메뉴 건너뛰기




Volumn 38, Issue 24-25, 2001, Pages 4395-4437

Numerical solution procedures for nonlinear elastic rods using the theory of a cosserat point

Author keywords

Buckling; Elastic; Nonlinear; Rod

Indexed keywords

DEFORMATION; DERIVATIVES; MODELS; ROTATION; SHEAR DEFORMATION; STRAIN;

EID: 0035853869     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(00)00271-7     Document Type: Article
Times cited : (32)

References (37)
  • 1
    • 0014808651 scopus 로고
    • Analysis of thick and thin shell structures by curved finite elements
    • S. Ahmad B.M. Irons O.C. Zienkiewicz Analysis of thick and thin shell structures by curved finite elements Int. J. Numer. Meth. Engng. 2 1970 419 451
    • (1970) Int. J. Numer. Meth. Engng. , vol.2 , pp. 419-451
    • Ahmad, S.1    Irons, B.M.2    Zienkiewicz, O.C.3
  • 2
    • 85120097538 scopus 로고    scopus 로고
    • Antman, S.S., 1972. The theory of rods. In: Handbuch der Physik VIa/2. Springer, Berlin, pp. 641–703
  • 3
    • 0016120331 scopus 로고
    • Kirchhoff's problem for nonlinearly elastic rods
    • S.S. Antman Kirchhoff's problem for nonlinearly elastic rods Quart. Appl. Math. 32 1974 221 240
    • (1974) Quart. Appl. Math. , vol.32 , pp. 221-240
    • Antman, S.S.1
  • 4
    • 0000668495 scopus 로고
    • Pseudo-rigid bodies
    • H. Cohen Pseudo-rigid bodies Utilitas Math. 20 1981 221 247
    • (1981) Utilitas Math. , vol.20 , pp. 221-247
    • Cohen, H.1
  • 5
    • 0021446823 scopus 로고
    • The dynamics of pseudo-rigid bodies: general structure and exact solutions
    • H. Cohen R.G. Muncaster The dynamics of pseudo-rigid bodies: general structure and exact solutions J. Elast. 14 1984 127 154
    • (1984) J. Elast. , vol.14 , pp. 127-154
    • Cohen, H.1    Muncaster, R.G.2
  • 7
    • 0001176723 scopus 로고
    • The method of weighted residuals – a review
    • B.A. Finlayson L.E. Scriven The method of weighted residuals – a review Appl. Mech. Rev. 9 1966 735 748
    • (1966) Appl. Mech. Rev. , vol.9 , pp. 735-748
    • Finlayson, B.A.1    Scriven, L.E.2
  • 8
    • 0006280110 scopus 로고
    • Thermodynamic relations for high elastic materials
    • P.J. Flory Thermodynamic relations for high elastic materials Trans. Faraday Soc. 57 1961 829 838
    • (1961) Trans. Faraday Soc. , vol.57 , pp. 829-838
    • Flory, P.J.1
  • 9
    • 85120118438 scopus 로고    scopus 로고
    • Gladwell, G.M.L., 1998. Private communication
  • 10
    • 85120125311 scopus 로고    scopus 로고
    • Graff, K.F., 1975. Wave Motion in Elastic Solids. Ohio State University Press, Columbus, Ohio
  • 11
    • 0000715308 scopus 로고
    • On the theory of rods I: derivations from the three-dimensional equations
    • A.E. Green P.M. Naghdi M.L. Wenner On the theory of rods I: derivations from the three-dimensional equations Proc. Royal Soc. Lond. A A337 1974 451 483
    • (1974) Proc. Royal Soc. Lond. A , vol.A337 , pp. 451-483
    • Green, A.E.1    Naghdi, P.M.2    Wenner, M.L.3
  • 12
  • 13
    • 0001240020 scopus 로고
    • A thermodynamical theory of a Cosserat point with application to composite materials
    • A.E. Green P.M. Naghdi A thermodynamical theory of a Cosserat point with application to composite materials Q. J. Mech. Appl. Math. 44 1991 335 355
    • (1991) Q. J. Mech. Appl. Math. , vol.44 , pp. 335-355
    • Green, A.E.1    Naghdi, P.M.2
  • 14
    • 85120125708 scopus 로고
    • A.E.H. Love A Treatise on the Mathematical Theory of Elasticity fourth ed 1944 Dover New York
    • (1944)
    • Love, A.E.H.1
  • 15
    • 0021155578 scopus 로고
    • Invariant manifolds in mechanics I: zero-dimensional elastic bodies with directors
    • R.G. Muncaster Invariant manifolds in mechanics I: zero-dimensional elastic bodies with directors Arch. Ration. Mech. Anal. 84 1984 353 373
