메뉴 건너뛰기




Volumn 58, Issue 1-2, 2009, Pages 295-306

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation

Author keywords

Boundary element method; Moderate large displacements; Nonlinear dynamic analysis; Shear center; Shear deformation coefficients; Timoshenko beam

Indexed keywords

MODERATE LARGE DISPLACEMENTS; NONLINEAR DYNAMIC ANALYSIS; SHEAR CENTER; SHEAR DEFORMATION COEFFICIENTS; TIMOSHENKO BEAM;

EID: 70349206306     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-009-9481-4     Document Type: Article
Times cited : (15)

References (49)
  • 1
    • 49249151462 scopus 로고
    • Nonlinear vibrations of simply supported beams
    • 10.1016/0362-546X(79)90032-4
    • T. Küpper A. Molitor 1977 Nonlinear vibrations of simply supported beams Nonlinear Anal. Theory Methods Appl. 3 1 45 48 10.1016/0362-546X(79)90032- 4
    • (1977) Nonlinear Anal. Theory Methods Appl. , vol.3 , Issue.1 , pp. 45-48
    • Küpper, T.1    Molitor, A.2
  • 2
    • 0001149152 scopus 로고
    • Nonlinear vibration of a beam
    • 0698.35040 10.1016/0362-546X(89)90002-3
    • J.Q. Liu 1989 Nonlinear vibration of a beam Nonlinear Anal. Theory Methods Appl. 13 10 1139 1148 0698.35040 10.1016/0362-546X(89)90002-3
    • (1989) Nonlinear Anal. Theory Methods Appl. , vol.13 , Issue.10 , pp. 1139-1148
    • Liu, J.Q.1
  • 3
    • 0018005153 scopus 로고
    • LARGE AMPLITUDE VIBRATION OF HINGED BEAMS.
    • DOI 10.1016/0045-7949(78)90141-4
    • G. Prathap T.K. Varadan 1978 The large amplitude vibration of hinged beams Comput. Struct. l9 219 222 10.1016/0045-7949(78)90141-4 (Pubitemid 8632918)
    • (1978) Computers and Structures , vol.9 , Issue.2 , pp. 219-222
    • Prathap, G.1    Varadan, T.K.2
  • 4
    • 0018263185 scopus 로고
    • LARGE AMPLITUDE VIBRATION OF TAPERED CLAMPED BEAMS.
    • G. Prathap T.K. Varadan 1978 The large amplitude vibration of tapered clamped beams J. Sound Vib. 58 1 87 94 0371.70006 10.1016/S0022-460X(78)80062-5 (Pubitemid 8613793)
    • (1978) Journal of Sound and Vibration , vol.58 , Issue.1 , pp. 87-94
    • Prathap, G.1    Varadan, T.K.2
  • 5
    • 3743073304 scopus 로고
    • Nonlinear free vibration of beams with clamped ends and with one end clamped, other end simply supported
    • K. Sato 1968 Nonlinear free vibration of beams with clamped ends and with one end clamped, other end simply supported Bull. J. Soc. Mech. Eng. 11 1027 1036
    • (1968) Bull. J. Soc. Mech. Eng. , vol.11 , pp. 1027-1036
    • Sato, K.1
  • 6
    • 0015340627 scopus 로고
    • Nonlinear free vibrations of elastic structures
    • 0286.73049 10.1016/0020-7683(73)90071-1 341983
    • L.W. Rehfield 1973 Nonlinear free vibrations of elastic structures Int. J. Solids Struct. 9 581 590 0286.73049 10.1016/0020-7683(73)90071-1 341983
    • (1973) Int. J. Solids Struct. , vol.9 , pp. 581-590
    • Rehfield, L.W.1
  • 7
    • 0015567290 scopus 로고
    • Finite element displacement method for large amplitude free flexural vibrations of beams and plates
    • 10.1016/0045-7949(73)90081-3
    • Ch. Mei 1973 Finite element displacement method for large amplitude free flexural vibrations of beams and plates Comput. Struct. 3 163 174 10.1016/0045-7949(73)90081-3
    • (1973) Comput. Struct. , vol.3 , pp. 163-174
    • Mei, Ch.1
  • 8
    • 0019064775 scopus 로고
    • GALERKIN FINITE ELEMENT METHOD FOR NON-LINEAR BEAM VIBRATIONS.
