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Volumn 9, Issue 2, 2014, Pages 195-226

Solutions of the von kármán plate equations by a galerkin method, without inverting the tangent stiffness matrix

Author keywords

Buckling behavior; Global galerkin method; Initial imperfection; Nonlinear algebraic equations; Scalar homotopy methods; Von k rm n plate equations

Indexed keywords

FINITE ELEMENT METHOD; GALERKIN METHODS; JACOBIAN MATRICES; MATHEMATICAL TRANSFORMATIONS; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; STIFFNESS MATRIX;

EID: 84902279821     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2014.9.195     Document Type: Article
Times cited : (16)

References (38)
  • 1
    • 0041315110 scopus 로고    scopus 로고
    • Methods of computer modeling in engineering and the sciences, I: A unified treatment of finite volume, finite element, field-boundary element, meshless, and boundary methods
    • Atluri 2005, Tech Science Press, Forsyth, GA
    • [Atluri 2005] S. N. Atluri, Methods of computer modeling in engineering and the sciences, I: A unified treatment of finite volume, finite element, field-boundary element, meshless, and boundary methods, Tech Science Press, Forsyth, GA, 2005.
    • (2005)
    • Atluri, S.N.1
  • 2
    • 70350164756 scopus 로고    scopus 로고
    • A modified Newton method for solving non-linear algebraic equations
    • Atluri et al. 2009
    • [Atluri et al. 2009] S. N. Atluri, C.-S. Liu, and C.-L. Kuo, "A modified Newton method for solving non-linear algebraic equations", J. Marine Sci. and Tech. 17:3 (2009), 238-247.
    • (2009) J. Marine Sci. and Tech , vol.17 , Issue.3 , pp. 238-247
    • Atluri, S.N.1    Liu, C.-S.2    Kuo, C.-L.3
  • 3
    • 0000894509 scopus 로고
    • Large deflection analysis of plates and shallow shells using the finite element method
    • Bergan and Clough 1973, Int. J. Numer. Methods Engin
    • [Bergan and Clough 1973] P. G. Bergan and R. W. Clough, "Large deflection analysis of plates and shallow shells using the finite element method", Int. J. Numer. Methods Engin. 5 (1973), 543-556.
    • (1973) , vol.5 , pp. 543-556
    • Bergan, P.G.1    Clough, R.W.2
  • 4
    • 0000150756 scopus 로고
    • Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature
    • Bert et al. 1989
    • [Bert et al. 1989] C. W. Bert, S. K. Jang, and A. G. Striz, "Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature", Comput. Mech. 5:2-3 (1989), 217-226.
    • (1989) Comput. Mech , vol.5 , Issue.2-3 , pp. 217-226
    • Bert, C.W.1    Jang, S.K.2    Striz, A.G.3
  • 5
    • 0012725082 scopus 로고
    • Geometrically nonlinear finite-element analysis
    • Brebbia and Connor 1969
    • [Brebbia and Connor 1969] C. Brebbia and J. Connor, "Geometrically nonlinear finite-element analysis", J. Engng. Mech. Div. ASCE/95 (1969), 463-483.
    • (1969) J. Engng. Mech. Div. ASCE/ , vol.95 , pp. 463-483
    • Brebbia, C.1    Connor, J.2
  • 6
    • 0014520697 scopus 로고
    • Large deflections of rectangular plates subjected to uniform lateral pressure and compressive edge loading
    • Brown and Harvey 1969
    • [Brown and Harvey 1969] J. C. Brown and J. M. Harvey, "Large deflections of rectangular plates subjected to uniform lateral pressure and compressive edge loading", J. Mech. Engin. Sci. 11:3 (1969), 305-317.
    • (1969) J. Mech. Engin. Sci , vol.11 , Issue.3 , pp. 305-317
    • Brown, J.C.1    Harvey, J.M.2
  • 7
    • 0004100063 scopus 로고
    • Nonlinear analysis of plates
    • Chia 1980, McGraw-Hill, New York, NY
    • [Chia 1980] C. Y. Chia, Nonlinear analysis of plates, McGraw-Hill, New York, NY, 1980.
