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Volumn 105, Issue 1-2, 2011, Pages 117-136

On stability analyses of three classical buckling problems for the elastic strut

Author keywords

Buckling; Elastic stability; Elastica; Variational methods

Indexed keywords

ELASTIC STABILITY; ELASTIC STRUTS; ELASTICA; EXISTENCE OF SOLUTIONS; JACOBI'S NECESSARY CONDITION; LEGENDRE; RICCATI DIFFERENTIAL EQUATION; SECOND VARIATION; STABILITY ANALYSIS; STABLE CONFIGURATION; VARIATIONAL FORMULATION; VARIATIONAL METHODS;

EID: 80051692893     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-010-9299-9     Document Type: Article
Times cited : (26)

References (24)
  • 5
    • 55349148656 scopus 로고    scopus 로고
    • Modeling the growth and branching of plants: A simple rod-based model
    • doi:10.1016/j.jmps.2008.06.005
    • Faruk Senan, N.A., O'Reilly, O.M., Tresierras, T.N.: Modeling the growth and branching of plants: a simple rod-based model. J. Mech. Phys. Solids 56(10), 3021-3036 (2008). doi:10.1016/j.jmps.2008.06.005.
    • (2008) J. Mech. Phys. Solids , vol.56 , Issue.10 , pp. 3021-3036
    • Faruk Senan, N.A.1    O'Reilly, O.M.2    Tresierras, T.N.3
  • 7
    • 0014599259 scopus 로고
    • A new necessary condition of optimality for singular control problems
    • doi:10.1137/0307042
    • Jacobson, D.H.: A new necessary condition of optimality for singular control problems. SIAM J. Control 7, 578-595 (1969). doi:10.1137/0307042.
    • (1969) SIAM J. Control , vol.7 , pp. 578-595
    • Jacobson, D.H.1
  • 8
    • 38849118380 scopus 로고    scopus 로고
    • Sufficient conditions for stability of Euler elasticas
    • DOI 10.1016/j.mechrescom.2007.09.001, PII S0093641307000638
    • Jin, M., Bao, Z.B.: Sufficient conditions for stability of Euler elasticas. Mech. Res. Commun. 35(3), 193-200 (2008). doi:10.1016/j.mechrescom. 2007.09.001. (Pubitemid 351192007)
    • (2008) Mechanics Research Communications , vol.35 , Issue.3 , pp. 193-200
    • Jin, M.1    Bao, Z.B.2
  • 9
    • 0348115266 scopus 로고
    • Singular solutions in problems of optimal control
    • Johnson, C.D., Gibson, J.E.: Singular solutions in problems of optimal control. IEEE Trans. Autom. Control AC-8, 4-15 (1963).
    • (1963) IEEE Trans. Autom. Control , vol.AC-8 , pp. 4-15
    • Johnson, C.D.1    Gibson, J.E.2
  • 10
    • 0036722175 scopus 로고    scopus 로고
    • Complete solution of the stability problem for elastica of Euler's column
    • DOI 10.1016/S0020-7462(00)00114-1, PII S0020746200001141
    • Kuznetsov, V.V., Levyakov, S.V.: Complete solution of the stability problem for elastica of Euler's column. Int. J. Non-Linear Mech. 37(6), 1003-1009 (2002). doi:10.1016/S0020-7462(00)00114-1. (Pubitemid 34222682)
    • (2002) International Journal of Non-Linear Mechanics , vol.37 , Issue.6 , pp. 1003-1009
    • Kuznetsov, V.V.1    Levyakov, S.V.2
  • 12
    • 65549166348 scopus 로고    scopus 로고
    • Stability analysis of curvilinear configurations of an inextensible elastic rod with clamped ends
    • doi:10.1016/j.mechrescom.2009.01.005
    • Levyakov, S.V.: Stability analysis of curvilinear configurations of an inextensible elastic rod with clamped ends. Mech. Res. Commun. 36(5), 612-617 (2009). doi:10.1016/j.mechrescom.2009.01.005.
    • (2009) Mech. Res. Commun. , vol.36 , Issue.5 , pp. 612-617
    • Levyakov, S.V.1
  • 13
    • 77949491462 scopus 로고    scopus 로고
