메뉴 건너뛰기




Volumn 21, Issue 6, 1998, Pages 449-460

Parametrized formulations of Hamilton's law for numerical solutions of dynamic problems: Part II. Time finite element approximation

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; INTERPOLATION; PROBLEM SOLVING;

EID: 0032095810     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004660050324     Document Type: Article
Times cited : (7)

References (59)
  • 1
    • 0026754825 scopus 로고
    • Mixed finite element formulations in the time domain for solution of dynamics
    • Aharoni D, Bar-Yoseph P (1992) Mixed finite element formulations in the time domain for solution of dynamics. Comput. Mech. 9:359-374
    • (1992) Comput. Mech. , vol.9 , pp. 359-374
    • Aharoni, D.1    Bar-Yoseph, P.2
  • 4
    • 0015650607 scopus 로고
    • An assumed stress hybrid finite element model for linear elastodynamic analysis
    • Atluri SN (1973) An assumed stress hybrid finite element model for linear elastodynamic analysis. AIAA J. 7:1028-1031
    • (1973) AIAA J. , vol.7 , pp. 1028-1031
    • Atluri, S.N.1
  • 5
    • 0016554233 scopus 로고
    • Application of Hamilton's Law of Varying Action
    • Bailey CD (1975) Application of Hamilton's Law of Varying Action. AIAA J. 13:1154-1157
    • (1975) AIAA J. , vol.13 , pp. 1154-1157
    • Bailey, C.D.1
  • 6
    • 0016923716 scopus 로고
    • The method of Ritz applied to the equation of Hamilton
    • Bailey CD (1976a) The method of Ritz applied to the equation of Hamilton. Comput. Meth. Appl. Mech. Eng. 7:235-247
    • (1976) Comput. Meth. Appl. Mech. Eng. , vol.7 , pp. 235-247
    • Bailey, C.D.1
  • 7
    • 0020125243 scopus 로고
    • Hamilton's principle, Hamilton's law-6 correct formulations
    • Baruch M, Riff R (1982) Hamilton's principle, Hamilton's law-6 correct formulations. AIAA J. 22:687-692
    • (1982) AIAA J. , vol.22 , pp. 687-692
    • Baruch, M.1    Riff, R.2
  • 10
    • 85002938167 scopus 로고
    • Comment on time finite element discretization of Hamilton's law of varying action
    • Borri M, Lanz M, Mantegazza P (1985a) Comment on time finite element discretization of Hamilton's law of varying action. AIAA J. 23:1457-1458
    • (1985) AIAA J. , vol.23 , pp. 1457-1458
    • Borri, M.1    Lanz, M.2    Mantegazza, P.3
  • 11
    • 0021589983 scopus 로고
    • Dynamic response of mechanical systems by a weak Hamilton formulation
    • Borri M, Ghiringhelli GL, Lanz M (1985b) Dynamic response of mechanical systems by a weak Hamilton formulation. Comput. Struct. 20:495-508
    • (1985) Comput. Struct. , vol.20 , pp. 495-508
    • Borri, M.1    Ghiringhelli, G.L.2    Lanz, M.3
  • 12
    • 0022484826 scopus 로고
    • Helicopter rotor dynamics by finite element time approximation
    • Borri M (1986) Helicopter rotor dynamics by finite element time approximation. Comp. Maths. Appl. 12a:149-160
    • (1986) Comp. Maths. Appl. , vol.12 A , pp. 149-160
    • Borri, M.1
  • 13
    • 11344263697 scopus 로고
    • Time-finite element method for the constrained dynamics of a rigid body
    • Borri M, Atluri SN (1988a) Time-finite element method for the constrained dynamics of a rigid body. Proc. ICES-88 41.i.:1-4
    • (1988) Proc. ICES-88 , vol.41 , Issue.1 , pp. 1-4
    • Borri, M.1    Atluri, S.N.2
  • 14
    • 11344260260 scopus 로고
    • Multi-body dynamics by the finite element method in time domain
