References

1

Argyris, J. H. and Scharpf, D. W. (1969), ``Finite Elements in Time and Space'', The Aeronautical Journal of the Royal Aeronautical Society, 73, 1041.

2

Argyris, J. H., Vaz, L. E. and Willam, K. J. (1977), ``Higher Order Methods for Transient Diffusion Analysis'', Computer Methods in Applied Mechanics and Engineering, 12, 243.

3

Bathe, K. J. (1982), Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, New Jersey.

4

Belytschko, T. and Hughes, T.J. R. (1983), Computational Methods in Transient Analysis, North Holland.

5

Biot, M. A. (1967), ``Complementary Forms of the Variational Principle for Heat Conduction and Convection'', Journal of Franklin Institute, 283, 372.

6

Chen, X., Mohan, R. V. and Tamma, K. K. (1994), ``Instantaneous Response of Elastic Thin-Walled Structures to Rapid Heating'', International Journal for Numerical Methods in Engineering, 37, 2389.

7

Chen, X., Tamma, K. K. and Sha, D. (1993), ``New Virtual-Pulse Time Integral Methodology for Linear Transient Heat Transfer Problem'', Numerical Heat Transfer B, 24, 301.

8

Chen, X., Tamma, K. K. and Sha, D. (1995), ``Virtual-Pulse Time Integral Methodology: A New Approach for Computational Dynamics. Part 2: Theory for Nonlinear Structural Dynamics'', Finite Elements in Analysis and Design, 20, 195.

9

Chung and Hulbert (1993), ``A Time Integration Method for Structural Dynamics With Improved Numerical Dissipation: The Generalized -Method'', Journal of Applied Mechanics, 30 (371).

10

Claret, A. and Venacio-Filho, F. (1991), ``A Modal Superposition Pseudo-Force Method for Dynamic Analysis of Structural Systems with Non-Proportional Damping'', Earthquake Engineering and Structural Dynamics, 20, 303.

11

Crank, J. and Nicolson, P. (1947), ``A Practical Method for the Numerical Evaluation of Solutions of Partial Differential Equations of the Heat Conduction Type'', Proc. Cambridge Phil. Soc., 43, 50.

12

Cronin, D. (1976), ``Approximation for Determining Harmonically Excited Response of Non-classically Damped Systems'', Journal of Engineering for Industry, 98, 43.

13

Dahlquist, G. (1963), ``A Special Stability Problem for Linear Multistep Methods'', BIT, 3, 27.

14

Demkowicz, L., Oden, J. T., Rachowicz, W. and Hardy, O. (1991), ``An h-p Taylor-Galerkin Finite Element Methodology for Compressible Euler Equations'', Computer Methods in Applied Mechanics and Engineering, 88, 363.

15

Donea, J. (1984), ``A Taylor-Galerkin Method for Convective Transport Problems'', International Journal for Numerical Methods in Engineering, 20, 101.

16

Donea, J., Giuliani, S., Laval, H. and Quartapelle, L. (1984), ``Time-Accurate Solutions of Advection-Diffusion Problems by Finite Elements'', Computer Methods in Applied Mechanics and Engineering, 45, 1233.

17

DuFort, E. C. and Frankel, S. P. (1953), ``Stability Conditions in the Numerical Treatment of Parabolic Differential Equations'', Mathematical Tables and Other Aids to Computation, 7, 135.

18

Dupont, T., Fairweather, G. and Johnson, P. (1974), ``Three-Level Galerkin Methods for Parabolic Equations'', SIAMJ, 11, 392.

19

Euler, L. (1913), ``De Integratione Aequationum Differentialium Per Appriximationem'', Opera Omnia, 11, 424.

20

Fost, R. B., Oden, J. T. and Jr., L.C. W. (1975), ``A Finite-Amplitude Analysis of Shocks and Finite-Amplitude Waves in One-Dimensional Hyperbolic Bodies at Finite Strain'', International J. Solids and Structures, 11, 377.

21

Fried, I. (1969), ``Finite Element Analysis of Time-Dependent Phenomena'', AIAA J, 7, 1170.

