An Exact Three-Dimensional Beam Element With Nonuniform Cross Section

In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

[1]  Amir Ayoub,et al.  NONLINEAR FINITE - ELEMENT ANALYSIS OF RC SHEAR PANELS AND WALLS , 2001 .

[2]  A. Krishnan,et al.  A SIMPLE CUBIC LINEAR ELEMENT FOR STATIC AND FREE VIBRATION ANALYSES OF CURVED BEAMS , 1998 .

[3]  Francesco Ubertini,et al.  A flexibility‐based finite element for linear analysis of arbitrarily curved arches , 2006 .

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

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

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

[7]  Robert L. Taylor,et al.  A mixed finite element method for beam and frame problems , 2003 .

[8]  Gangan Prathap,et al.  Analysis of locking and stress oscillations in a general curved beam element , 1990 .

[9]  F. Filippou,et al.  Mixed formulation of nonlinear beam finite element , 1996 .

[10]  Jong-Shyong Wu,et al.  Out-of-plane responses of a circular curved Timoshenko beam due to a moving load , 2003 .

[11]  G. Prathap,et al.  Consistency aspects of out‐of‐plane bending, torsion and shear in a quadratic curved beam element , 1990 .

[12]  Gennady M. Kulikov,et al.  Non-conventional non-linear two-node hybrid stress-strain curved beam elements , 2004 .

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

[14]  Przemysław Litewka,et al.  The exact thick arch finite element , 1998 .

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

[16]  Jong-Shyong Wu,et al.  Free vibration of a circularly curved Timoshenko beam normal to its initial plane using finite curved beam elements , 2004 .