform Elements," Int. J. Num. Meth. Engng., Vol. 2, No. 2, 1970, pp. 265-275.
14.10 R. S. Barsoum, "Finite Element Method Applied to the Problem of Stability of a Non-Conservative System," Int. J. Num. Meth. Engng., Vol. 3, No. 1, 1971, pp. 63–87.
14.11 D. Bushnell, "Analysis of Ring-Stiffened Shells of Revolution Under Combined Thermal and Mechanical Loadings," AIAA Jnl., Vol. 9, No. 3, 1971, pp. 401-410.
14.12 D. R. Navaratna, T. H. H. Pian, and E. A. Witmer, "Analysis of Elastic Stability of Shells of Revolution by the Finite Element Method," AIAA Jnl., Vol. 6, No. 2, 1968, pp. 355–361.
14.13 A. D. Kerr and M. T. Soifer, "The Linearization of the Prebuckling State and Its Effect on the Determined Stability Loads," J. Appl. Mech., Vol. 36, No. 4, 1969, pp. 775–783.
14.14 D. Bushnell, "Buckling of Shells—Pitfall for Designers," AIAA Jnl., Vol. 19, No. 9, 1981, pp. 1183–1226.
14.15 D. Bushnell, "Computerized Analysis of Shells—Governing Equations," Computers & Structures, Vol. 18, No. 3, 1984, pp. 471–536.

CHAPTER 15

15.1 S. H. Crandall, Engineering Analysis, McGraw-Hill, New York, 1956.

15.2 B. A. Finlayson and L. E. Scriven, "The Method of Weighted Residuals—A Review," Applied Mechanics Reviews, Vol. 19, No. 9, 1966, pp. 735–748.

15.3 E. D. Eason, "A Review of Least-Squares Methods for Solving Partial Differential Equations," Int. J. Num. Meth. Engng., Vol. 10, No. 5, 1976, pp. 1021-1046.
15.4 W. L. Kwok, Y. K. Cheung, and C. Delcourt, “Application of Least Squares Collocation Technique in Finite Element and Finite Strip Formulation,” Int. J. Num. Meth. Engng., Vol. 11, No. 9, 1977, pp. 1391–1404.
15.5 M. F. N. Mohsen, "Some Details of the Galerkin Finite Element Method," Appl. Math. Modelling, Vol. 6, No. 3, 1982, pp. 165-170.
15.6 B. A. Finlayson, The Method of Weighted Residuals and Variational Principles, Academic Press, New York, 1972.
15.7 P. C. M. Lau and C. A. Brebbia, "The Cell Collocation Method in Continuum Mechanics," Int. J. Mech. Sci., Vol. 20, No. 2, 1978, pp. 83–95.
15.8 R. H. Gallagher, J. A. Liggett, and S. T. K. Chan, “Finite Element Shallow Lake Circulation Analysis,” J. Hydraulics Div., Proc. ASCE, Vol. 99, No. HY7, 1973, pp. 1083–1096.