    • Borri M, Atluri SN (1988b) Multi-body dynamics by the finite element method in time domain. Proc. ICES-88 64.ii.:1-4
    • (1988) Proc. ICES-88 , vol.64 , Issue.2 , pp. 1-4
    • Borri, M.1    Atluri, S.N.2
  • 15
    • 0002004446 scopus 로고
    • Variational approaches for dynamics and time-finite-elements: Numerical studies
    • Borri M, Mello F, Atluri SN (1990a) Variational approaches for dynamics and time-finite-elements: Numerical studies. Comput. Mech. 7:49-76
    • (1990) Comput. Mech. , vol.7 , pp. 49-76
    • Borri, M.1    Mello, F.2    Atluri, S.N.3
  • 17
    • 0008485947 scopus 로고
    • Primal and mixed forms of Hamilton's principle for constrained rigid body systems: Numerical studies
    • Borri M, Mello F, Atluri SN (1991) Primal and mixed forms of Hamilton's principle for constrained rigid body systems: numerical studies. Comput. Mech. 7:205-220
    • (1991) Comput. Mech. , vol.7 , pp. 205-220
    • Borri, M.1    Mello, F.2    Atluri, S.N.3
  • 18
    • 51249170672 scopus 로고
    • Basic features of the time finite element approach for dynamics
    • Borri M, Bottasso C, Mantegazza P (1992) Basic features of the time finite element approach for dynamics. Maccanica 27:119-130
    • (1992) Maccanica , vol.27 , pp. 119-130
    • Borri, M.1    Bottasso, C.2    Mantegazza, P.3
  • 19
    • 0027851173 scopus 로고
    • A general framework for interpreting time finite element formulations
    • Borri M, Bottasso C (1993) A general framework for interpreting time finite element formulations. Comput. Mech. 13:133-142
    • (1993) Comput. Mech. , vol.13 , pp. 133-142
    • Borri, M.1    Bottasso, C.2
  • 20
    • 0028465980 scopus 로고
    • An intrinsic beam model based on a helicoidal approximation - Part I: Formulation
    • Borri M, Bottasso C (1994) An intrinsic beam model based on a helicoidal approximation - Part I: formulation. Int. J. Numeri. Method Eng. 37:2267-2289
    • (1994) Int. J. Numeri. Method Eng. , vol.37 , pp. 2267-2289
    • Borri, M.1    Bottasso, C.2
  • 21
    • 0027063187 scopus 로고
    • A non-linear beam space-time finite element formulation using quaternion algebra: Interpolation of the Lagrange multipliers and the appearance of spurious modes
    • Bottasso C (1992) A non-linear beam space-time finite element formulation using quaternion algebra: interpolation of the Lagrange multipliers and the appearance of spurious modes. Comput. Mech. 10:359-368
    • (1992) Comput. Mech. , vol.10 , pp. 359-368
    • Bottasso, C.1
  • 22
    • 0011782554 scopus 로고    scopus 로고
    • Parametrized variational principles in dynamics applied to the optimization of dynamic models of plates
    • Brito Castro FJ, Militello C, Felippa CA (1997) Parametrized variational principles in dynamics applied to the optimization of dynamic models of plates. Comput. Mech. 20:285-294
    • (1997) Comput. Mech. , vol.20 , pp. 285-294
    • Brito Castro, F.J.1    Militello, C.2    Felippa, C.A.3
  • 24
    • 0026941823 scopus 로고
    • A finite element structural dynamics model of a beam with an arbitrary moving base-Part II: Numerical examples and solutions
    • Du H, Hitchings D, Davies GAO (1992) A finite element structural dynamics model of a beam with an arbitrary moving base-Part II: Numerical examples and solutions. Finite element in Anl. & Des. 12:133-150
