메뉴 건너뛰기




Volumn 194, Issue 21-24 SPEC. ISS., 2005, Pages 2285-2335

A unified formulation of small-strain corotational finite elements: I. Theory

Author keywords

Corotational description; Geometrically nonlinear structural analysis; Shell finite elements

Indexed keywords

DEFORMATION; MATHEMATICAL MODELS; STIFFNESS MATRIX; STRAIN; STRUCTURAL ANALYSIS;

EID: 16244368053     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.07.035     Document Type: Article
Times cited : (393)

References (86)
  • 2
    • 0037085997 scopus 로고    scopus 로고
    • Co-rotational beam elements with warping effects in instability problems
    • J.-M. Battini C. Pacoste Co-rotational beam elements with warping effects in instability problems Comput. Methods Appl. Mech. Engrg. 191 2002 1755-1789
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 1755-1789
    • Battini, J.-M.1    Pacoste, C.2
  • 3
    • 0037147411 scopus 로고    scopus 로고
    • Plastic instability of beam structures using co-rotational elements
    • J.-M. Battini C. Pacoste Plastic instability of beam structures using co-rotational elements Comput. Methods Appl. Mech. Engrg. 191 2002 5811-5831
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 5811-5831
    • Battini, J.-M.1    Pacoste, C.2
  • 5
    • 16244418190 scopus 로고
    • Finite element formulations for large deformation dynamic analysis
    • K.-J. Bathe E. Ramm E.L. Wilson Finite element formulations for large deformation dynamic analysis Int. J. Numer. Methods Engrg. 7 1973 255-271
    • (1973) Int. J. Numer. Methods Engrg. , vol.7 , pp. 255-271
    • Bathe, K.-J.1    Ramm, E.2    Wilson, E.L.3
  • 7
    • 0015724866 scopus 로고
    • Nonlinear transient finite element analysis with convected coordinates
    • T. Belytschko B.J. Hsieh Nonlinear transient finite element analysis with convected coordinates Int. J. Numer. Methods Engrg. 7 1973 255-271
    • (1973) Int. J. Numer. Methods Engrg. , vol.7 , pp. 255-271
    • Belytschko, T.1    Hsieh, B.J.2
  • 8
    • 0017951580 scopus 로고
    • Application of higher order corotational stretch theories to nonlinear finite element analysis
    • T. Belytschko B.J. Hsieh Application of higher order corotational stretch theories to nonlinear finite element analysis Comput. Struct. 11 1979 175-182
    • (1979) Comput. Struct. , vol.11 , pp. 175-182
    • Belytschko, T.1    Hsieh, B.J.2
  • 9
    • 0020862818 scopus 로고
    • An overview of semidiscretization and time integration operators
    • T. Belytschko T.J.R. Hughes (Eds.) North-Holland Amsterdam
    • T. Belytschko An overview of semidiscretization and time integration operators in: T. Belytschko T.J.R. Hughes (Eds.) Computational Methods for Transient Analysis 1983 North-Holland Amsterdam 1-66
    • (1983) Computational Methods for Transient Analysis , pp. 1-66
    • Belytschko, T.1
  • 10
    • 0016922980 scopus 로고
    • Incremental variational principles and finite element models for nonlinear problems
    • P.G. Bergan G. Horrigmoe Incremental variational principles and finite element models for nonlinear problems Comput. Methods Appl. Mech. Engrg. 7 1976 201-217
    • (1976) Comput. Methods Appl. Mech. Engrg. , vol.7 , pp. 201-217
    • Bergan, P.G.1    Horrigmoe, G.2
  • 11
    • 0001170528 scopus 로고
    • A new approach for deriving 'good' finite elements
    • J.R. Whiteman (Ed.) MAFELAP II Conference, Brunel University, 1975 Academic Press London
    • P.G. Bergan L. Hanssen A new approach for deriving 'good' finite elements in: J.R. Whiteman (Ed.) MAFELAP II Conference, Brunel University, 1975 The Mathematics of Finite Elements and Applications vol. II 1976 Academic Press London 483-497
    • (1976) The Mathematics of Finite Elements and Applications , vol.2 , pp. 483-497
    • Bergan, P.G.1    Hanssen, L.2
  • 12
    • 0019070028 scopus 로고
    • Finite elements based on energy orthogonal functions