CHAPTER 16

16.1 E. L. Wilson, K. J. Bathe and F. E. Peterson, "Finite Element Analysis of Linear and Nonlinear Heat Transfer," Nucl. Engng. Design, Vol. 29, No. 1, 1974, pp. 110–124.
16.2 J. F. Lyness, D. R. J. Owen, and O. C. Zienkiewicz, "The Finite Element Analysis of Engineering Systems Governed by a Non-Linear Quasi-Harmonic Equation," Computers & Structures, Vol. 5, No. 1, 1975, pp. 65–79.
16.3 B. Nour-Omid, "Lanczos Method for Heat Conduction Analysis," Int. J. Num. Meth. Engng., Vol. 24, No. 1, 1987, pp. 251-262.
16.4 T. J. R. Hughes, "Unconditionally Stable Algorithms for Nonlinear Heat Conduction," Comp. Meth. Appl. Mech. Engng., Vol. 10, No. 2, 1977, pp. 135–139.
16.5 T. J. R. Hughes, I. Levit, and J. Winget, “Element-by-Element Implicit Algorithms for Heat Conduction,” J. of Engng. Mech., Vol. 109, No. 2, 1983, pp. 576–585.
16.6 G. C. Everstine, “Structural Analogies for Scalar Field Problems,” Int. J. Num. Meth. Engng., Vol. 17, No. 3, 1981, pp. 471–476.
16.7 P. Tong and Y. C. Fung, "Slow Particulate Flow in Channels and Tubes—Application to Biomechanics," J. Appl. Mech., Vol. 38, No. 4, 1971, pp. 721–728.
16.8 S. T. K. Chan, B. E. Larock, and L. R. Herrmann, "Free-Surface Ideal Fluid Flows by Finite Elements," J. Hydraulics Div., Proc. ASCE, Vol. 99, No. HY6, 1973, pp. 959–974.
16.9 O. C. Zienkiewicz, R. W. Lewis, and K. G. Stagg, Numerical Methods in Offshore Engineering, John Wiley & Sons, Chichester, England, 1978.
16.10 O. C. Zienkiewicz and P. Bettess, “Fluid-Structure Dynamic Interaction and Wave Forces. An Introduction to Numerical Treatment,” Int. J. Num. Meth. Engng., Vol. 13, No. 1, 1978, pp. 1–16.
16.11 R. J Astley and W. Eversman, "Finite Element Formulations for Acoustical Radiation," J. Sound Vibration, Vol. 88, No. 1, 1983, pp. 47–64.
16.12 A. Craggs, “A Note on the Theory and Application of a Simple Pipe Acoustic Element,” J. Sound Vibration, Vol. 85, No. 2, 1982, pp. 292–295.
16.13 R. D. Cook, “Comment on ‘Discrete Element Idealization of an Incompressible Liquid for Vibration Analysis’ and ‘Discrete Element Structural Theory of Fluids,’ ” AIAA Jnl., Vol. 11, No. 5, 1973, pp. 766–767.
16.14 M. A. Hamdi, Y. Ousset, and G. Verchery, "A Displacement Method for the Analysis of Vibrations of Coupled Fluid-Structure Systems," Int. J. Num. Meth. Engng., Vol. 13, No. 1, 1978, pp. 139–150.
16.15 L. G. Olson and K. J. Bathe, "A Study of Displacement-Based Fluid Finite Elements for Calculating Frequencies of Fluid and Fluid-Structure Systems," Nucl. Engng. Design, Vol. 76, No. 2, 1983, pp. 137–151.