    • (1992) Finite Element in Anl. & Des. , vol.12 , pp. 133-150
    • Du, H.1    Hitchings, D.2    Davies, G.A.O.3
  • 25
    • 0024738329 scopus 로고
    • The extended free formulation of finite elements in linear elasticity
    • Felippa CA (1989a) The extended free formulation of finite elements in linear elasticity. J. Appl. Mech. 56:609-616
    • (1989) J. Appl. Mech. , vol.56 , pp. 609-616
    • Felippa, C.A.1
  • 26
    • 0024608943 scopus 로고
    • Parametrized multifield variational principles in elasticity: I. Mixed functionals
    • Felippa CA (1989b) Parametrized multifield variational principles in elasticity: I. Mixed functionals. Commun. Appl. Numer. Meth. 5:69-78
    • (1989) Commun. Appl. Numer. Meth. , vol.5 , pp. 69-78
    • Felippa, C.A.1
  • 27
    • 0024608943 scopus 로고
    • Parametrized multifield variational principles in elasticity: II. Hybrid functionals and the free formulation
    • Felippa CA (1989c) Parametrized multifield variational principles in elasticity: II. Hybrid functionals and the free formulation. Commum. Appl. Numer. Meth. 5:79-88
    • (1989) Commum. Appl. Numer. Meth. , vol.5 , pp. 79-88
    • Felippa, C.A.1
  • 28
    • 0025553988 scopus 로고
    • Variational formulation of high-performance finite elements: Parametrized variational principles
    • Felippa CA (1990) Variational formulation of high-performance finite elements: Parametrized variational principles. Comput. & Struct. 36:1-11
    • (1990) Comput. & Struct. , vol.36 , pp. 1-11
    • Felippa, C.A.1
  • 29
    • 0030189828 scopus 로고    scopus 로고
    • Recent development in parametrized variational principles for mechanics
    • Felippa CA (1996) Recent development in parametrized variational principles for mechanics. Comput. Mech. 18:159-174
    • (1996) Comput. Mech. , vol.18 , pp. 159-174
    • Felippa, C.A.1
  • 30
    • 85007700819 scopus 로고
    • Finite-element analysis of time-dependent phenomena
    • Fried I (1969) Finite-element analysis of time-dependent phenomena, AIAA J. 7:1170-1173
    • (1969) AIAA J. , vol.7 , pp. 1170-1173
    • Fried, I.1
  • 31
    • 0025594388 scopus 로고
    • Numerical methods for the treatment of periodic systems with applications to structural dynamics and helicopter rotor dynamics
    • Friedmann PP (1990) Numerical methods for the treatment of periodic systems with applications to structural dynamics and helicopter rotor dynamics. Comput. & Struct. 35:329-347
    • (1990) Comput. & Struct. , vol.35 , pp. 329-347
    • Friedmann, P.P.1
  • 32
    • 0001149803 scopus 로고
    • Rotary-wing aeroelasticity with application to VTOL Vehicles
    • Noor AK, Venneri SL (eds.), ASME
    • Friedmann PP, Hodges DH (1993) Rotary-wing aeroelasticity with application to VTOL Vehicles. Structural Dynamics and Aeroelasticity, Noor AK, Venneri SL (eds.), ASME, pp 299-392
    • (1993) Structural Dynamics and Aeroelasticity , pp. 299-392
    • Friedmann, P.P.1    Hodges, D.H.2
  • 33
    • 11344257080 scopus 로고
    • Nonlinear analysis using temporal finite elements
    • Gellin S, Pitarresi J (1988) Nonlinear analysis using temporal finite elements. Eng. Analy. 5:126-132
    • (1988) Eng. Analy. , vol.5 , pp. 126-132
    • Gellin, S.1    Pitarresi, J.2
  • 34
    • 0041297500 scopus 로고
    • Augmented Lagrangian techniques for solving frictionless contact problems in finite elasticity