    • Stability analysis of planar equilibrium configurations of elastic rods subjected to end loads
    • doi:10.1007/s00707-009-0213-0
    • Levyakov, S.V., Kuznetsov, V.V.: Stability analysis of planar equilibrium configurations of elastic rods subjected to end loads. Acta Mech. 211(1-2), 73-87 (2010). doi:10.1007/s00707-009-0213-0.
    • (2010) Acta Mech. , vol.211 , Issue.1-2 , pp. 73-87
    • Levyakov, S.V.1    Kuznetsov, V.V.2
  • 15
    • 0021317182 scopus 로고
    • Stability of nonlinearly elastic rods
    • doi:10.1007/BF00275737
    • Maddocks, J.H.: Stability of nonlinearly elastic rods. Arch. Ration. Mech. Anal. 85(4), 311-354 (1984). doi:10.1007/BF00275737.
    • (1984) Arch. Ration. Mech. Anal. , vol.85 , Issue.4 , pp. 311-354
    • Maddocks, J.H.1
  • 16
    • 59749101465 scopus 로고    scopus 로고
    • Conjugate points revisited and Neumann-Neumann problems
    • doi:10.1137/060668547
    • Manning, R.S.: Conjugate points revisited and Neumann-Neumann problems. SIAM Rev. 51(1), 193- 212 (2009). doi:10.1137/060668547.
    • (2009) SIAM Rev. , vol.51 , Issue.1 , pp. 193-212
    • Manning, R.S.1
  • 18
    • 0014837410 scopus 로고
    • New Jacobi-type necessary and sufficient conditions for singular optimization problems
    • doi:10.2514/3.5917
    • McDanell, J.P., Powers, W.F.: New Jacobi-type necessary and sufficient conditions for singular optimization problems. AIAA J. 8, 1416-1420 (1970). doi:10.2514/3.5917.
    • (1970) AIAA J. , vol.8 , pp. 1416-1420
    • McDanell, J.P.1    Powers, W.F.2
  • 19
    • 78651228781 scopus 로고    scopus 로고
    • On the static equilibria of branched elastic rods
    • doi:10.1016/j.ijengsci.2010.11.008
    • O'Reilly, O.M., Tresierras, T.N.: On the static equilibria of branched elastic rods. Int. J. Eng. Sci. 49(2), 212-227 (2011). doi:10.1016/j.ijengsci. 2010.11.008.
    • (2011) Int. J. Eng. Sci. , vol.49 , Issue.2 , pp. 212-227
    • O'Reilly, O.M.1    Tresierras, T.N.2
  • 21
    • 34250894634 scopus 로고    scopus 로고
    • Conjugate journey in optimal control
    • Rosenblueth, J.F.: Conjugate journey in optimal control. Int. Math. Forum 2(13-16), 633-674 (2007). http://www.m-hikari.com/imf-password2007/13-16-2007/ index.html.
    • (2007) Int. Math. Forum , vol.2 , Issue.13-16 , pp. 633-674
    • Rosenblueth, J.F.1
  • 22
    • 65449129132 scopus 로고    scopus 로고
    • Optimality of Euler elasticae
    • doi:10.1134/S106456240706004X
    • Sachkov, Y.L.: Optimality of Euler elasticae. Dokl. Akad. Nauk 417(1), 23-25 (2007). doi:10.1134/S106456240706004X.
    • (2007) Dokl. Akad. Nauk , vol.417 , Issue.1 , pp. 23-25
    • Sachkov, Y.L.1
  • 23
    • 47649111879 scopus 로고    scopus 로고
    • Conjugate points in the Euler elastic problem
    • doi:10.1007/s10883-008-9044-x
    • Sachkov, Y.L.: Conjugate points in the Euler elastic problem. J. Dyn. Control Syst. 14(3), 409-439 (2008). doi:10.1007/s10883-008-9044-x.
    • (2008) J. Dyn. Control Syst. , vol.14 , Issue.3 , pp. 409-439
    • Sachkov, Y.L.1
  • 24
    • 0000423999 scopus 로고
    • Sufficient conditions for variational problems with variable endpoints: Coupled points
    • doi:10.1007/BF01195982
    • Zeidan, V.: Sufficient conditions for variational problems with variable endpoints: Coupled points. Appl. Math. Optim. 27(2), 191-209 (1993). doi:10.1007/BF01195982.
    • (1993) Appl. Math. Optim. , vol.27 , Issue.2 , pp. 191-209
    • Zeidan, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.