    • DOI 10.1016/0022-460X(80)90652-5
    • G.R. Bhashyam G. Prathap 1980 Galerkin finite element method for non-linear beam vibrations J. Sound Vib. 72 2 191 203 0444.73063 10.1016/0022-460X(80)90652-5 (Pubitemid 11470641)
    • (1980) Journal of Sound and Vibration , vol.72 , Issue.2 , pp. 191-203
    • Bhashyam, G.R.1    Prathap, G.2
  • 9
    • 0021424916 scopus 로고
    • A simple element for static and dynamic response of beams with material and geometric nonlinearities
    • 0528.73062 10.1002/nme.1620200506
    • T.Y. Yang S. Saigal 1984 A simple element for static and dynamic response of beams with material and geometric nonlinearities Int. J. Numer. Methods Eng. 20 851 867 0528.73062 10.1002/nme.1620200506
    • (1984) Int. J. Numer. Methods Eng. , vol.20 , pp. 851-867
    • Yang, T.Y.1    Saigal, S.2
  • 10
    • 0022445222 scopus 로고
    • DISCUSSION OF FINITE ELEMENT FORMULATIONS OF NONLINEAR BEAM VIBRATIONS.
    • DOI 10.1016/0045-7949(86)90087-8
    • Ch. Mei 1986 Discussion of finite element formulations of nonlinear beam vibrations Comput. Struct. 22 1 83 85 10.1016/0045-7949(86)90087-8 (Pubitemid 16518117)
    • (1986) Computers and Structures , vol.22 , Issue.1 , pp. 83-85
    • Chuh Mei1
  • 11
    • 0029273421 scopus 로고
    • Symplectic integration of an accurate beam finite element in non-linear vibration
    • 0871.73068 10.1016/0045-7949(94)00388-J
    • A.Y.T. Leung S.G. Mao 1995 Symplectic integration of an accurate beam finite element in non-linear vibration Comput. Struct. 54 1135 1147 0871.73068 10.1016/0045-7949(94)00388-J
    • (1995) Comput. Struct. , vol.54 , pp. 1135-1147
    • Leung, A.Y.T.1    Mao, S.G.2
  • 12
    • 0030150389 scopus 로고    scopus 로고
    • Dynamic finite element analysis of a nonlinear beam subjected to a moving load
    • DOI 10.1016/0020-7683(95)00128-X
    • T.P. Chang Y.-N. Liu 1996 Dynamic finite element analysis of a nonlinear beam subjected to a moving load Int. J. Solids Struct. 33 12 1673 1688 0928.74089 10.1016/0020-7683(95)00128-X (Pubitemid 126395820)
    • (1996) International Journal of Solids and Structures , vol.33 , Issue.12 , pp. 1673-1688
    • Chang, T.-P.1    Liu, Y.-N.2
  • 13
    • 34447506006 scopus 로고    scopus 로고
    • Dynamic analysis of very flexible beams
    • DOI 10.1016/j.jsv.2007.01.032, PII S0022460X07001095
    • R. Fotouhi 2007 Dynamic analysis of very flexible beams J. Sound Vib. 305 521 533 10.1016/j.jsv.2007.01.032 (Pubitemid 47069434)
    • (2007) Journal of Sound and Vibration , vol.305 , Issue.3 , pp. 521-533
    • Fotouhi, R.1
  • 14
    • 1442265955 scopus 로고    scopus 로고
    • Non-linear dynamic analysis of beams with variable stiffness
    • 10.1016/S0022-460X(03)00635-7
    • J.T. Katsikadelis G.C. Tsiatas 2004 Non-linear dynamic analysis of beams with variable stiffness J. Sound Vib. 270 847 863 10.1016/S0022-460X(03)00635-7
    • (2004) J. Sound Vib. , vol.270 , pp. 847-863
    • Katsikadelis, J.T.1    Tsiatas, G.C.2
  • 15
    • 34247175856 scopus 로고    scopus 로고
    • Non-linear dynamic stability of damped Beck's column with variable cross-section
    • DOI 10.1016/j.ijnonlinmec.2006.10.019, PII S0020746207000327
    • J.T. Katsikadelis G.C. Tsiatas 2007 Non-linear dynamic stability of damped Beck's column with variable cross section Int. J. Non-Linear Mech. 42 164 171 10.1016/j.ijnonlinmec.2006.10.019 (Pubitemid 46589479)