CHAPTER 17

17.1 ANSYS News, Swanson Analysis Systems Inc., Houston, PA, Second Issue, 1982.
17.2 A. Ralston and P. Rabinowitz, A First course in Numerical Analysis, 1978, McGraw-Hill, New York, 1978.
17.3 D. M. Gay, "Some Convergence Properties of Bloyd's Method," (2004) Num. Anal., Vol. 16, No. 4, 1979, pp. 623–630.
17.4 FIDAP Theoretical Manual, 1986, 27, anston, IL 60201, 1986, pp. 7-1, 7-34.
17.5 J. E. Dennis and R. Schnabel, Numerical Methods for Constrained Optimization, Prentice-Hall, Englewood Cliffs, NJ, 1983. Introduction to the Finite Element Method with Applications to
17.6 R. E. White, An Introduction to the Times-Lin. Nonlinear Problems, John Wiley & Sons, New York, 1985.
17.7 M. A. Crisfield, "An Arc-Length Methods: Engng., Vol. 19, No. 9, 1983, pp. 1269–1289. tions," Int. J. Num. Meth. Engng., Vol. 19, No. 9, 1983, pp. 1269–1289.
17.8 E. Riks, "Progress in Collapse Analysis," 1, 1987, pp. 33–41.
17.9 R. L. Webster, "On the Static Analysis of Structural Structure," "Linearity," Computers & Structures, Vol. 11, Nos. 1/2, 1980, pp. 137–145.
17.10 O. C. Zienkiewicz and R. Lohner, "Accelerated Renalment Future Prospects for FEM," Int. J. Num. Meth. Engng., Vol. 21, No. 1, 1985, pp. 1–11.
17.11 S. W. Sloan, "Substepping Schemes for the Numerical Strategies for Stress-Strain Relations," Int. J. Num. Meth. Engng., Vol. 24, No. 5, 1987, pp. 893-911.
17.12 A. Levy and B. Pifko, "On Computational Strategies 18, 1981, pp. 747-771. ticity and Creep," Int. J. Num. Meth. Engng., Vol. 17, No. 5, 1981, pp. 747-771.
17.13 P. C. Kollmick, ANSYS Engineering, 1986. Analysis Systems, Inc., Houston, PA, March 1986.
17.14 D. R. J. Owen and E. Hinton, Finite Elements in Plasticity, Pineridge Press Ltd., Swansea, U.K., 1980.
17.15 H. R. Evans, D. O. Peska, and A. R. Tanerhan, "The Analysis of the Ultimate Load Behavior of Plated Structures by the Finite Element Method," Engineering Computations, Vol. 2, No. 4, 1985, pp. 271–284.
17.16 P. V. Marcal, "Large Deflection Analysis of Elastic AIAA Jnl., Vol. 8, No. 9, 1970, pp. 1627-1633.
17.17 D. Bushnell, "Large Deflection Elastic-Plastic Group," in Numerical Solution, of Nonlinear Structural Problems, R. F. Hartung, ed., ASME AMD, Vol. 38, 1973, pp. 103-138.
17.18 J. A. Stricklin, W. E. Haisler, and W. A. Von Riesemann, "Solution Procedures for Nonlinear Analysis by Combined Finite Element-Finite Difference Methods," Computers & Structures, Vol. 2, Nos. 5/6, 1972, pp. 955–974.
17.19 J. A. Stricklin, W. E. Haisler, and W. A. Von Klosehmann,putation and Solution Procedures for Material and/or Geometric Nonlinear Structural Analysis by the Finite Element Method," Report SC-CR-72-3102, Sandia Laboratories, Albuquerque, NM, July 1972.
17.20 L. D. Hofmeister, G. A. Greenbaum, and D. A. Evenson, "Large Strain, Elastic Plastic Finite Element Analysis," AIAA Jnl., Vol. 9, No. 7, 1971, pp. 1248–1254.
17.21 D. Bushnell, "BUSORS—Program for Building of Revolution Including Large Deflections and Creep," Computers & Structures, Vol. 6, No. 3, 1976, pp. 221–239.
17.22 G. C. Nayak and O. C. Zienkiewicz, "Elasto-Plastic Stress Analysis for Various Constitutive Relations Including Strain Softening," Int. J. Num. Meth. Engng., Vol. 5, No. 1, 1972, pp. 113–135.