22

Fu, C. C. (1970), ``A Method for the Numerical Integration of Equations of Motion Arising From a Finite Element Analysis'', Journal of Applied Mechanics, 39, 559.

23

Fung, T. C. (1997a), ``A Precise Time-Step Integration Method by Step-Response and Impulsive-Response Matrices for Dynamic Problems'', International Journal for Numerical Methods in Engineering, 40, 4501.

24

Fung, T. C. (1997b), ``Third-Order Time-Step Integration Methods with Controllable Numerical Dissipation'', Communications in Numerical Methods in Engineering, 13, 307.

25

Fung, T. C. (1998), ``Complex-Time-Step Newmark Methods with Controllable Numerical Dissipation'', International Journal for Numerical Methods in Engineering, 41, 65.

26

Fung, T. C. (1999a), ``Complex-Time-Step Methods for Transient Analysis'', International Journal for Numerical Methods in Engineering, 46, 1253.

27

Fung, T. C. (1999b), ``Weighted Parameters for Unconditionally Stable Higher-Order Accurate Time Step Integration Algorithms. Part 1 - First-Order Equations'', International Journal for Numerical Methods in Engineering, 45, 941.

28

Fung, T. C. (1999c), ``Weighted Parameters for Unconditionally Stable Higher-Order Accurate Time Step Integration Algorithms. Part 2 - Second-Order Equations'', International Journal for Numerical Methods in Engineering, 45, 971.

29

Gear, C. W. (1969), ``The Automatic Integration of Stiff Ordinary Differential Equations'', In Morrell, A. J. H., editor, Information Processing, Volume 68, page 187, North Holland, Dordrecht.

30

Gellert, M. (1978), ``A New Algorithm for Integration of Dynamic System'', Comput. Struct., 9, 401-408.

31

Golley, B. W. (1998), ``A Weighted Residual Development of a Time-Stepping Algorithm for Structural Dynamics Using Two General Weighted Functions'', International Journal for Numerical Methods in Engineering, 42, 93.

32

Gurtin, M. (1964), ``Variational Principles for Linear Initial-Value Problems'', Q. Appl. Math, 22, 252.

33

Hahn, G. D. (1991), ``A Modified Euler Method for Dynamic Analysis'', International Journal for Numerical Methods in Engineering, 32, 943.

34

Haji-Sheikh, A. and Lakshminarayanan, R. (1987), ``Integral Solution of Diffusion Equation:Part 2-Boundary Conditions of Second and Third Kinds'', Journal of Heat Transfer, 109, 557.

35

Haji-Sheikh, A. and Mashena, M. (1987), ``Integral Solution of Diffusion Equation:Part 1-General Solution'', Journal of Heat Transfer, 109, 551.

36

Hilber, H. M. and Hughes, T. J. R. (1978), ``Collocation, Dissipation and `Overshoot' for Time Integration Schemes in Structural Dynamics'', Earthquake Engineering and Structural Dynamics, 6, 99.

37

Hilber, H. M., Hughes, T. J. R. and Taylor, R. L. (1977), ``Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics'', Earthquake Engineering and Structural Dynamics, 5, 283.

38

Hinton, E. and Owen, D. R. J. (1980), Finite Element in Plasticity: Theory and Practice, Pineridge, Swansea, UK.

39

Hoff, C., Hughes, T.J. R., Hulbert, G. and Pahl, P. J. (1989), ``Comparison of the HHT- -Method and the -method'', Computer Methods Applied Mechanics and Engineering, 76, 87-93.

40

Hoff, C. and Pahl, P. J. (1988a), ``Development of an Implicit Method with Numerical Dissipation from a Generalized Single Step Algorithm for Structural Dynamics'', Computer Methods Appl. Mech. Eng., 67, 367.

41

Hoff, C. and Pahl, P. J. (1988b), ``Practical Performance of the -Method and Comparison with Other Dissipative Algorithms in Structural Dynamics'', Computer Methods Applied Mechanics and Engineering, 67, 87.