    • P.G. Bergan Finite elements based on energy orthogonal functions Int. J. Numer. Methods Engrg. 15 1980 1141-1555
    • (1980) Int. J. Numer. Methods Engrg. , vol.15 , pp. 1141-1555
    • Bergan, P.G.1
  • 13
    • 0021405329 scopus 로고
    • Finite elements with increased freedom in choosing shape functions
    • P.G. Bergan M.K. Nygård Finite elements with increased freedom in choosing shape functions Int. J. Numer. Methods Engrg. 20 1984 643-664
    • (1984) Int. J. Numer. Methods Engrg. , vol.20 , pp. 643-664
    • Bergan, P.G.1    Nygård, M.K.2
  • 14
    • 0022100808 scopus 로고
    • A triangular membrane element with rotational degrees of freedom
    • P.G. Bergan C.A. Felippa A triangular membrane element with rotational degrees of freedom Comput. Methods Appl. Mech. Engrg. 50 1985 25-69
    • (1985) Comput. Methods Appl. Mech. Engrg. , vol.50 , pp. 25-69
    • Bergan, P.G.1    Felippa, C.A.2
  • 15
  • 18
    • 4243574341 scopus 로고
    • Finite element formulations and solution algorithms for buckling and collapse analysis of thin shells
    • Dr. Ing. Thesis, Division of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway
    • R.O. Bjærum, Finite element formulations and solution algorithms for buckling and collapse analysis of thin shells. Dr. Ing. Thesis, Division of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway, 1992
    • (1992)
    • Bjærum, R.O.1
  • 20
    • 0024622609 scopus 로고
    • An historical note on finite rotations
    • H. Cheng K.C. Gupta An historical note on finite rotations J. Appl. Mech. 56 1989 139-145
    • (1989) J. Appl. Mech. , vol.56 , pp. 139-145
    • Cheng, H.1    Gupta, K.C.2
  • 21
    • 0036494421 scopus 로고    scopus 로고
    • Closed form line spring yield surfaces for deep and shallow cracks: Formulation and numerical performance
    • M. Chiesa B. Skallerud D. Gross Closed form line spring yield surfaces for deep and shallow cracks: Formulation and numerical performance Comput. Struct. 80 2002 533-545
    • (2002) Comput. Struct. , vol.80 , pp. 533-545
    • Chiesa, M.1    Skallerud, B.2    Gross, D.3
  • 22
    • 0025468397 scopus 로고
    • A consistent corotational formulation for nonlinear three-dimensional beam element
    • M.A. Crisfield A consistent corotational formulation for nonlinear three-dimensional beam element Comput. Methods Appl. Mech. Engrg. 81 1990 131-150
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.81 , pp. 131-150
    • Crisfield, M.A.1
  • 23
    • 0030212657 scopus 로고    scopus 로고
    • A unified co-rotational for solids, shells and beams
    • M.A. Crisfield G.F. Moita A unified co-rotational for solids, shells and beams Int. J. Solids Struc. 33 1996 2969-2992
    • (1996) Int. J. Solids Struc. , vol.33 , pp. 2969-2992
    • Crisfield, M.A.1    Moita, G.F.2
  • 26
    • 0036390834 scopus 로고    scopus 로고
    • Application of a three-field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter
    • C. Farhat P. Geuzaine G. Brown Application of a three-field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter Computers and Fluids 32 2003 3-29
    • (2003) Computers and Fluids , vol.32 , pp. 3-29
    • Farhat, C.1    Geuzaine, P.2    Brown, G.3
  • 27
    • 0026966830 scopus 로고
    • Membrane triangles with corner drilling freedoms: II. The ANDES element
    • C.A. Felippa C. Militello Membrane triangles with corner drilling freedoms: II. The ANDES element Finite Elements Anal. Des. 12 1992 189-201
    • (1992) Finite Elements Anal. Des. , vol.12 , pp. 189-201
    • Felippa, C.A.1    Militello, C.2
  • 28
    • 0026966101 scopus 로고
    • Membrane triangles with corner drilling freedoms: III. Implementation and performance evaluation
    • C.A. Felippa S. Alexander Membrane triangles with corner drilling freedoms: III. Implementation and performance evaluation Finite Elements Anal. Des. 12 1992 203-239