    • (2007) International Journal of Non-Linear Mechanics , vol.42 , Issue.1 , pp. 164-171
    • Katsikadelis, J.T.1    Tsiatas, G.C.2
  • 16
    • 39549103848 scopus 로고    scopus 로고
    • Discussion of "On the comparison of Timoshenko and shear models in beam dynamics" by Noé Challamel
    • DOI 10.1061/(ASCE)0733-9399(2008)134:3(269)
    • J.D. Aristizabal-Ochoa 2008 On the comparison of Timoshenko and shear models in beam dynamics ASCE J. Eng. Mech. 134 3 269 270 10.1061/(ASCE)0733- 9399(2008)134:3(269) (Pubitemid 351279666)
    • (2008) Journal of Engineering Mechanics , vol.134 , Issue.3 , pp. 269-270
    • Aristizabal-Ochoa, J.D.1
  • 17
    • 60449088269 scopus 로고    scopus 로고
    • Shear deformation effect in flexural-torsional vibrations of beams by BEM
    • 05555418 10.1007/s00707-008-0041-7
    • E.J. Sapountzakis J.A. Dourakopoulos 2009 Shear deformation effect in flexural-torsional vibrations of beams by BEM Acta Mech. 203 197 221 05555418 10.1007/s00707-008-0041-7
    • (2009) Acta Mech. , vol.203 , pp. 197-221
    • Sapountzakis, E.J.1    Dourakopoulos, J.A.2
  • 18
    • 8644248874 scopus 로고    scopus 로고
    • Timoshenko beam-column with generalized end conditions and nonclassical modes of vibration of shear beams
    • 10.1061/(ASCE)0733-9399(2004)130:10(1151)
    • J.D. Aristizabal-Ochoa 2004 Timoshenko beam-column with generalized end conditions and nonclassical modes of vibration of shear beams ASCE J. Eng. Mech. 130 10 1151 1159 10.1061/(ASCE)0733-9399(2004)130:10(1151)
    • (2004) ASCE J. Eng. Mech. , vol.130 , Issue.10 , pp. 1151-1159
    • Aristizabal-Ochoa, J.D.1
  • 19
    • 34548219959 scopus 로고    scopus 로고
    • Stability and natural frequencies of a weakened Timoshenko beam-column with generalized end conditions under constant axial load
    • DOI 10.1016/j.jsv.2007.06.059, PII S0022460X07004968
    • L.G. Arboleda-Monsalve D.G. Zapata-Medina J.D. Aristizabal-Ochoa 2007 Stability and natural frequencies of a weakened Timoshenko beam-column with generalized end conditions under constant axial load J. Sound Vib. 307 1-2 89 112 10.1016/j.jsv.2007.06.059 (Pubitemid 47332500)
    • (2007) Journal of Sound and Vibration , vol.307 , Issue.1-2 , pp. 89-112
    • Arboleda-Monsalve, L.G.1    Zapata-Medina, D.G.2    Aristizabal-Ochoa, J.D.3
  • 20
    • 34548244026 scopus 로고    scopus 로고
    • Static and dynamic stability of uniform shear beam-columns under generalized boundary conditions
    • DOI 10.1016/j.jsv.2007.06.049, PII S0022460X07004919
    • J.D. Aristizabal-Ochoa 2007 Static and dynamic stability of uniform shear beam-columns under generalized boundary conditions J. Sound Vib. 307 1-2 69 88 10.1016/j.jsv.2007.06.049 (Pubitemid 47332498)
    • (2007) Journal of Sound and Vibration , vol.307 , Issue.1-2 , pp. 69-88
    • Aristizabal-Ochoa, J.D.1
  • 21
    • 37849023859 scopus 로고    scopus 로고
    • Timoshenko beam-column with generalized end conditions on elastic foundation: Dynamic-stiffness matrix and load vector
    • 10.1016/j.jsv.2007.08.014
    • L.G. Arboleda-Monsalve D.G. Zapata-Medina J.D. Aristizabal-Ochoa 2008 Timoshenko beam-column with generalized end conditions on elastic foundation: dynamic-stiffness matrix and load vector J. Sound Vib. 310 1057 1079 10.1016/j.jsv.2007.08.014
    • (2008) J. Sound Vib. , vol.310 , pp. 1057-1079
    • Arboleda-Monsalve, L.G.1    Zapata-Medina, D.G.2    Aristizabal-Ochoa, J.D.3