42

Hoff, C. and Taylor, R. L. (1990a), ``Higher Derivative Explicit One Step Methods for Non-Linear Dynamic Problems. Part I: Design and Theory'', International Journal for Numerical Methods in Engineering, 29, 275.

43

Hoff, C. and Taylor, R. L. (1990b), ``Higher Derivative Explicit One Step Methods for Non-Linear Dynamic Problems. Part II: Practical Calculations and Comparisons With Other Higher Methods'', International Journal for Numerical Methods in Engineering, 29, 291.

44

Hogge, M. A. (1976), ``Integration Operators for First Order Linear Matrix Differential Equations'', Computer Methods in Applied Mechanics and Engineering, 11, 281.

45

Houbolt, J. C. (1950), ``A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft'', J. Aero. Science, 17, 540.

46

Hughes, T.J. R. (1987), The Finite Element Method, Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, New Jersey.

47

Hughes, T.J. R. and Belytschko, T. (1983), ``A Precis of Developments in Computational Methods for Transient Analysis'', Journal of Applied Mechanics, 50, 1033.

48

Hulbert, G. M. (1994), ``A Unified Set of Single-Step Asymptotic Annihilation Algorithms for Structural Dynamics'', Comput. Methods Appl. Mech. Engrg., 113, 1-9.

49

Hulbert, G. M. and Chung, J. (1996), ``Explicit Time Integration Algorithms for Structural Dynamics with Optiomal Numerical Dissipation'', Comput. Methods Appl. Mech. Engrg, 137, 175.

50

Hulbert, G. M. and Hughes, T. J. R. (1987), ``An Error Analysis of Truncated Starting Conditions in Step-by-Step Time Integration: Consequences for Structural Dynamics'', Earthquake Eng. and Struct. Dynamics, 15, 901.

51

Hulbert, G. M. and Jang, I. (1995), ``Automatic Time Step Control Algorithms for Structural Dynamics'', Comput. Methods Appl. Mech. Engrg., 126, 155.

52

Humar, J. L. (1990), Dynamics of Structures. Prentice-Hall, Englewood Cliffs, New Jersey.

53

Itoh, T. (1973), ``Damped Vibration Mode Superposition Method for Dynamic Response Analysis'', Earthquake Engineering and Structural Dynamics, 2, 47.

54

Krieg, R. D. (1973), ``Unconditional Stability of Numerical Time Integration Methods'', Journal of Applied Mechanics, 40, 417.

55

Kujawski, J. and Gallagher, R. H. (1984), ``A Family of Higher-Order Explicit Algorithms for the Transient Dynamic Analysis'', Trans. Soc. Comp. Simulation, 1, 155.

56

Landry, D. W. and Kaplan, B. (1986), ``Addendum to Eigenvalue Method for Solving Transient Heat Conduction Problems'', Numerical Heat Transfer, 9, 247.

57

Lax, P. D. and Wendroff, B. (1964), ``Difference Schemes for Hyperbolic Equations with High Order Accuracy'', Comm. Pure Appl. Math., 17, 381.

58

Lees, H. (1966), ``A Linear Three-Level Differences Scheme for Quasilinear Parabolic Equations'', Mech. Comp., 20, 516.

59

Li, M., Tamma, K. K. and Namburu, R. R. (1991), ``Evaluation and Applicability of Explicit Self-Starting Formulations for Nonlinear Structural Dynamics'', AIAA SDM Conference, San Diego, CA, April.

60

Liniger, W. (1968), ``Optimization of a Numerical Integration Method for Stiff Systems of Ordinary Differential Equations'', Research Report RC2198, IBM.

61

Liniger, W. (1969), ``Global Accuracy Stability of One and Two Step Integration Formulae for Stiff Ordinary Differential Equation'', Conf. Numerical Solution of Differential Equations - Dundee Univ.

62

Manolis, G. D. and Beskos, D. E. (1980), ``Thermally Induced Vibrations of Beam Structures'', Computer Methods in Applied Mechanics and Engineering, 21 (337).

63

Mei, Y., Chen, X., Tamma, K. K. and Sha, D. (1993), ``On the Generalized VIP Time Integral Methodology for Transient Thermal Problems'', In AIAA-93-2771, 28th Thermophysics Conference, Orando, FL.

