Conservative Semidiscrete Difference Schemes for Timoshenko Systems

Other literature type, Article English OPEN
D. S. Almeida Júnior;
(2014)

We present a parameterized family of finite-difference schemes to analyze the energy properties for linearly elastic constant-coefficient Timoshenko systems considering shear deformation and rotatory inertia. We derive numerical energies showing the positivity, an... View more
  • References (20)
    20 references, page 1 of 2

    Han, S. M., Benaroya, H., Wei, T.. Dynamics of transversely vibrating beams using four engineering theories. Journal of Sound and Vibration. 1999; 225 (5): 935-988

    Timoshenko, S. P.. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Philosophical Magazine. 1921; 6: 744-746

    Huang, T. C.. The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions. Journal of Applied Mechanics. 1961; 28: 579-584

    Krieg, R. D.. On the behavior of a numerical approximation to the rotatory inertia and transverse shear plate. Journal of Applied Mechanics. 1973; 40 (4): 977-982

    Belytschko, T., Mindle, W. L.. Flexural wave propagation behavior of lumped mass approximations. Computers and Structures. 1980; 12 (6): 805-812

    Mindle, W. L., Belytschko, T.. A study of shear factors in reduced-selective integration mindlin beam elements. Computers and Structures. 1983; 17 (3): 339-344

    Wright, J. P.. A mixed time integration method for Timoshenko and Mindlin type elements. Communications in Applied Numerical Methods. 1987; 3 (3): 181-185

    Wright, J. P.. Numerical stability of a variable time step explicit method for Timoshenko and Mindlin type structures. Communications in Numerical Methods in Engineering. 1998; 14 (2): 81-86

    Arnold, D. N.. Discretization by finite elements of a model parameter dependent problem. Numerische Mathematik. 1981; 37 (3): 405-421

    Hughes, T. J. R., Taylor, R. L., Kanoknukulchai, W.. A simple and efficient finite element method for plate bending. International Journal for Numerical Methods in Engineering. 1977; 11 (10): 1529-1543

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