    • (1980)
    • Chia, C.Y.1
  • 8
    • 79961072474 scopus 로고    scopus 로고
    • The global nonlinear Galerkin method for the analysis of elastic large deflections of plates under combined loads: a scalar homotopy method for the direct solution of nonlinear algebraic equations
    • Dai et al. 2011a
    • [Dai et al. 2011a] H. H. Dai, J. K. Paik, and S. N. Atluri, "The global nonlinear Galerkin method for the analysis of elastic large deflections of plates under combined loads: a scalar homotopy method for the direct solution of nonlinear algebraic equations", Comput. Mater. Continua 23:1 (2011), 69-99.
    • (2011) Comput. Mater. Continua , vol.23 , Issue.1 , pp. 69-99
    • Dai, H.H.1    Paik, J.K.2    Atluri, S.N.3
  • 9
    • 80051704276 scopus 로고    scopus 로고
    • The global nonlinear Galerkin method for the solution of von Karman nonlinear plate equations: an optimal and faster iterative method for the direct solution of nonlinear algebraic equations F.(x)= 0, using x=λ[αF C.1-α/BT F]
    • Dai et al. 2011b
    • [Dai et al. 2011b] H. H. Dai, J. K. Paik, and S. N. Atluri, "The global nonlinear Galerkin method for the solution of von Karman nonlinear plate equations: an optimal and faster iterative method for the direct solution of nonlinear algebraic equations F.(x)= 0, using x=λ[αF C.1-α/BT F]", Comput. Mater. Continua 23:2 (2011), 155-185.
    • (2011) Comput. Mater. Continua , vol.23 , Issue.2 , pp. 155-185
    • Dai, H.H.1    Paik, J.K.2    Atluri, S.N.3
  • 10
    • 84898772761 scopus 로고    scopus 로고
    • A time domain collocation method for studying the aeroelasticity of a two dimensional airfoil with a structural nonlinearity
    • Dai et al. 2014a
    • [Dai et al. 2014a] H. H. Dai, X. K. Yue, J. P. Yuan, and S. N. Atluri, "A time domain collocation method for studying the aeroelasticity of a two dimensional airfoil with a structural nonlinearity", J. Comput. Phys. 270 (2014), 214-237.
    • (2014) J. Comput. Phys , vol.270 , pp. 214-237
    • Dai, H.H.1    Yue, X.K.2    Yuan, J.P.3    Atluri, S.N.4
  • 11
    • 84902249072 scopus 로고    scopus 로고
    • A fast harmonic balance technique for periodic oscillations of an aeroelastic airfoil
    • Dai et al. 2014b, Submitted for publication in J. Fluids Struct
    • [Dai et al. 2014b] H. H. Dai, X. K. Yue, J. P. Yuan, and D. Xie, "A fast harmonic balance technique for periodic oscillations of an aeroelastic airfoil", 2014. Submitted for publication in J. Fluids Struct.
    • (2014)
    • Dai, H.H.1    Yue, X.K.2    Yuan, J.P.3    Xie, D.4
  • 12
    • 84980134538 scopus 로고
    • On algorithms for solving f(x)= 0
    • Hirsch and Smale 1979
    • [Hirsch and Smale 1979] M. W. Hirsch and S. Smale, "On algorithms for solving f(x)= 0 ", Comm. Pure Appl. Math. 32:3 (1979), 281-313.
    • (1979) Comm. Pure Appl. Math , vol.32 , Issue.3 , pp. 281-313
    • Hirsch, M.W.1    Smale, S.2
  • 13
    • 0004215766 scopus 로고
    • Dynamics, theory and applications
    • Kane and Levinson 1985, McGraw-Hill, New York, NY
    • [Kane and Levinson 1985] T. R. Kane and D. A. Levinson, Dynamics, theory and applications, McGraw-Hill, New York, NY, 1985.
    • (1985)
    • Kane, T.R.1    Levinson, D.A.2
  • 14
    • 84872289021 scopus 로고    scopus 로고
    • Dynamical Newton-like methods with adaptive stepsize for solving nonlinear algebraic equations
    • Ku and Yeih 2012
    • [Ku and Yeih 2012] C.-Y. Ku and W. Yeih, "Dynamical Newton-like methods with adaptive stepsize for solving nonlinear algebraic equations", Comput. Mater. Continua 31:3 (2012), 173-200.