  • 22
    • 40649106710 scopus 로고    scopus 로고
    • Static and dynamic stability of an elastically restrained Beck column with an attached end mass
    • J.A. Hernández-Urrea J.D. Aristizábal-Ochoa 2008 Static and dynamic stability of an elastically restrained Beck column with an attached end mass J. Sound Vib. 312 4-5 789 800
    • (2008) J. Sound Vib. , vol.312 , Issue.45 , pp. 789-800
    • Hernández-Urrea, J.A.1    Aristizábal-Ochoa, J.D.2
  • 23
    • 0016950345 scopus 로고
    • Nonlinear vibrations of beams considering shear deformation and rotary inertia
    • 0343.73034 10.2514/3.7138
    • G.V. Rao I.S. Raju K. Kanaka Raju 1976 Nonlinear vibrations of beams considering shear deformation and rotary inertia AIAA J. 14 5 685 687 0343.73034 10.2514/3.7138
    • (1976) AIAA J. , vol.14 , Issue.5 , pp. 685-687
    • Rao, G.V.1    Raju, I.S.2    Kanaka Raju, K.3
  • 24
    • 0032668472 scopus 로고    scopus 로고
    • Influence of shear deformation and rotary inertia on nonlinear free vibration of a beam with pinned ends
    • 10.1016/S0045-7949(98)00299-5
    • M.A. Foda 1999 Influence of shear deformation and rotary inertia on nonlinear free vibration of a beam with pinned ends Comput. Struct. 71 663 670 10.1016/S0045-7949(98)00299-5
    • (1999) Comput. Struct. , vol.71 , pp. 663-670
    • Foda, M.A.1
  • 25
    • 0041344361 scopus 로고    scopus 로고
    • Nonlinear vibration analysis of Timoshenko beams using the differential quadrature method
    • 1062.74063 10.1023/A:1024463711325
    • H. Zhong Q. Guo 2003 Nonlinear vibration analysis of Timoshenko beams using the differential quadrature method Nonlinear Dyn. 32 223 234 1062.74063 10.1023/A:1024463711325
    • (2003) Nonlinear Dyn. , vol.32 , pp. 223-234
    • Zhong, H.1    Guo, Q.2
  • 26
    • 3042709768 scopus 로고    scopus 로고
    • Nonlinear vibrations of Timoshenko beams with various boundary conditions
    • Q. Guo X. Liu H. Zhong 2004 Nonlinear vibrations of Timoshenko beams with various boundary conditions Tsinghua Sci. Technol. 9 2 125 129
    • (2004) Tsinghua Sci. Technol. , vol.9 , Issue.2 , pp. 125-129
    • Guo, Q.1    Liu, X.2    Zhong, H.3
  • 27
    • 36049012365 scopus 로고    scopus 로고
    • Higher-order nonlinear vibration analysis of Timoshenko beams by the spline-based differential quadrature method
    • H. Zhong M. Liao 2007 Higher-order nonlinear vibration analysis of Timoshenko beams by the spline-based differential quadrature method Shock Vib. 14 407 416
    • (2007) Shock Vib. , vol.14 , pp. 407-416
    • Zhong, H.1    Liao, M.2
  • 28
    • 38649091985 scopus 로고    scopus 로고
    • Nonlinear vibration analysis of tapered Timoshenko beams
    • DOI 10.1016/j.chaos.2006.07.055, PII S0960077906007880
    • M. Liao H. Zhong 2008 Nonlinear vibration analysis of tapered Timoshenko beams Chaos Solitons Fractals 36 1267 1272 1135.74021 10.1016/j.chaos.2006.07. 055 (Pubitemid 351172775)
    • (2008) Chaos, Solitons and Fractals , vol.36 , Issue.5 , pp. 1267-1272
    • Liao, M.1    Zhong, H.2
  • 29
    • 0024131352 scopus 로고
    • Large amplitude vibration of a beam based on a higher-order deformation theory
    • 10.1016/0003-682X(88)90062-X
    • J.L. Doong C.S. Chen 1988 Large amplitude vibration of a beam based on a higher-order deformation theory Appl. Acoustics 25 281 293 10.1016/0003-682X(88) 90062-X