    • (1992) Finite Elements Anal. Des. , vol.12 , pp. 203-239
    • Felippa, C.A.1    Alexander, S.2
  • 29
    • 0013189945 scopus 로고    scopus 로고
    • A systematic approach to the element-independent corotational dynamics of finite elements
    • Report CU-CAS-00-03, Center for Aerospace Structures, College of Engineering and Applied Sciences, University of Colorado at Boulder, January
    • C.A. Felippa, A systematic approach to the element-independent corotational dynamics of finite elements, Report CU-CAS-00-03, Center for Aerospace Structures, College of Engineering and Applied Sciences, University of Colorado at Boulder, January 2000
    • (2000)
    • Felippa, C.A.1
  • 30
    • 0036501661 scopus 로고    scopus 로고
    • The construction of free-free flexibility matrices for multilevel structural analysis
    • C.A. Felippa K.C. Park The construction of free-free flexibility matrices for multilevel structural analysis Comput. Methods Appl. Mech. Engrg. 191 2002 2111-2140
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 2111-2140
    • Felippa, C.A.1    Park, K.C.2
  • 31
    • 0008687679 scopus 로고    scopus 로고
    • Recent advances in finite element templates
    • B.H.V. Topping (Ed.) Saxe-Coburn Publications Edinburgh
    • C.A. Felippa Recent advances in finite element templates in: B.H.V. Topping (Ed.) Computational Mechanics for the Twenty-First Century 2000 Saxe-Coburn Publications Edinburgh 71-98
    • (2000) Computational Mechanics for the Twenty-First Century , pp. 71-98
    • Felippa, C.A.1
  • 32
    • 0038364169 scopus 로고    scopus 로고
    • A study of optimal membrane triangles with drilling freedoms
    • C.A. Felippa A study of optimal membrane triangles with drilling freedoms Comput. Methods Appl. Mech. Engrg. 192 2003 2125-2168
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 2125-2168
    • Felippa, C.A.1
  • 34
    • 17344387490 scopus 로고
    • Finite element approach to kinematic and dynamic analysis of mechanisms using Euler parameters
    • C. Taylor E. Hinton D.R.J. Owen (Eds.) Pineridge Press Swansea
    • M. Geradin Finite element approach to kinematic and dynamic analysis of mechanisms using Euler parameters in: C. Taylor E. Hinton D.R.J. Owen (Eds.) Numerical Methods for Nonlinear Problems II 1984 Pineridge Press Swansea
    • (1984) Numerical Methods for Nonlinear Problems II
    • Geradin, M.1
  • 35
  • 37
    • 0003582352 scopus 로고
    • Buckling and stability problems for thin shell structures using high-performance finite elements
    • Ph.D. Dissertation, Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO
    • B. Haugen, Buckling and stability problems for thin shell structures using high-performance finite elements, Ph.D. Dissertation, Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO, 1994
    • (1994)
    • Haugen, B.1
  • 38
    • 16244394158 scopus 로고    scopus 로고
    • A unified formulation of small-strain corotational finite elements: II. Applications to shells and mechanisms
    • (in preparation)
    • B. Haugen, C.A. Felippa, A unified formulation of small-strain corotational finite elements: II. Applications to shells and mechanisms (in preparation)
    • Haugen, B.1    Felippa, C.A.2
  • 39
    • 0343944939 scopus 로고
    • Finite element instability analysis of free-form shells
    • Dr. Ing. Thesis, Division of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway
    • G. Horrigmoe, Finite element instability analysis of free-form shells, Dr. Ing. Thesis, Division of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway, 1977
    • (1977)
    • Horrigmoe, G.1
  • 40
    • 0018020886 scopus 로고
    • Instability analysis of free-form shells by flat finite elements
    • G. Horrigmoe P.G. Bergan Instability analysis of free-form shells by flat finite elements Comput. Methods Appl. Mech. Engrg. 16 1978 11-35
    • (1978) Comput. Methods Appl. Mech. Engrg. , vol.16 , pp. 11-35