    • (2012) Comput. Mater. Continua , vol.31 , Issue.3 , pp. 173-200
    • Ku, C.-Y.1    Yeih, W.2
  • 15
    • 76249127210 scopus 로고    scopus 로고
    • Applications of the fictitious time integration method using a new time-like function
    • Ku et al. 2009
    • [Ku et al. 2009] C.-Y. Ku, W. Yeih, C.-S. Liu, and C.-C. Chi, "Applications of the fictitious time integration method using a new time-like function", CMES Comput. Model. Eng. Sci. 43:2 (2009), 173-190.
    • (2009) CMES Comput. Model. Eng. Sci , vol.43 , Issue.2 , pp. 173-190
    • Ku, C.-Y.1    Yeih, W.2    Liu, C.-S.3    Chi, C.-C.4
  • 16
    • 80955172297 scopus 로고    scopus 로고
    • Dynamical Newton-like methods for solving ill-conditioned systems of nonlinear equations with applications to boundary value problems
    • Ku et al. 2011
    • [Ku et al. 2011] C.-Y. Ku, W. Yeih, and C.-S. Liu, "Dynamical Newton-like methods for solving ill-conditioned systems of nonlinear equations with applications to boundary value problems", CMES Comput. Model. Eng. Sci. 76:2 (2011), 83-108.
    • (2011) CMES Comput. Model. Eng. Sci , vol.76 , Issue.2 , pp. 83-108
    • Ku, C.-Y.1    Yeih, W.2    Liu, C.-S.3
  • 17
    • 0011396689 scopus 로고
    • Bending of rectangular plates with large deflections
    • Levy 1942a, technical report 737, National Advisory Committee for Aeronautics
    • [Levy 1942a] S. Levy, "Bending of rectangular plates with large deflections", technical report 737, National Advisory Committee for Aeronautics, 1942, http://naca.central.cranfield.ac.uk/reports/1942/naca-report-737.pdf.
    • (1942)
    • Levy, S.1
  • 18
    • 0011396689 scopus 로고
    • Bending of rectangular plates with large deflections
    • Levy 1942b, technical note 846, National Advisory Committee for Aeronautics
    • [Levy 1942b] S. Levy, "Bending of rectangular plates with large deflections", technical note 846, National Advisory Committee for Aeronautics, 1942, http://www.dtic.mil/dtic/tr/fulltext/u2/a800848.pdf.
    • (1942)
    • Levy, S.1
  • 19
    • 0342807576 scopus 로고
    • Simply supported long rectangular plate under combined axial load and normal pressure
    • Levy et al. 1944, technical note 949, National Advisory Committee for Aeronautics
    • [Levy et al. 1944] S. Levy, D. Goldenberg, and G. Zibritosky, "Simply supported long rectangular plate under combined axial load and normal pressure", technical note 949, National Advisory Committee for Aeronautics, 1944, http://digital.library.unt.edu/ark:/67531/metadc59844/m1/1/.
    • (1944)
    • Levy, S.1    Goldenberg, D.2    Zibritosky, G.3
  • 20
    • 55349116390 scopus 로고    scopus 로고
    • A novel time integration method for solving a large system of non-linear algebraic equations
    • Liu and Atluri 2008
    • [Liu and Atluri 2008] C.-S. Liu and S. N. Atluri, "A novel time integration method for solving a large system of non-linear algebraic equations", CMES Comput. Model. Eng. Sci. 31:2 (2008), 71-83.
    • (2008) CMES Comput. Model. Eng. Sci , vol.31 , Issue.2 , pp. 71-83
    • Liu, C.-S.1    Atluri, S.N.2
  • 22
    • 79955519618 scopus 로고    scopus 로고
    • Simple 'residual-norm' based algorithms, for the solution of a large system of non-linear algebraic equations, which converge faster than the Newton's method
    • Liu and Atluri 2011b
    • [Liu and Atluri 2011b] C.-S. Liu and S. N. Atluri, "Simple 'residual-norm' based algorithms, for the solution of a large system of non-linear algebraic equations, which converge faster than the Newton's method", CMES Comput. Model. Eng. Sci. 71:3 (2011), 279-304.
    • (2011) CMES Comput. Model. Eng. Sci , vol.71 , Issue.3 , pp. 279-304
    • Liu, C.-S.1    Atluri, S.N.2
  • 23
    • 84862702621 scopus 로고    scopus 로고
    • c, for solving a system of nonlinear algebraic equations F(x) = 0
    • Liu and Atluri 2012
    • c, for solving a system of nonlinear algebraic equations F(x) = 0", CMES Comput. Model. Eng. Sci. 84:6 (2012), 575-602.