17.23 A. Grill and K. Sorimachi, "The Thermal Loads in the Finite Element Analysis of Elasto-Plastic Stresses," Int. J. Num. Meth. Engng., Vol. 14, No. 4, 1979, pp. 499–505.
17.24 T. Belytschko and T. J. R. Hughes, eds., Computational Methods for Transient Analysis, North Holland, Amsterdam, 1983.
17.25 M. E. Plesha, "Eigenvalue Estimation for Dynamic Contact Problems," J. of Engng. Mech., Vol. 113, No. 3, 1987, pp. 457-462.
17.26 T. Belytschko, “A Survey of Numerical Methods and Computer Programs for Dynamic Structural Analysis,” Nucl. Engng. Design, Vol. 37, No. 1, 1976, pp. 23–34.
17.27 T. Belytschko and D. F. Schoeberle, "On the Unconditional Stability of an Implicit Algorithm for Nonlinear Structural Dynamics," J. Appl. Mech., Vol. 42, No. 4, 1975, pp. 865–869.
17.28 M. S. Gadala, M. A. Dokainish, and G. A. Oravas, "Formulation Methods of Geometric and Material Nonlinearity Problems," Int. J. Num. Meth. Engng., Vol. 20, No. 5, 1984, pp. 887–914.
17.29 K. Mattiasson, A. Bengtsson, and A. Samuelsson, “On the Accuracy and Efficiency of Numerical Algorithms for Geometrically Nonlinear Structural Analysis,” in Finite Element Methods for Nonlinear Problems, P. G. Bergan, K. J. Bathe, and W. Wunderlich, eds., Springer, Berlin, 1986.
17.30 T. Belytschko and B. J. Hsieh, "Non-Linear Transient Finite Element Analysis with Convected Coordinates," Int. J. Num. Meth. Engng., Vol. 7, No. 3, 1973, pp. 255–271.
17.31 D. W. Murray and E. L. Wilson, “Finite-Element Large Deflection Analysis of Plates,” J. Engr. Mech. Div., Proc. ASCE, Vol. 95, No. EM1, 1969, pp. 143–165.
17.32 R. Schmidt and D. A. DaDeppo, "A Survey of Literature on Large Deflection of Nonshallow Arches. Bibliography of Finite Deflections of Straight and Curved Beams, Rings, and Shallow Arches," J. Industrial Math. Soc., Vol. 21, Part 2, 1971, pp. 91–114.
17.33 J. H. Lau, "Large Deflections of Beams with Combined Loads," J. Engr. Mech. Div., Proc. ASCE, Vol. 108, No. EM1, 1982, pp. 180–185.
17.34 M. D. Snyder and K. J. Bathe, "A Solution Procedure for Thermo-Elastic-Plastic-Creep Problems," Nucl. Engng. Design, Vol. 64, No. 1, 1981, pp. 49–80.
17.35 J. F. T. Pittman, O. C. Zienkiewicz, R. D. Wood, and J. M. Alexander, Numerical Analysis of Forming Processes, John Wiley & Sons, Chichester, England, 1984.
17.36 J. Padovan, S. Tovichakchaikul, and I. Zeid, "Finite Element Analysis of Steadily Moving Contact Fields," Computers & Structures, Vol. 18, No. 2, 1984, pp. 191–200.
17.37 C. S. Desai, M. M. Zaman, J. G. Lightner, and H. J. Siriwardane, “Thin-Layer Element For Interfaces and Joints,” Int. J. Num. An. Meth. Geomech., Vol. 8, No. 1, 1984, pp. 19–43.
17.38 E. L. Wilson, “Finite Elements for Foundations, Joints and Fluids,” in Finite Elements in Geomechanics, G. Gudehus, ed., John Wiley & Sons, London, 1977, pp. 319–350.
17.39 K. Schweizerhof and E. Ramm, “Displacement Dependent Pressure Loads in Nonlinear Finite Element Analysis,” Computers & Structures, Vol. 18, No. 6, 1984, pp. 1099–1114.
17.40 A. H. Peyrot and A. M. Goulois, “Analysis of Cable Structures,” Computers & Structures, Vol. 10, No. 5, 1979, pp. 805–813.
17.41 H. B. Jayaraman and W. C. Knudson, “A Curved Element for the Analysis of Cable Structures,” Computers & Structures, Vol. 14, Nos. 3–4, 1981, pp. 325–333.
7.42 M. Sathyamoorthy, “Nonlinear Vibrations of Plates—A Review,” Shock and Vibration Digest, Vol. 15, No. 6, 1983, pp. 3–16.