    • (1984) Arch. Ration. Mech. Anal. , vol.84 , pp. 353-373
    • Muncaster, R.G.1
  • 16
    • 85120128311 scopus 로고    scopus 로고
    • Naghdi, P.M., 1972. The theory of shells and plates. In: Truesdell, C. (Ed.), S. Flügge's Handbuch der Physik, Mechanics of Solids II, vol. VIa/2, Springer, Berlin, pp. 425–640
  • 17
    • 0021575949 scopus 로고
    • Constrained theories of rods
    • P.M. Naghdi M.B. Rubin Constrained theories of rods J. Elast. 14 1984 343 361
    • (1984) J. Elast. , vol.14 , pp. 343-361
    • Naghdi, P.M.1    Rubin, M.B.2
  • 18
    • 0024946361 scopus 로고
    • On the significance of normal cross-sectional extension in beam theory with application to contact problems
    • P.M. Naghdi M.B. Rubin On the significance of normal cross-sectional extension in beam theory with application to contact problems Int. J. Solids Struct. 25 1989 249 265
    • (1989) Int. J. Solids Struct. , vol.25 , pp. 249-265
    • Naghdi, P.M.1    Rubin, M.B.2
  • 19
    • 0029307467 scopus 로고
    • Restrictions on nonlinear constitutive equations for elastic shells
    • P.M. Naghdi M.B. Rubin Restrictions on nonlinear constitutive equations for elastic shells J. Elast. 39 1995 133 163
    • (1995) J. Elast. , vol.39 , pp. 133-163
    • Naghdi, P.M.1    Rubin, M.B.2
  • 20
    • 0032043531 scopus 로고    scopus 로고
    • On constitutive relations for elastic rods
    • O.M. O'Reilly On constitutive relations for elastic rods Int. J. Solids Struct. 35 1998 1009 1024
    • (1998) Int. J. Solids Struct. , vol.35 , pp. 1009-1024
    • O'Reilly, O.M.1
  • 21
    • 0032375005 scopus 로고    scopus 로고
    • A unified treatment of constraints in the theory of a Cosserat point
    • O.M. O'Reilly P.C. Vardi A unified treatment of constraints in the theory of a Cosserat point J. Math. Phys. (ZAMP) 49 1998 205 223
    • (1998) J. Math. Phys. (ZAMP) , vol.49 , pp. 205-223
    • O'Reilly, O.M.1    Vardi, P.C.2
  • 22
    • 0022079606 scopus 로고
    • On the theory of a Cosserat point and its application to the numerical solution of continuum problems
    • M.B. Rubin On the theory of a Cosserat point and its application to the numerical solution of continuum problems ASME J. Appl. Mech. 52 1985 368 372
    • (1985) ASME J. Appl. Mech. , vol.52 , pp. 368-372
    • Rubin, M.B.1
  • 23
    • 0022078203 scopus 로고
    • On the numerical solution of one-dimensional continuum problems using the theory of a Cosserat point
    • M.B. Rubin On the numerical solution of one-dimensional continuum problems using the theory of a Cosserat point ASME J. Appl. Mech. 52 1985 373 378
    • (1985) ASME J. Appl. Mech. , vol.52 , pp. 373-378
    • Rubin, M.B.1
  • 24
    • 0022679737 scopus 로고
    • Free vibration of a rectangular parallelepiped using the theory of a Cosserat point
    • M.B. Rubin Free vibration of a rectangular parallelepiped using the theory of a Cosserat point ASME J. Appl. Mech. 53 1986 45 50
    • (1986) ASME J. Appl. Mech. , vol.53 , pp. 45-50
    • Rubin, M.B.1
  • 25
    • 0023207011 scopus 로고
    • On the numerical solution of nonlinear string problems using theory of a Cosserat point
    • M.B. Rubin On the numerical solution of nonlinear string problems using theory of a Cosserat point Int. J. Solids Struct. 23 1987 335 349
    • (1987) Int. J. Solids Struct. , vol.23 , pp. 335-349
    • Rubin, M.B.1
  • 26
    • 85120134427 scopus 로고    scopus 로고
    • Rubin, M.B., 1995. Numerical solution of two- and three-dimensional thermomechanical problems using the theory of a Cosserat point. In: Casey J., Crochet M.J. (Eds.), Theoretical, Experimental, and Numerical Contributions to the Mechanics of Fluids and Solids (Special Issue). J. Math. Phys. (ZAMP) 46, S308–S334