    • Horrigmoe, G.1    Bergan, P.G.2
  • 42
    • 0019574991 scopus 로고
    • Nonlinear finite element analysis of shells: Part I. Three-dimensional shells
    • T.J.R. Hughes W.-K. Liu Nonlinear finite element analysis of shells: Part I. Three-dimensional shells Comput. Methods Appl. Mech. Engrg. 26 1981 331-362
    • (1981) Comput. Methods Appl. Mech. Engrg. , vol.26 , pp. 331-362
    • Hughes, T.J.R.1    Liu, W.-K.2
  • 43
    • 0019584313 scopus 로고
    • Nonlinear finite element analysis of shells: Part II. Two-dimensional shells
    • T.J.R. Hughes W.-K. Liu Nonlinear finite element analysis of shells: Part II. Two-dimensional shells Comput. Methods Appl. Mech. Engrg. 27 1981 167-182
    • (1981) Comput. Methods Appl. Mech. Engrg. , vol.27 , pp. 167-182
    • Hughes, T.J.R.1    Liu, W.-K.2
  • 44
    • 0019229765 scopus 로고
    • Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis
    • T.J.R. Hughes J. Winget Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis Int. J. Numer. Methods Engrg. 15 1980 1862-1867
    • (1980) Int. J. Numer. Methods Engrg. , vol.15 , pp. 1862-1867
    • Hughes, T.J.R.1    Winget, J.2
  • 46
    • 16244396845 scopus 로고
    • Large displacement analysis of shells considering elastoplastic and elastoviscoplastic materials
    • Dr. Ing. Thesis, Division of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway
    • B. Kråkeland, Large displacement analysis of shells considering elastoplastic and elastoviscoplastic materials, Dr. Ing. Thesis, Division of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway, 1977
    • (1977)
    • Kråkeland, B.1
  • 47
    • 0011778428 scopus 로고
    • Solid mechanics and material models including large deformations
    • Dr. Ing. Thesis, Div. of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway
    • E. Levold, Solid mechanics and material models including large deformations, Dr. Ing. Thesis, Div. of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway, 1990
    • (1990)
    • Levold, E.1
  • 48
    • 0010365868 scopus 로고
    • Large displacement analysis of flexible and rigid systems considering displacement-dependent loads and nonlinear constraints
    • Dr. Ing. Thesis, Division of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway
    • K.M. Mathisen, Large displacement analysis of flexible and rigid systems considering displacement-dependent loads and nonlinear constraints. Dr. Ing. Thesis, Division of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway, 1990
    • (1990)
    • Mathisen, K.M.1
  • 49
    • 0003471594 scopus 로고
    • Adaptive strategies for nonlinear finite element analysis of shell structures
    • C. Hirsch (Ed.) Elsevier Science Publishers B.V. Amsterdam
    • K.M. Mathisen T. Kvamsdal K.M. Okstad Adaptive strategies for nonlinear finite element analysis of shell structures in: C. Hirsch (Ed.) Numerical Methods in Engineering '92 1992 Elsevier Science Publishers B.V. Amsterdam
    • (1992) Numerical Methods in Engineering '92
    • Mathisen, K.M.1    Kvamsdal, T.2    Okstad, K.M.3
  • 50
    • 0009854444 scopus 로고
    • On the corotational finite element formulation for large deformation problems
    • Dr. Ing. Thesis, Department of Structural Mechanics, Chalmers University of Technology, Göteborg
    • K. Mattiasson, On the corotational finite element formulation for large deformation problems, Dr. Ing. Thesis, Department of Structural Mechanics, Chalmers University of Technology, Göteborg, 1983
    • (1983)
    • Mattiasson, K.1
  • 51
    • 0005593417 scopus 로고
    • Total and updated Lagrangian forms of the co-rotational finite element formulation in geometrically and materially nonlinear analysis
    • C. Taylor E. Hinton D.R.J. Owen (Eds.) Pineridge Press Swansea