    • Bergan PG, Bath KJ, Wunderlich W, (eds.), Spring-Verling
    • Glowinski R, Vidrascu M, Letallec P (1986) Augmented Lagrangian techniques for solving frictionless contact problems in finite elasticity. Finite Element methods for Nonlinear Problems, Bergan PG, Bath KJ, Wunderlich W, (eds.), Spring-Verling pp 745-758
    • (1986) Finite Element Methods for Nonlinear Problems , pp. 745-758
    • Glowinski, R.1    Vidrascu, M.2    Letallec, P.3
  • 35
    • 85003383696 scopus 로고
    • Weak Hamiltonian finite element method for optimal control problems
    • Hodges DH, Bless RR (1989) Weak Hamiltonian finite element method for optimal control problems. J. Guid. 14:148-155
    • (1989) J. Guid. , vol.14 , pp. 148-155
    • Hodges, D.H.1    Bless, R.R.2
  • 36
    • 0026419520 scopus 로고
    • Shape functions for mixed p-version finite elements in the time domain. I
    • Hodges DH, Hou LJ (1991) Shape functions for mixed p-version finite elements in the time domain. I. Sound Vib, 145:169-178
    • (1991) Sound Vib , vol.145 , pp. 169-178
    • Hodges, D.H.1    Hou, L.J.2
  • 37
    • 11344278061 scopus 로고
    • A mixed space-time finite elements formulation for linear dynamic response of beams
    • Hodges DH, Zhou WY, Ozbek A (1992) A mixed space-time finite elements formulation for linear dynamic response of beams. Developments in Theor. & Appl. Mech. XVI, II:309-311
    • (1992) Developments in Theor. & Appl. Mech. , vol.16 , Issue.2 , pp. 309-311
    • Hodges, D.H.1    Zhou, W.Y.2    Ozbek, A.3
  • 38
    • 0028457970 scopus 로고
    • Application of triangular space-time finite elements to problems of wave propagation
    • Hou LJ, Peters DA (1994) Application of triangular space-time finite elements to problems of wave propagation. J. Sound Vib. 173(5):611-632
    • (1994) J. Sound Vib. , vol.173 , Issue.5 , pp. 611-632
    • Hou, L.J.1    Peters, D.A.2
  • 39
    • 0000263374 scopus 로고
    • A recurrence matrix solution for the dynamic response of elastic aircraft
    • Houbolt JC (1950) A recurrence matrix solution for the dynamic response of elastic aircraft. J. Aeronaut. Sci. 17:540-550
    • (1950) J. Aeronaut. Sci. , vol.17 , pp. 540-550
    • Houbolt, J.C.1
  • 41
    • 0023960856 scopus 로고
    • Space-time finite element methods for elastodynamics: Formulations and error estimates
    • Hughes TJR, Hulbert GM (1988) Space-time finite element methods for elastodynamics: Formulations and error estimates. Comput. Meth. Appl. Mech. Eng. 66:339-363
    • (1988) Comput. Meth. Appl. Mech. Eng. , vol.66 , pp. 339-363
    • Hughes, T.J.R.1    Hulbert, G.M.2
  • 42
    • 0025693468 scopus 로고
    • Space-time finite element methods for second-order hyperbolic equations
    • Hulbert GM, Hughes TJR (1990) Space-time finite element methods for second-order hyperbolic equations. Comp. Methods Appl. Mech. Eng. 84:327-348
    • (1990) Comp. Methods Appl. Mech. Eng. , vol.84 , pp. 327-348
    • Hulbert, G.M.1    Hughes, T.J.R.2
  • 43
    • 0026678731 scopus 로고
    • Time finite element methods for structural dynamics
    • Hulbert GM (1992) Time finite element methods for structural dynamics. Int. J. Numer. Meth. Eng. 33:307-331
    • (1992) Int. J. Numer. Meth. Eng. , vol.33 , pp. 307-331
    • Hulbert, G.M.1
  • 44
    • 0028384753 scopus 로고
