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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 3 (1992), S. 431-463 
    ISSN: 1573-269X
    Keywords: Anisotropic shell ; geometric nonlinearity ; third-order shear deformation theory ; extension-bending-shear vibrations ; general nonlinear equations of motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A general nonlinear theory for the dynamics of elastic anisotropic circular cylindrical shells undergoing small strains and moderate-rotation vibrations is presented. The theory fully accounts for extensionality and geometric nonlinearities by using local stress and strain measures and an exact coordinate transformation, which result in nonlinear curvatures and strain-displacement expressions that contain the von Karman strains as a special case. Moreover, the linear part of the theory contains, as special cases, most of the classical linear theories when appropriate stress resultants and couples are defined. Parabolic distributions of the transverse shear strains are accounted for by using a third-order theory and hence shear correction factors are not required. Five third-order nonlinear partial differential equations describing the extension, bending, and shear vibrations of shells are obtained using the principle of virtual work and an asymptotic analysis. These equations show that laminated shells display linear elastic and nonlinear geometric couplings among all motions.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 3 (1992), S. 273-303 
    ISSN: 1573-269X
    Keywords: Composite beams ; geometric nonlinearity ; third-order shear deformation theory ; extensional-flexural-flexuraltorsional-shearing-shearing vibrations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Presented here is a general theory for the three-dimensional nonlinear dynamics of elastic anisotropic initially straight beams undergoing moderate displacements and rotations. The theory fully accounts for geometric nonlinearities (large rotations and displacements) by using local stress and strain measures and an exact coordinate transformation, which result in nonlinear curvature and strain-displacement expressions that contain the von Karman strains as a special case. Extensionality is included in the formulation, and transverse shear deformations are accounted for by using a third-order theory. Six third-order nonlinear partial-differential equations are derived for describing one extension, two bending, one torsion, and two shearing vibrations of composite beams. They show that laminated beams display linear elastic and nonlinear geometric couplings among all motions. The theory contains, as special cases, the Euler-Bernoulli theory, Timoshenko's beam theory, the third-order shear theory, and the von Karman type nonlinear theory.
    Type of Medium: Electronic Resource
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