    • (2012) CMES Comput. Model. Eng. Sci , vol.84 , Issue.6 , pp. 575-602
    • Liu, C.-S.1    Atluri, S.N.2
  • 24
    • 77949806014 scopus 로고    scopus 로고
    • A scalar homotopy method for solving an over/underdetermined system of non-linear algebraic equations
    • Liu et al. 2009
    • [Liu et al. 2009] C.-S. Liu, W. Yeih, C.-L. Kuo, and S. N. Atluri, "A scalar homotopy method for solving an over/underdetermined system of non-linear algebraic equations", CMES Comput. Model. Eng. Sci. 53:1 (2009), 47-72.
    • (2009) CMES Comput. Model. Eng. Sci , vol.53 , Issue.1 , pp. 47-72
    • Liu, C.-S.1    Yeih, W.2    Kuo, C.-L.3    Atluri, S.N.4
  • 25
    • 84863230414 scopus 로고    scopus 로고
    • Iterative solution of a system of nonlinear algebraic equations F(x)=0, using x =λ[αR+βP]or x =λ[αF+βP]is a normal to a hyper-surface function of F, P normal to R, and P* normal to F
    • Liu et al. 2011a
    • [Liu et al. 2011a] C.-S. Liu, H.-H. Dai, and S. N. Atluri, "Iterative solution of a system of nonlinear algebraic equations F(x)=0, using x =λ[αR+βP]or x =λ[αF+βP]is a normal to a hyper-surface function of F, P normal to R, and P* normal to F", CMES Comput. Model. Eng. Sci. 81:3-4 (2011), 335-363.
    • (2011) CMES Comput. Model. Eng. Sci , vol.81 , Issue.3-4 , pp. 335-363
    • Liu, C.-S.1    Dai, H.-H.2    Atluri, S.N.3
  • 26
    • 84863229344 scopus 로고    scopus 로고
    • 2 in iteratively solving the nonlinear system of algebraic equations F(x) = 0
    • Liu et al. 2011b
    • 2 in iteratively solving the nonlinear system of algebraic equations F(x) = 0", CMES Comput. Model. Eng. Sci. 81:2 (2011), 195-228.
    • (2011) CMES Comput. Model. Eng. Sci , vol.81 , Issue.2 , pp. 195-228
    • Liu, C.-S.1    Dai, H.-H.2    Atluri, S.N.3
  • 27
    • 0023538397 scopus 로고
    • Field/boundary element approach to the large deflection of thin flat plates
    • O'Donoghue and Atluri 1987
    • [O'Donoghue and Atluri 1987] P. E. O'Donoghue and S. N. Atluri, "Field/boundary element approach to the large deflection of thin flat plates", Comput. Struct. 27:3 (1987), 427-435.
    • (1987) Comput. Struct , vol.27 , Issue.3 , pp. 427-435
    • O'Donoghue, P.E.1    Atluri, S.N.2
  • 28
    • 0004880883 scopus 로고
    • Compressive strength of long rectangular plates under hydrostatic pressure
    • Okada et al. 1979
    • [Okada et al. 1979] H. Okada, K. Oshima, and Y. Fukumoto, "Compressive strength of long rectangular plates under hydrostatic pressure", J. Soc. Naval Arch. Japan 146:1 (1979), 270-280.
    • (1979) J. Soc. Naval Arch. Japan , vol.146 , Issue.1 , pp. 270-280
    • Okada, H.1    Oshima, K.2    Fukumoto, Y.3
  • 29
    • 0034836205 scopus 로고    scopus 로고
    • Large deflection orthotropic plate approach to develop ultimate strength formulations for stiffened panels under combined biaxial compression/tension and lateral pressure
    • Paik et al. 2001
    • [Paik et al. 2001] J. K. Paik, A. K. Thayamballi, and B. Ju Kim, "Large deflection orthotropic plate approach to develop ultimate strength formulations for stiffened panels under combined biaxial compression/tension and lateral pressure", Thin- Walled Struct. 39:3 (2001), 215-246.
    • (2001) Thin- Walled Struct , vol.39 , Issue.3 , pp. 215-246
    • Paik, J.K.1    Thayamballi, A.K.2    Ju Kim, B.3
  • 30
    • 0004686120 scopus 로고
    • Large displacement analysis of plates by a stress-based finite element approach
    • Punch and Atluri 1986
    • [Punch and Atluri 1986] E. F. Punch and S. N. Atluri, "Large displacement analysis of plates by a stress-based finite element approach", Comput. Struct. 24:1 (1986), 107-117.