CHAPTER 18

18.1 R. A. Rosanoff, J. F. Gloudeman, and S. Levy, "Numerical Conditioning of Stiffness Matrix Formulations for Frame Structures," Proc. Second Conf. on Matrix Meth. in Struct. Mech., Wright-Patterson AFB, Ohio, 1968, (AFFDL-TR-68-150, Dec. 1969; AD-703-685, N.T.I.S.), pp. 1029–1060.
18.2 S. Utku and R. J. Melosh, "Solution Errors in Finite Element Analysis," Computers & Structures, Vol. 18, No. 3, 1984, pp. 379-393.
18.3 S. Kelsey, K. N. Lee, and C. K. Mak, "The Condition of Some Finite Element Coefficient Matrices," in Computer Aided Engineering, G. M. L. Gladwell, ed., University of Waterloo Press, Waterloo, Ontario, 1971.
18.4 G. Forsythe and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, Englewood Cliffs, NJ, 1967.
18.5 I. Fried, "Condition of Finite Element Matrices Generated from Nonuniform Meshes, AIAA Jul., Vol. 10, No. 2, 1972, pp. 219-221.
18.6 B. M. Irons, "Roundoff Criteria in Direct Stiffness Solutions," AIAA Jmt., Vol. 6, No. 7, 1968, pp. 1308–1312.
18.7 R. H. MacNeal, ed., The NASTRAN Theoretical Manual (Level 10.0), NASA-SP-221(03), March 1976 (N79-27531, N.T.I.S.).
18.8 B. Noble, Applied Linear Algebra, Prentice-Hall, Englewood Cliffs, NJ, 1969.
18.9 G. Strang and G. J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1973 (now copyrighted by Wellesley–Cambridge Press, Wellesley, MA, 1988).
18.10 I. Fried, "Accuracy and Condition of Curved (Isoparametric) Finite Elements," J. Sound Vibration, Vol. 31, No. 3, 1973, pp. 345–355.
18.11 S. H. Crandall, Engineering Analysis, McGraw-Hill, New York, 1956.
18.12 J. Robinson, "An Introduction to Hierarchical Displacement Elements and the Adaptive Technique," Finite Elements in Analysis and Design, Vol. 2, No. 4, 1986, pp. 377–388.
18.13 N. Kikuchi, "Adaptive Grid-Design Methods for Finite Element Analysis," Comp. Meth. Appl. Mech. Engng., Vol. 55, Nos. 1-2, 1986, pp. 129-160.
18.14 G. L. Rigby and G. M. McNeice, "A Strain Energy Basis for Studies of Element Stiffness Matrices," AIAA Jnl., Vol. 10, No. 11, 1972, pp. 1490–1493.
18.15 J. O. Dow, T. H. Ho, and H. D. Cabiness, "Generalized Finite Element Evaluation Procedure," J. of Struct. Engng., Vol. 111, No. 6, 1984, pp. 435-452.
18.16 W. P. Doherty, E. L. Wilson, and R. L. Taylor, "Stress Analysis of Axisymmetric Solids Utilizing Higher-Order Quadrilateral Finite Elements," Report UC-SESM-69-3, Civil Engineering Department, University of California, Berkeley, 1969, (PB-190-321, NTIS).
18.17 J. Robinson, "A Single Element Test," Comp. Meth. Appl. Mech. Engng., Vol. 7, No. 2, 1976, pp. 191–200.
18.18 I. Fried, "Influence of Poisson's Ratio on the Condition of the Finite Element Stiffness Matrix." Int. J. Solids Structures, Vol. 9, No. 3, 1973, pp. 323-329.
18.19 P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North Holland, New York, 1978.
18.20 R. J. Roark and W. C. Young, Formulas for Stress and Strain, 5th ed., McGraw-Hill, New York, 1975.
18.21 Anon., A Finite Element Primer, Dept. of Trade and Industry, National Engineering Laboratory, Glasgow G75 OQU, U.K., 1986.

CHAPTER 19

19.1 G. J. DeSalvo, ANSYS Engineering Analysis System Verification Manual, Swanson Analysis Systems Inc., Houston, PA, 1985.