    • K. Mattiasson A. Samuelsson Total and updated Lagrangian forms of the co-rotational finite element formulation in geometrically and materially nonlinear analysis in: C. Taylor E. Hinton D.R.J. Owen (Eds.) Numerical Methods for Nonlinear Problems II 1984 Pineridge Press Swansea 134-151
    • (1984) Numerical Methods for Nonlinear Problems II , pp. 134-151
    • Mattiasson, K.1    Samuelsson, A.2
  • 52
    • 0039049675 scopus 로고
    • On the accuracy and efficiency of numerical algorithms for geometrically nonlinear structural analysis
    • P.G. Bergan K.J. Bathe W. Wunderlich (Eds.) Springer-Verlag Berlin
    • K. Mattiasson A. Bengston A. Samuelsson On the accuracy and efficiency of numerical algorithms for geometrically nonlinear structural analysis in: P.G. Bergan K.J. Bathe W. Wunderlich (Eds.) Finite Element Methods for Nonlinear Problems 1986 Springer-Verlag Berlin 3-23
    • (1986) Finite Element Methods for Nonlinear Problems , pp. 3-23
    • Mattiasson, K.1    Bengston, A.2    Samuelsson, A.3
  • 54
    • 0001490854 scopus 로고
    • Finite rotation analysis and consistent linearization using projectors
    • B. Nour-Omid C.C. Rankin Finite rotation analysis and consistent linearization using projectors Comput. Methods Appl. Mech. Engrg. 93 1991 353-384
    • (1991) Comput. Methods Appl. Mech. Engrg. , vol.93 , pp. 353-384
    • Nour-Omid, B.1    Rankin, C.C.2
  • 56
    • 0024935494 scopus 로고
    • Advances in treating large rotations for nonlinear problems
    • A.K. Noor J.T. Oden (Eds.) ASME New York
    • M.K. Nygård P.G. Bergan Advances in treating large rotations for nonlinear problems in: A.K. Noor J.T. Oden (Eds.) State-of the Art Surveys on Computational Mechanics 1989 ASME New York 305-332
    • (1989) State-of the Art Surveys on Computational Mechanics , pp. 305-332
    • Nyg̊rd, M.K.1    Bergan, P.G.2
  • 57
    • 16244395580 scopus 로고
    • Large displacement analysis of flexible and rigid systems considering displacement-dependent loads and nonlinear constraints
    • Ing. Thesis, Division of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway
    • M.K. Nygård, Large displacement analysis of flexible and rigid systems considering displacement-dependent loads and nonlinear constraints. Dr. Ing. Thesis, Division of Structural Mechanics, Norwegian Institute of Technology, Trondheim, Norway, 1990
    • (1990)
    • Nygård, M.K.1
  • 58
    • 0002786897 scopus 로고    scopus 로고
    • Co-rotational flat facet triangular elements for shell instability analysis
    • C. Pacoste Co-rotational flat facet triangular elements for shell instability analysis Comput. Methods Appl. Mech. Engrg. 156 1998 75-110
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.156 , pp. 75-110
    • Pacoste, C.1
  • 59
    • 0022736020 scopus 로고
    • 0 shell element based on assumed natural-coordinate strains
    • 0 shell element based on assumed natural-coordinate strains J. Appl. Mech. 53 1986 278-290
    • (1986) J. Appl. Mech. , vol.53 , pp. 278-290
    • Park, K.C.1    Stanley, G.M.2
  • 60
    • 0009427918 scopus 로고
    • Finite rotations in shells
    • Proceedings of the 3rd IUTAM Symp on Shell Theory, Tsibili, 1978 North Holland Amsterdam
    • W. Pietraszkiewicz Finite rotations in shells in: Theory of Shells, Proceedings of the 3rd IUTAM Symp on Shell Theory, Tsibili, 1978 1980 North Holland Amsterdam 445-471
    • (1980) Theory of Shells , pp. 445-471
    • Pietraszkiewicz, W.1
  • 61
    • 5844232522 scopus 로고
    • Finite Rotations in Structural Mechanics
    • (Ed.) Springer-Verlag Berlin
    • W. Pietraszkiewicz (Ed.) Finite Rotations in Structural Mechanics Lecture Notes in Engineering 19 1985 Springer-Verlag Berlin
    • (1985) Lecture Notes in Engineering , vol.19
    • Pietraszkiewicz, W.1
  • 63
    • 0022715531 scopus 로고
    • An element-independent corotational procedure for the treatment of large rotations