64

Mei, Y., Mohan, R. V. and Tamma, K. K. (1994), ``Evaluation and Applicability of a New Explicit Time Integral Methodology for Transient Thermal Problems - Finite Volume Formulations'', Numerical Heat Transfer, 6(3), 313.

65

Miranda, I., Hulbert, R. M. and Hughes, T.J. R. (1989), ``An Improved Implicit-Explicit Time Integration Method for Sturctural Dynamics'', Earthquake Engrg. Struct. Dyn., 18, 643.

66

Namburu, R. R. and Tamma, K. K. (1991), ``Applicability/Evaluation of Flux Based Representations for Linear/Higher Order Elements for Heat Transfer in Structures: Generalized -family'', In AIAA 29th Aerospace Sciences Meeting, Reno, Nevada.

67

Namburu, R. R. and Tamma, K. K. (1992), ``A Generalized -Family of Self-Starting Algorithms for Computational Structural Dynamics'', AIAA SDM Conference, AIAA-92-2330, Dallas, Tx, April.

68

Newmark, N. M. (1959), ``A Method of Computation for Structural Dynamics'', Journal American Society of Civil Engineers, 1, 67.

69

Nørsett, S. P. (1974), ``One-Step Methods of Hermite Type for Numerical Integration of Stiff Systems'', BIT, 14, 63.

70

Oden, J. T. (1969), ``A General Theory of Finite Elements, Part II'', International Journal for Numerical Methods in Engineering, 1, 247.

71

Oden, J. T. (1973), ``Formulation and Application of Certain Primal and Mixed Finite Element Models of Finite Deformation of Elastic Bodies'', In Glowinski, R. and Lions, J. L., editors, International Conference on Computing Methods in Applied Science and Engineering, Part 1, page 334, Versailles, France.

72

Oden, J. T., Safjan, A., Geng, P. and Demkowicz, L. (1994), ``High-Order, Multi-Level, Adaptive Time Domain Methods for Structural Acoustics Simulations'', Technical report, Univ. of Texas, Austin, TICAM Report 94-14.

73

Owen, D. R. J. and Li, Z. H. (1988), ``Elastic-Plastic Dynamic Analysis of Anisotropic Laminated Plates'', Computer Methods in Applied Mechanics and Engineering, 70, 349.

74

Park, K. C. (1975), ``An Improved Stiffly Stable Method for Direct Integration of Nonlinear Structural Dynamic Equations'', Transactions of the American Society of Mechanical Engineers, 1, 464.

75

Penry, S. N. and Wood, W. L. (1985), ``Comparison of Some Single-Step Methods for the Numerical Solution of the Structural Dynamic Equation'', International Journal for Numerical Methods in Engineering, 21, 1941.

76

Pezeshk, S. and Camp, C. V. (1995), ``An Explicit Time Integration Technique for Dynamic Analysis'', International Journal for Numerical Methods in Engineering, 38, 2265.

77

Safjan, A. and Oden, J. T. (1991), ``h-p Adaptive Finite Element Methods in Transient Acoustics'', In Keltie, R. F., Seybert, A. F., Kang, D. S., Olson, L., and Pinsky, P., editors, Structural Acoustics, number H00178. ASME Reprint.

78

Safjan, A. and Oden, J. T. (1993), ``High-Order Taylor-Galerkin and Adaptive h-p Methods for Second-Order Hyperbolic Systems: Application to Elastodynamics'', Computer Methods in Applied Mechanics and Engineering, 103, 187.

79

Safjan, A. and Oden, J. T. (1995), ``High-Order Taylor-Galerkin Methods for Linear Hyperbolic Systems'', Journal of Computational Physics, 120, 206.

80

Saul'yev, V. K. (1964), Integration of Equations of the Parabolic Type by the Method of Nets. Pergamon Press, New York.

81

Sha, D., Chen, X. and Tamma, K. K. (1995), ``A New Virtual-Pulse Time Integral Methodology: A New Approach for Computational Dynamics'', Finite Elements in Analysis and Design, also, see Erratum(1996): Parts 1 and 2, 20 and 22, 179.