    • A unified set of single-step asymptotic annihilation algorithms for structural dynamics
    • Hulbert GM (1994) A unified set of single-step asymptotic annihilation algorithms for structural dynamics. Comput. Methods Appl. Mech. Eng. 113:1-9
    • (1994) Comput. Methods Appl. Mech. Eng. , vol.113 , pp. 1-9
    • Hulbert, G.M.1
  • 45
    • 11344263190 scopus 로고
    • Space-time formulation of Hamilton's law
    • Leipholz HHE (1982) Space-time formulation of Hamilton's law. Mech. Res. Comm. 9:317-323
    • (1982) Mech. Res. Comm. , vol.9 , pp. 317-323
    • Leipholz, H.H.E.1
  • 49
    • 0025588403 scopus 로고
    • Time finite element methods for large rotational dynamics of multi-body systems
    • Mello FJ, Borri M, Atluri SN (1990) Time finite element methods for large rotational dynamics of multi-body systems. Comput. Struct. 37:231-240
    • (1990) Comput. Struct. , vol.37 , pp. 231-240
    • Mello, F.J.1    Borri, M.2    Atluri, S.N.3
  • 50
    • 0027642991 scopus 로고
    • High-order hierarchical A- And L-stable integration methods
    • Möller PW (1993) High-order hierarchical A- and L-stable integration methods, Int. J. Numer. Methods Engrg. 36:2607-2624
    • (1993) Int. J. Numer. Methods Engrg. , vol.36 , pp. 2607-2624
    • Möller, P.W.1
  • 51
    • 0014537398 scopus 로고
    • A general theory of finite element.2. Application
    • Oden JT (1969) A general theory of finite element.2. Application. Int. J. Numer. Meth. Eng. 1:247-259
    • (1969) Int. J. Numer. Meth. Eng. , vol.1 , pp. 247-259
    • Oden, J.T.1
  • 52
    • 0003022338 scopus 로고
    • hp-version finite elements for the space-time domain
    • Peters DA, Izadpanah AP (1988) hp-version finite elements for the space-time domain. Comput. Mech. 3:73-88
    • (1988) Comput. Mech. , vol.3 , pp. 73-88
    • Peters, D.A.1    Izadpanah, A.P.2
  • 54
    • 0026383979 scopus 로고
    • The temporal finite element method in structural dynamics
    • Pitarresi JM, Manolis GD (1991) The temporal finite element method in structural dynamics. Comput. & Struct. 41:647-655
    • (1991) Comput. & Struct. , vol.41 , pp. 647-655
    • Pitarresi, J.M.1    Manolis, G.D.2
  • 55
    • 85008266722 scopus 로고
    • Comment on "Finite Elements for Initial value problems in dynamics"
    • Riff R, Weller T, Baruch M (1984a) Comment on "Finite Elements for Initial value problems in dynamics". AIAA J. 21:318-319
    • (1984) AIAA J. , vol.21 , pp. 318-319
    • Riff, R.1    Weller, T.2    Baruch, M.3
  • 56
    • 0021481458 scopus 로고
    • Stability of time finite elements
    • Riff R, Baruch M (1984b) Stability of time finite elements. AIAA J. 22:1171-1173
    • (1984) AIAA J. , vol.22 , pp. 1171-1173
    • Riff, R.1    Baruch, M.2
  • 57
    • 0021494973 scopus 로고
    • Time finite element discretization of Hamilton's law of varying action
    • Riff R, Baruch M (1984c) Time finite element discretization of Hamilton's law of varying action. AIAA J. 22:1310-1318
    • (1984) AIAA J. , vol.22 , pp. 1310-1318
    • Riff, R.1    Baruch, M.2
  • 59
    • 0019625595 scopus 로고
    • Finite elements for initial value problems in dynamics
    • Simkins SE (1981) Finite elements for initial value problems in dynamics. AIAA J. 19:1357-1362
    • (1981) AIAA J. , vol.19 , pp. 1357-1362
    • Simkins, S.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.