    • (1986) Comput. Struct , vol.24 , Issue.1 , pp. 107-117
    • Punch, E.F.1    Atluri, S.N.2
  • 31
    • 1642570232 scopus 로고    scopus 로고
    • Dynamical systems method for solving operator equations
    • Ramm 2004
    • [Ramm 2004] A. G. Ramm, "Dynamical systems method for solving operator equations", Commun. Nonlinear Sci. Numer. Simul. 9:4 (2004), 383-402.
    • (2004) Commun. Nonlinear Sci. Numer. Simul , vol.9 , Issue.4 , pp. 383-402
    • Ramm, A.G.1
  • 32
    • 0024897749 scopus 로고
    • Postbuckling behaviour of rectangular plates under combined loading
    • Shen 1989
    • [Shen 1989] H. S. Shen, "Postbuckling behaviour of rectangular plates under combined loading", Thin-walled Struct. 8:3 (1989), 203-216.
    • (1989) Thin-walled Struct , vol.8 , Issue.3 , pp. 203-216
    • Shen, H.S.1
  • 33
    • 0003513999 scopus 로고
    • Theory of elastic stability
    • Timoshenko 1961, 2nd ed., McGraw-Hill Book Co., New York
    • [Timoshenko 1961] S. P. Timoshenko, Theory of elastic stability, 2nd ed., McGraw-Hill Book Co., New York, 1961.
    • (1961)
    • Timoshenko, S.P.1
  • 34
    • 0022951027 scopus 로고
    • An incremental Galerkin method for plates and stiffened plates
    • Ueda et al. 1987, Comput. Struct
    • [Ueda et al. 1987] Y. Ueda, M. H. Rashed, and J. K. Paik, "An incremental Galerkin method for plates and stiffened plates", Comput. Struct. 27:1 (1987), 147-156.
    • (1987) , vol.27 , Issue.1 , pp. 147-156
    • Ueda, Y.1    Rashed, M.H.2    Paik, J.K.3
  • 35
    • 0001024464 scopus 로고
    • Festigkeitsprobleme im maschinenbau
    • Von Kármán 1910
    • [Von Kármán 1910] T. Von Kármán, "Festigkeitsprobleme im maschinenbau", Encykl. Math. Wiss. 4 (1910), 314-385.
    • (1910) Encykl. Math. Wiss , vol.4 , pp. 314-385
    • Von Kármán, T.1
  • 36
    • 0007458871 scopus 로고
    • Uniformly loaded, clamped, rectangular plates with large deflection
    • Way 1939, in Proceedings of the Fifth International Congress of Applied Mechanics (Cambridge, MA), Wiley, Cambridge, MA
    • [Way 1939] S. Way, "Uniformly loaded, clamped, rectangular plates with large deflection", pp. 123-128 in Proceedings of the Fifth International Congress of Applied Mechanics (Cambridge, MA), Wiley, Cambridge, MA, 1939.
    • (1939) , pp. 123-128
    • Way, S.1
  • 37
    • 25444474133 scopus 로고
    • Clamped long rectangular plate under combined axial load and normal pressure
    • Woolley et al. 1946, technical note 1047, National Advisory Committee for Aeronautics
    • [Woolley et al. 1946] R. M. Woolley, J. N. Correick, and S. Levy, "Clamped long rectangular plate under combined axial load and normal pressure", technical note 1047, National Advisory Committee for Aeronautics, 1946, http://www.dtic.mil/dtic/tr/fulltext/u2/a800975.pdf.
    • (1946)
    • Woolley, R.M.1    Correick, J.N.2    Levy, S.3
  • 38
    • 0000589476 scopus 로고
    • Buckling of plates subjected to edge thrusts and lateral pressure
    • Yamamoto et al. 1970, In Japanese
    • [Yamamoto et al. 1970] Y. Yamamoto, N. Matsubara, and T. Murakami, "Buckling of plates subjected to edge thrusts and lateral pressure", J. Soc. Naval Arch. Japan 127 (1970), 171-179. In Japanese.
    • (1970) J. Soc. Naval Arch. Japan , vol.127 , pp. 171-179
    • Yamamoto, Y.1    Matsubara, N.2    Murakami, T.3


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