82

Sha, D., Zhou, X., and Tamma, K. K. (2000), ``Time Discretized Operators: Towards the Theoretical Design of a New Generation of Implicit and Explicit Representations of Time Operators for Structural Dynamics: Part 2'', Computer Methods in Applied Mechanics and Engineering (to appear).

83

Shih, T. M. and Skladany, J. T. (1983), ``An Eigenvalue Method for Solving Transient Heat Conduction Problems'', Numerical Heat Transfer, 6, 409.

84

Simo, J. C., Tarnow, N., and Wang, K. K. (1992), ``Exact Energy-Momentum Conserving Algorithms and Symplectic Schemes for Nonlinear Dynamics'', Comput. Methods Appl. Mech. Engrg., 100, 63.

85

Simo, J. C. and Wong, K. K. (1991), ``Unconditional Stable Algorithm for Rigid Body Dynamics That Exactly Preserve Energy and Momentum'', International Journal for Numerical Methods in Engineering, 31, 19.

86

Tamma, K. K. (1997), Advances in Numerical Heat Transfer, Volume 1, Chapter An Overview of Recent Advances and Computational Methods for Thermal Problems, page 287, Taylor and Francis.

87

Tamma, K. K., Chen, X. and Sha, D. (1994), ``Further Developments Towards a New Virtual-Pulse Time Integral Methodology for General Non-linear Transient Thermal Analysis'', Communications in Applied Numerical Methods in Engineering, 10, 961.

88

Tamma, K. K., Chen, X. and Sha, D. (1996), ``An Overview of Recent Advances and Evaluation of the Virtual-Pulse (VIP) Time Integral Methodology for General Structural Dynamics Problems: Computational Issues and Implementation Aspects'', International Journal for Numerical Methods in Engineering, 39, 1955.

89

Tamma, K. K., Mei, Y., Chen, X. and Sha, D. (1995), ``Recent Advances Towards an Effective Virtual-Pulse (VIP) Explicit Time Integral Methodology For Multidimensional Thermal Analysis'', International Journal of Numerical Methods in Fluids, 20, 523.

90

Tamma, K. K. and Namburu, R. R. (1988a), ``A New Finite Element Based Lax-Wendroff/Taylor-Galerkin Methodology for Computational Dynamics'', Comp. Meths. Appl. Mech. Eng., 71, 137.

91

Tamma, K. K. and Namburu, R. R. (1988b), ``Explicit Second-Order Accurate Taylor-Galerkin Based Finite Element Formulation for Linear/Nonlinear Transient Heat Transfer'', Numerical Heat Transfer, 13, 409.

92

Tamma, K. K. and Namburu, R. R. (1990a), ``A Robust Self-Starting Explicit Computational Methodology for Structural Dynamic Applications: Architecture and Representations'', International Journal for Numerical Methods in Engineering, 29, 1441.

93

Tamma, K. K. and Namburu, R. R. (1990b), ``Applicability and Evaluation of an Implicit Self-Starting Unconditionally Stable Methodology for the Dynamics of Structures'', Computers and Structures, 34(6), 835.

94

Tamma, K. K. and Namburu, R. R. (1991), ``An Overview of New Computational Developments for Thermo-Mechanical Problems'', Proc. ASME Winter Annual Meeting, 91-WA-CIE-3, Altanta, GA, December.

95

Tamma, K. K. and Railkar, S. B. (1987a), ``A Generalized Hybrid Transfinite Element Computational Approach for Nonlinear/Linear Unified Thermal/Structural Analysis'', Computers and Structures, 26, 655.

96

Tamma, K. K. and Railkar, S. B. (1987b), ``Nonlinear/Linear Unified Thermal Stress Formulations: Transfinite Element Approach'', Comp. Meths. Appl. Mech. Eng., 64, 415.

97

Tamma, K. K. and Railkar, S. B. (1988a), ``A New Hybrid Transfinite Element Methodology for Applicability to Conduction/Convection/Radiation Heat Transfer'', International Journal for Numerical Methods In Engineering, 26, 1087.