  • 27
    • 0030182277 scopus 로고    scopus 로고
    • Restrictions on nonlinear constitutive equations for elastic rods
    • M.B. Rubin Restrictions on nonlinear constitutive equations for elastic rods J. Elast. 44 1996 9 36
    • (1996) J. Elast. , vol.44 , pp. 9-36
    • Rubin, M.B.1
  • 28
    • 0031274310 scopus 로고    scopus 로고
    • An intrinsic formulation for nonlinear elastic rods
    • M.B. Rubin An intrinsic formulation for nonlinear elastic rods Int. J. Solids Struct. 34 1997 4191 4212
    • (1997) Int. J. Solids Struct. , vol.34 , pp. 4191-4212
    • Rubin, M.B.1
  • 29
    • 0030263245 scopus 로고    scopus 로고
    • Numerical solutions of forced vibration and whirling of a non-linear string using the theory of a Cosserat point
    • M.B. Rubin O. Gottlieb Numerical solutions of forced vibration and whirling of a non-linear string using the theory of a Cosserat point J. Sound Vibrat. 197 1996 85 101
    • (1996) J. Sound Vibrat. , vol.197 , pp. 85-101
    • Rubin, M.B.1    Gottlieb, O.2
  • 30
    • 0022060633 scopus 로고
    • A finite strain beam formulation. The three-dimensional dynamic problem part I
    • J.C. Simo A finite strain beam formulation. The three-dimensional dynamic problem part I Comp. Meth. Appl. Mech. Engng. 49 1985 55 70
    • (1985) Comp. Meth. Appl. Mech. Engng. , vol.49 , pp. 55-70
    • Simo, J.C.1
  • 31
    • 0022792209 scopus 로고
    • A three-dimensional finite strain rod model part II. Computational aspects
    • J.C. Simo L. Vu-Quoc A three-dimensional finite strain rod model part II. Computational aspects Comp. Meth. Appl. Mech. Engng. 58 1986 79 116
    • (1986) Comp. Meth. Appl. Mech. Engng. , vol.58 , pp. 79-116
    • Simo, J.C.1    Vu-Quoc, L.2
  • 32
    • 0025457448 scopus 로고
    • On a stress resultant geometrically exact shell model part IV: variable thickness shells with through-the thickness stretching
    • J.C. Simo M.S. Rifai D.D. Fox On a stress resultant geometrically exact shell model part IV: variable thickness shells with through-the thickness stretching Comp. Meth. Appl. Mech. Engng. 81 1990 91 126
    • (1990) Comp. Meth. Appl. Mech. Engng. , vol.81 , pp. 91-126
    • Simo, J.C.1    Rifai, M.S.2    Fox, D.D.3
  • 33
    • 0013044934 scopus 로고
    • Newtonian dynamics of homogeneous strains
    • J.J. Slawianowski Newtonian dynamics of homogeneous strains Arch. Mech. 26 1975 569 587
    • (1975) Arch. Mech. , vol.26 , pp. 569-587
    • Slawianowski, J.J.1
  • 34
    • 84983965324 scopus 로고
    • The mechanics of the homogeneously-deformable body. Dynamical models with high symmetries
    • J.J. Slawianowski The mechanics of the homogeneously-deformable body. Dynamical models with high symmetries S. Angew. Math. Mech. 62 1982 229 240
    • (1982) S. Angew. Math. Mech. , vol.62 , pp. 229-240
    • Slawianowski, J.J.1
  • 35
    • 85120102904 scopus 로고
    • I.S. Sokolnikoff Mathematical Theory of Elasticity 1956 McGraw-Hill New York
    • (1956)
    • Sokolnikoff, I.S.1
  • 36
    • 0000500038 scopus 로고    scopus 로고
    • A simple finite element-based framework for the analysis of elastic pseudo-rigid bodies
    • J.M. Solberg P. Papadopoulos A simple finite element-based framework for the analysis of elastic pseudo-rigid bodies Int. J. Numer. Meth. Engng. 45 1999 1297 1314
    • (1999) Int. J. Numer. Meth. Engng. , vol.45 , pp. 1297-1314
    • Solberg, J.M.1    Papadopoulos, P.2
  • 37
    • 85120098421 scopus 로고    scopus 로고
    • Zienkiewicz, O.C., Taylor, R.L., 1991. The finite element method, solid and fluid mechanics, dynamics and non-linearity. fourth ed. vol. 2, McGraw-Hill, New York


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.