    • (1988) Appl. Acoustics , vol.25 , pp. 281-293
    • Doong, J.L.1    Chen, C.S.2
  • 30
    • 0028501048 scopus 로고
    • Nonlinear finite element modelling of a high speed rotating Timoshenko beam structure
    • 0810.73062 10.1016/0020-7403(94)90013-2
    • S.H.Y. Lai 1994 Nonlinear finite element modelling of a high speed rotating Timoshenko beam structure Int. J. Mech. Sci. 36 9 849 861 0810.73062 10.1016/0020-7403(94)90013-2
    • (1994) Int. J. Mech. Sci. , vol.36 , Issue.9 , pp. 849-861
    • Lai, S.H.Y.1
  • 31
    • 0029634501 scopus 로고
    • Nonlinear dynamics analysis of flexible beams under large overall motions and the flexible manipulator simulation
    • 0900.73351 10.1016/0045-7949(94)00542-B
    • J.L. Meek H. Liu 1995 Nonlinear dynamics analysis of flexible beams under large overall motions and the flexible manipulator simulation Comput. Struct. 56 1 1 14 0900.73351 10.1016/0045-7949(94)00542-B
    • (1995) Comput. Struct. , vol.56 , Issue.1 , pp. 1-14
    • Meek, J.L.1    Liu, H.2
  • 32
    • 0032207747 scopus 로고    scopus 로고
    • Non-linear vibration of Timoshenko beam due to a moving force and the weight of beam
    • 10.1006/jsvi.1998.1827
    • R.T. Wang T.H. Chou 1998 Non-linear vibration of Timoshenko beam due to a moving force and the weight of beam J. Sound Vib. 218 1 117 131 10.1006/jsvi.1998.1827
    • (1998) J. Sound Vib. , vol.218 , Issue.1 , pp. 117-131
    • Wang, R.T.1    Chou, T.H.2
  • 33
    • 34948869264 scopus 로고    scopus 로고
    • Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams
    • DOI 10.1007/s11044-007-9077-z, Commemorating the 10th Anniversary
    • L.G. Maqueda A.A. Shabana 2007 Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams J. Multibody Syst. Dyn. 18 3 375 396 05207048 10.1007/s11044-007-9077-z 2430591 (Pubitemid 47519601)
    • (2007) Multibody System Dynamics , vol.18 , Issue.3 , pp. 375-396
    • Maqueda, L.G.1    Shabana, A.A.2
  • 34
    • 32844472948 scopus 로고    scopus 로고
    • The analog equation method. A boundary-only integral equation method for nonlinear static and dynamic problems in general bodies
    • 1051.74052 2015530
    • J.T. Katsikadelis 2002 The analog equation method. A boundary-only integral equation method for nonlinear static and dynamic problems in general bodies Theor. Appl. Mech. 27 13 38 1051.74052 2015530
    • (2002) Theor. Appl. Mech. , vol.27 , pp. 13-38
    • Katsikadelis, J.T.1
  • 35
    • 4544383266 scopus 로고    scopus 로고
    • Studies of Newmark method for solving nonlinear systems: (I) basic analysis
    • S.Y. Chang 2004 Studies of Newmark method for solving nonlinear systems: (I) basic analysis J. Chin. Inst. Eng. 27 5 651 662
    • (2004) J. Chin. Inst. Eng. , vol.27 , Issue.5 , pp. 651-662
    • Chang, S.Y.1
  • 37
    • 5844330633 scopus 로고
    • A model for plane elastica with simple shear deformation pattern
    • 0810.73021 10.1007/BF01170067 1274741
    • T.M. Atanackovic D.T. Spasic 1994 A model for plane elastica with simple shear deformation pattern Acta Mech. 104 241 253 0810.73021 10.1007/BF01170067 1274741
    • (1994) Acta Mech. , vol.104 , pp. 241-253
    • Atanackovic, T.M.1    Spasic, D.T.2
  • 38
    • 0346723156 scopus 로고    scopus 로고
    • Tension buckling in multilayer elastomeric bearings
    • DOI 10.1061/(ASCE)0733-9399(2003)129:12(1363)