98

Tamma, K. K. and Railkar, S. B. (1988b), ``Transfinite Element Methodology for Nonlinear/Linear Transient Modeling/Analysis: Progress and Recent Advances'', International Journal for Numerical Methods in Engineering, 25, 475.

99

Tamma, K. K., Sha, D. and Zhou, X. (1998a), ``Energy-Conserving/L-Stable Nth-Order Integration Operators [E/LNInO] for Computational Dynamics'', In Proc. World Congress in Computational Mechanics, IV, Buenos Aires, Argentina.

100

Tamma, K. K., Sha, D. and Zhou, X. (2000a), ``Time Discretized Operators: Towards the Theoretical Design of a New Generation of a Generalized Family of Time Operators for Structural Dynamics: Part 1'', Computer Methods in Applied Mechanics and Engineering (to appear).

101

Tamma, K. K., Zhou, X. and Sha, D. (1998b), ``Transient Algorithms for Heat Transfer: Theoretical Developments and Approaches for Generating Nth-Order Accurate Algorithms'', In 36th Aerospace Sciences Meeting, number AIAA-98-0847, Reno, Nevada.

102

Tamma, K. K., Kanapady, R., Zhou, X., Sha, D. (2000), "Recent Advances in Computational Structural Dynamics Algorithms", In Seventh Int-Conf. on Recent Advances in Structural Dyanmics ISVR, Southhampton, UK, July 24-28.

103

Tamma, K. K., Zhou, X. and Sha, D. (1999a), ``Towards a Formal Theory of Development/Evolution and Characterization of Time Discretized Operators for Heat Transfer'', International Journal of Numerical Methods for Heat and Fluid Flow, 9, 348.

104

Tamma, K. K., Zhou, X. and Sha, D. (1999b), ``Transient Algorithms for Heat Transfer: General Developments and Approaches for Generating Nth-Order Time Accurate Operators Including Practically Useful Second-Order Forms'', International Journal for Numerical Methods in Engineering, 44, 1545.

105

Tamma, K. K., Zhou, X. and Sha, D. (2000b), ``A Theory of Development and Design of Generalized Integration Operators for Computational Structural Dynamics'', International Journal for Numerical Methods in Engineering (to appear).

106

Tamma, K. K., Zhou, X. and Valasutean, R. (1997), ``Computational Algorithms for Transient Analysis: The Burden of Weight and Consequences Towards Formalizing Discrete Numerically Assigned [DNA] Algorithmic Markers: Wp-Family'', Computer Methods in Applied Mechanics and Engineering, 149, 153.

107

Tarnow, N. and Simo, J. C. (1994), ``How to Render Second-Order Accurate Time Stepping Algorithms Fourth-Order Accurate While Remaining the Stability and Conservation Properties'', Computer Methods in Applied Mechanics and Engineering, 115, 233.

108

Timoshenko, S. and Goodier, J. N. (1951), Theory of Elasticity. McGraw-Hill, New York, 2nd edition.

109

Traill-Nash, R. (1981), ``Modal Methods in the Dynamics of Systems with Non-Classical Damping'', Earthquake Engineering and Structural Dynamics, 9, 153.

110

Trujillo, D. M. (1975), ``The Direct Numerical Integration of Linear Matrix Differential Equations Using Padé Approximations'', International Journal for Numerical Methods in Engineering, 9, 259.

111

Trujillo, D. M. (1977a), ``An Unconditionally Stable Explicit Algorithm for Finite Element Heat Conduction Analysis'', Nuclear Engineering and Design, 44(99), 175.

112

Trujillo, D. M. (1977b), ``An Unconditionally Stable Explicit Algorithm for Structural Dynamics'', International Journal for Numerical Methods in Engineering, 11, 1579.

113

Valliappan, S. and Ang, K. K. (1989), `` -Method of Numerical Integration'', Computational Mechanics, 5, 321.

114

Volterra, E. and Zachmanoglou, E. C. (1965), Dynamics of Vibrations, Charles Merrill, Columbus, Ohio.

