A SIMPLE CUBIC LINEAR ELEMENT FOR STATIC AND FREE VIBRATION ANALYSES OF CURVED BEAMS

Abstract The effect of shear deformation on deflection and shear deformation together with rotatory inertia on natural and cross over frequencies of curved beams are obtained using a simple cubic linear beam element having 4 degrees of freedom per node viz u, w, θ and γ. Studies are carried out on beams with all classical boundary conditions. From the results obtained for static and free vibration problems with different curvatures and slenderness ratios, it is seen that this element is suitable to analyse any curved beam problem. Numerical results obtained without including the effect of shear deformation and rotatory inertia are made use of to quantify their effect on the static and free vibration behaviour of curved beams.

[1]  H. R. Meck An accurate polynomial displacement function for unite ring elements , 1980 .

[2]  Gangan Prathap,et al.  An isoparametric quadratic thick curved beam element , 1986 .

[3]  T. Belytschko,et al.  Shear and membrane locking in curved C0 elements , 1983 .

[4]  D. G. Ashwell,et al.  Limitations of certain curved finite elements when applied to arches , 1971 .

[5]  A. Sabir,et al.  The effect of shear deformation on the vibration of circular arches by the finite element method , 1994 .

[6]  Jang-Keun Lim,et al.  General curved beam elements based on the assumed strain fields , 1995 .

[7]  Robert D. Cook,et al.  Further development of a three‐node triangular shell element , 1993 .

[8]  Fred B. Seely,et al.  Advanced Mechanics of Materials , 1932 .

[9]  Jang-Keun Lim,et al.  Simple curved shear beam elements , 1993 .

[10]  D. G. Ashwell,et al.  Finite elements for thin shells and curved members , 1976 .

[11]  P.A.A. Laura,et al.  Dynamic stiffening of an arch clamped at one end and free at the other , 1993 .

[12]  Gangan Prathap,et al.  The curved beam/deep arch/finite ring element revisited , 1985 .

[13]  Hyo-Chol Sin,et al.  Locking‐free curved beam element based on curvature , 1994 .

[14]  Gangan Prathap,et al.  Reduced integration and the shear-flexible beam element , 1982 .

[15]  Gangan Prathap,et al.  Variationally correct assumed strain field for the simple curved beam element , 1993 .

[16]  F. A. Mirza,et al.  Consistent curved beam element , 1994 .

[17]  R. E. Rossi,et al.  Free vibration of a three-centered arc clamped at the ends , 1993 .

[18]  D. L. Thomas,et al.  Timoshenko beam finite elements , 1973 .

[19]  A. B. Sabir,et al.  Further studies in the application of curved finite elements to circular arches , 1971 .

[20]  J. Guimarães,et al.  On trigonometric basis functions for C1 curved beam finite elements , 1992 .

[21]  Y. J. Suresh,et al.  Free vibration studies of arches , 1995 .

[22]  Maurice Petyt,et al.  Free vibration of a curved beam , 1971 .

[23]  D. J. Dawe,et al.  A finite‐deflection analysis of shallow arches by the discrete element method , 1971 .

[24]  T. Belytschko,et al.  Membrane Locking and Reduced Integration for Curved Elements , 1982 .

[25]  Henry T. Y. Yang Finite Element Structural Analysis , 1985 .

[26]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[27]  D. J. Dawe,et al.  Numerical studies using circular arch finite elements , 1974 .

[28]  D. J. Dawe,et al.  Curved finite elements for the analysis of shallow and deep arches , 1974 .

[29]  Accuracy and locking-free property of the beam element approximation for arch problems , 1984 .