    • J.D. Aristizábal-Ochoa 2003 Tension buckling in multilayer elastomeric bearings by James M. Kelly ASCE J. Eng. Mech. 129 12 1363 1368 10.1061/(ASCE)0733-9399(2003)129:12(1363) Discussion: 131(1), 106-108 (2005) (Pubitemid 37554413)
    • (2003) Journal of Engineering Mechanics , vol.129 , Issue.12 , pp. 1363-1368
    • Kelly, J.M.1
  • 40
    • 0007653595 scopus 로고
    • The shear coefficient in Timoshenko's beam theory
    • 0151.37901
    • G.R. Cowper 1966 The shear coefficient in Timoshenko's beam theory ASME J. Appl. Mech. 33 2 335 340 0151.37901
    • (1966) ASME J. Appl. Mech. , vol.33 , Issue.2 , pp. 335-340
    • Cowper, G.R.1
  • 41
    • 0028424735 scopus 로고
    • On the shear deformation coefficient in beam theory
    • 0804.73024 10.1016/0168-874X(94)00008-5
    • U. Schramm L. Kitis W. Kang W.D. Pilkey 1994 On the shear deformation coefficient in beam theory Finite Elem. Anal. Des. 16 141 162 0804.73024 10.1016/0168-874X(94)00008-5
    • (1994) Finite Elem. Anal. Des. , vol.16 , pp. 141-162
    • Schramm, U.1    Kitis, L.2    Kang, W.3    Pilkey, W.D.4
  • 42
    • 0030871488 scopus 로고    scopus 로고
    • Beam stiffness matrix based on the elasticity equations
    • 10.1002/(SICI)1097-0207(19970130)40:2<211::AID-NME58>3.0.CO;2-P
    • U. Schramm V. Rubenchik W.D. Pilkey 1997 Beam stiffness matrix based on the elasticity equations Int. J. Numer. Methods Eng. 40 211 232 10.1002/(SICI)1097-0207(19970130)40:2<211::AID-NME58>3.0.CO;2-P
    • (1997) Int. J. Numer. Methods Eng. , vol.40 , pp. 211-232
    • Schramm, U.1    Rubenchik, V.2    Pilkey, W.D.3
  • 43
    • 0018990354 scopus 로고
    • Timoshenko's shear coefficient from a beam subjected to gravity loading
    • 0436.73057
    • N.G. Stephen 1980 Timoshenko's shear coefficient from a beam subjected to gravity loading ASME J. Appl. Mech. 47 121 127 0436.73057
    • (1980) ASME J. Appl. Mech. , vol.47 , pp. 121-127
    • Stephen, N.G.1
  • 44
    • 0000048562 scopus 로고    scopus 로고
    • Shear coefficients for Timoshenko beam theory
    • 1110.74489
    • J.R. Hutchinson 2001 Shear coefficients for Timoshenko beam theory ASME J. Appl. Mech. 68 87 92 1110.74489
    • (2001) ASME J. Appl. Mech. , vol.68 , pp. 87-92
    • Hutchinson, J.R.1
  • 45
    • 36749011273 scopus 로고
    • Stabtragwerke, der Ingenieurbau
    • G. Mehlhorn (eds). Ernst & Sohn Berlin
    • Ramm, E., Hofmann, T.J.: Stabtragwerke, Der Ingenieurbau. In: Mehlhorn, G. (ed.) Band Baustatik/Baudynamik. Ernst & Sohn, Berlin (1995)
    • (1995) Band Baustatik/Baudynamik
    • Ramm, E.1    Hofmann, T.J.2
  • 47
    • 24144484721 scopus 로고    scopus 로고
    • A BEM solution to transverse shear loading of beams
    • DOI 10.1007/s00466-005-0677-2
    • E.J. Sapountzakis V.G. Mokos 2005 A BEM solution to transverse shear loading of beams Comput. Mech. 36 384 397 1138.74413 10.1007/s00466-005-0677-2 (Pubitemid 41241786)
    • (2005) Computational Mechanics , vol.36 , Issue.5 , pp. 384-397
    • Sapountzakis, E.J.1    Mokos, V.G.2
  • 49
    • 0034224184 scopus 로고    scopus 로고
    • Analysis of plates reinforced with beams
    • DOI 10.1007/s004660000156
    • E.J. Sapountzakis J.T. Katsikadelis 2000 Analysis of plates reinforced with beams Comput. Mech. 26 66 74 1050.74684 10.1007/s004660000156 (Pubitemid 30915691)
    • (2000) Computational Mechanics , vol.26 , Issue.1 , pp. 66-74
    • Sapountzakis, E.J.1    Katsikadelis, J.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.