    • C.C. Rankin F.A. Brogan An element-independent corotational procedure for the treatment of large rotations ASME J. Pressure Vessel Technology 108 1986 165-174
    • (1986) ASME J. Pressure Vessel Technology , vol.108 , pp. 165-174
    • Rankin, C.C.1    Brogan, F.A.2
  • 64
    • 16244417294 scopus 로고
    • Consistent linearization of the element-independent corotational formulation for the structural analysis of general shells
    • NASA Contractor Report 278428, Lockheed Palo Alto Res. Lab., CA
    • C.C. Rankin, Consistent linearization of the element-independent corotational formulation for the structural analysis of general shells, NASA Contractor Report 278428, Lockheed Palo Alto Res. Lab., CA, 1988
    • (1988)
    • Rankin, C.C.1
  • 65
    • 38249029644 scopus 로고
    • The use of projectors to improve finite element performance
    • C.C. Rankin B. Nour-Omid The use of projectors to improve finite element performance Comput. Struct. 30 1988 257-267
    • (1988) Comput. Struct. , vol.30 , pp. 257-267
    • Rankin, C.C.1    Nour-Omid, B.2
  • 66
    • 16244417294 scopus 로고
    • Consistent linearization of the element-independent corotational formulation for the structural analysis of general shells
    • NASA Contractor Report 278428, Lockheed Palo Alto Research Laboratory, Palo Alto, CA
    • C.C. Rankin, Consistent linearization of the element-independent corotational formulation for the structural analysis of general shells, NASA Contractor Report 278428, Lockheed Palo Alto Research Laboratory, Palo Alto, CA, 1988
    • (1988)
    • Rankin, C.C.1
  • 67
    • 2142697009 scopus 로고    scopus 로고
    • On choice of best possible corotational element frame
    • S.N. Atluri P.E. O'Donoghue (Eds.) Tech Science Press Palmdale, CA
    • C.C. Rankin On choice of best possible corotational element frame in: S.N. Atluri P.E. O'Donoghue (Eds.) Modeling and Simulation Based Engineering 1998 Tech Science Press Palmdale, CA
    • (1998) Modeling and Simulation Based Engineering
    • Rankin, C.C.1
  • 69
    • 0000741026 scopus 로고
    • Des lois géometriques qui regissent les déplacements d'un systéme solide dans l'espace, et de la variation des coordonnées provenant de ces déplacement considerées indépendent des causes qui peuvent les produire
    • O. Rodrigues Des lois géometriques qui regissent les déplacements d'un systéme solide dans l'espace, et de la variation des coordonnées provenant de ces déplacement considerées indépendent des causes qui peuvent les produire J. de Mathématiques Pures et Appliquées 5 1840 380-400
    • (1840) J. de Mathématiques Pures et Appliquées , vol.5 , pp. 380-400
    • Rodrigues, O.1
  • 70
    • 0015490195 scopus 로고
    • Nonlinear shell theory with finite rotation and stress function vectors
    • J.G. Simmonds D.A. Danielson Nonlinear shell theory with finite rotation and stress function vectors J. Appl. Mech. 39 1972 1085-1090
    • (1972) J. Appl. Mech. , vol.39 , pp. 1085-1090
    • Simmonds, J.G.1    Danielson, D.A.2
  • 71
    • 0022060633 scopus 로고
    • A finite strain beam formulation. Part I: The three-dimensional dynamic problem
    • J.C. Simo A finite strain beam formulation. Part I: The three-dimensional dynamic problem Comput. Methods Appl. Mech. Engrg. 49 1985 55-70
    • (1985) Comput. Methods Appl. Mech. Engrg. , vol.49 , pp. 55-70
    • Simo, J.C.1
  • 72
    • 0022792209 scopus 로고
    • A finite strain beam formulation. Part II: Computational aspects
    • J.C. Simo L. Vu-Quoc A finite strain beam formulation. Part II: Computational aspects Comput. Methods Appl. Mech. Engrg. 58 1986 79-116
    • (1986) Comput. Methods Appl. Mech. Engrg. , vol.58 , pp. 79-116
    • Simo, J.C.1    Vu-Quoc, L.2
  • 74
    • 0033349307 scopus 로고    scopus 로고
    • Collapse of thin shell structures: Stress resultant plasticity modeling within a co-rotated ANDES finite element formulation