115

Warburton, G. and Soni, S. (1977), ``Errors in Response Calculations for Non-classically Damped Structures'', Earthquake Engineering and Structural Dynamics, 5, 365.

116

Washizu, K. (1975), Variational Methods in Elasticity and Plasticity, Pergamon Press, Oxford, 2 edition.

117

Williams, S. D. and Curry, D. M. (1977), An Implicit-Iterative Solution of the Heat Conduction Equation with a Radiation Boundary Condition. Int. J. Num. Meth. Eng., 11:1605.

118

Wilson, E. L. (1968), A Computer Program for Dynamic Stress Analysis of Underground Structures, SESM, Univ. California, Berkeley.

119

Witmer, E. A., and Balmer., H. A (1963) "Large Dynamic Deformations of Beams, Rings, Plates and Shells", AIAA J., 8:1848.

120

Wood, W. L. (1984), ``A Unified Set of Single-Step Algorithms, Part 2'', International Journal for Numerical Methods in Engineering, 20, 2303.

121

Wood, W. L. (1987), Numerical Methods for Transient and Coupled Problems, chapter 8, page 149. John Willey and Sons Ltd.

122

Wood, W. L. (1990), Practical Time Stepping Schemes, Clarendon Press, Oxford.

123

Wood, W. L., Bossak, M. and Zienkiewicz, O. C. (1980), ``An Alpha Modification of Newmark's Method'', International Journal for Numerical Methods in Engineering, 15, 1562.

124

Xu, K. and Igusa, T. (1991), ``Dynamic Characteristics of Non-Classically Damped Structures'', Earthquake Engineering and Structural Dynamics, 20, 1127.

125

Zhong, J. (1979), ``A Variational Principle in Heat Conduction and Its Applications (I)(II)'', Journal of Zhejiang University, 3, 91.

126

Zhong, J., Chow, L. C. and Chang, W. S. (1991), ``Finite Element Eigenvalue Method for Solving Phase-Change Problems'', Journal of Thermophysics, 5, 589.

127

Zhong, J., Chow, L. C. and Chang, W. S. (1992), ``A Finite Element Eigenvalue Method for Solving Transient Heat Conduction Problems'', Int. J. Num. Meth. Heat Fluid Flow, 2, 243.

128

Zhong, W. and Williams, F. W. (1994), ``A Precise Time Step Integration Method'', Proc. Inst. Mech. Engrs, 208, 427-436.

129

Zhong, W., Zhu, J. and Zhong, X. (1994), ``A Precise Time Integration Algorithm for Non-Linear System'', In Proc. 3rd World Congress on Computational Mechanics, pages 12-17, Chiba, Japan, 1994.

130

Zhong, W., Zhu, J. and Zhong, X. (1996), ``On a New Time Integration Method for Solving Time Dependent Partial Differential Equations'', Comput. Methods Appl. Mech. Engrg, 130, 163-178.

131

Zhou, X., Tamma, K. K., Kanapady, R., Sha, D. (2000), "The Time Dimension: New and Recent Advances and a Unified Framework Towards Design of Time Discretized Operators for Structural Dynamics", In European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS) 2000, Barcelona, Spain, Sep. 11-14.

132

Zienkiewicz, O. C. (1977), ``A New Look at Newmark, Houbolt and Other Time Stepping Formulas: A Weighted Residual Approach'', Earthquake Engineering and Structural Dynamics, 5, 283.

133

Zienkiewicz, O. C. and Taylor, R. L. (1994), The Finite Element Method, volume 1. McGraw-Hill, New York.

134

Zienkiewicz, O. C., Wood, W. L., Hine, N. W. and Taylor, R. L. (1984), ``A Unified Set of Single-Step Algorithms, Part 1: General Formulations and Applications'', International Journal for Numerical Methods in Engineering, 20, 1529.

135

Zlamal, M. (1975), ``Finite Element Methods in Heat Conduction Problem'', In Finite Element Methods. Brunel University.

136

Zlamal, M. (1977), Finite Elements Methods in Heat Conduction Problems. Academic Press.

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