    • B. Skallerud B. Haugen Collapse of thin shell structures: Stress resultant plasticity modeling within a co-rotated ANDES finite element formulation Int. J. Numer. Methods Engrg. 46 1999 1961-1986
    • (1999) Int. J. Numer. Methods Engrg. , vol.46 , pp. 1961-1986
    • Skallerud, B.1    Haugen, B.2
  • 76
    • 85003265755 scopus 로고
    • A comment on singularity-free extraction of a quaternion from a direction cosine matrix
    • R.A. Spurrier A comment on singularity-free extraction of a quaternion from a direction cosine matrix J. Spacecrafts Rockets 15 1978 255
    • (1978) J. Spacecrafts Rockets , vol.15 , pp. 255
    • Spurrier, R.A.1
  • 77
    • 0022874304 scopus 로고
    • Variational formulation in the geometrically nonlinear thin elastic shell theory
    • M.L. Szwabowicz Variational formulation in the geometrically nonlinear thin elastic shell theory Int. J. Solids Struc. 22 1986 1161-1175
    • (1986) Int. J. Solids Struc. , vol.22 , pp. 1161-1175
    • Szwabowicz, M.L.1
  • 79
    • 0003528983 scopus 로고
    • Nonlinear analysis of concrete structures based on a 3D shear-beam element formulation
    • Ph.D Dissertation, Department of Mathematics, Mechanics Division, University of Oslo, Oslo, Norway
    • J.G. Teigen, Nonlinear analysis of concrete structures based on a 3D shear-beam element formulation, Ph.D Dissertation, Department of Mathematics, Mechanics Division, University of Oslo, Oslo, Norway, 1994
    • (1994)
    • Teigen, J.G.1
  • 80
    • 0004978141 scopus 로고
    • Gordon & Breach, New York (corrected reprint of Continuum Mechanics I: The Mechanical Foundations of Elasticity and Fluid Dynamics, J. Rational Mech. Anal. 1 (1952) 125-300)
    • C. Truesdell, Continuum Mechanics I: The Mechanical Foundations of Elasticity and Fluid Dynamics, Gordon & Breach, New York, 1966 (corrected reprint of Continuum Mechanics I: The Mechanical Foundations of Elasticity and Fluid Dynamics, J. Rational Mech. Anal. 1 (1952) 125-300)
    • (1966) Continuum Mechanics I: The Mechanical Foundations of Elasticity and Fluid Dynamics
    • Truesdell, C.1
  • 81
    • 0001700852 scopus 로고
    • The classical field theories
    • S. Flügge (Ed.) Springer Verlag Berlin
    • C. Truesdell R.A. Toupin The classical field theories in: S. Flügge (Ed.) Handbuch der Physik vol. III/1 1960 Springer Verlag Berlin 226-790
    • (1960) Handbuch Der Physik , vol.3 , Issue.1 , pp. 226-790
    • Truesdell, C.1    Toupin, R.A.2
  • 82
    • 0345023082 scopus 로고
    • Hypoelasticity
    • 83-133 (Reprinted in Foundations of Elasticity Theory, Gordon & Breach, New York, 1965)
    • C. Truesdell Hypoelasticity J. Ration. Mech. 4 1955 pp. 83-133, 1019-1020 (Reprinted in Foundations of Elasticity Theory, Gordon & Breach, New York, 1965)
    • (1955) J. Ration. Mech. , vol.4 , pp. 1019-1020
    • Truesdell, C.1
  • 83
    • 0002565890 scopus 로고
    • The nonlinear field theories of mechanics
    • S. Flügge (Ed.) Springer-Verlag Berlin
    • C. Truesdell W. Noll The nonlinear field theories of mechanics in: S. Flügge (Ed.) Handbuch der Physik vol. III/3 1965 Springer-Verlag Berlin
    • (1965) Handbuch Der Physik , vol.3 , Issue.3
    • Truesdell, C.1    Noll, W.2
  • 85
    • 0000818662 scopus 로고
    • A theory of viscoplasticity without a yield surface, Part II: Application to mechanical behavior of metals
    • K.C. Valanis A theory of viscoplasticity without a yield surface, Part II: Application to mechanical behavior of metals Arch. Mech. 23 1971 535-551
    • (1971) Arch. Mech. , vol.23 , pp. 535-551
    • Valanis, K.C.1
  • 86
    • 0000056694 scopus 로고
    • Finite elements, finite rotations and small strains of flexible shells
    • G.A. Wempner Finite elements, finite rotations and small strains of flexible shells Int. J. Solids Struc. 5 1969 117-153
    • (1969) Int. J. Solids Struc. , vol.5 , pp. 117-153
    • Wempner, G.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.