Timoshenko beam theory

About: Timoshenko beam theory is a research topic. Over the lifetime, 9426 publications have been published within this topic receiving 200570 citations.

A three-noded shear-flexible curved beam element based on coupled displacement field interpolations

Abstract: An efficient shear-flexible three-noded curved beam element is proposed herein. The shear flexibility is based on Timoshenko beam theory and the element has three degrees of freedom, viz., tangential displacement (u), radial displacement (w) and the section-rotation (θ). A quartic polynomial interpolation for flexural rotation ψ is assumed a priori. Making use of the physical composition of θ in terms of ψ and u, a novel way of deriving the polynomial interpolations for u and w is presented, by solving force-moment and moment-shear equilibrium equations simultaneously. The field interpolation for θ is then constructed from that of ψ and u. The procedure leads to high-order polynomial field interpolations which share some of the generalized degrees of freedom, by means of coefficients involving material and geometric properties of the element. When applied to a straight Euler–Bernoulli beam, all the coupled coefficients vanish and the formulation reduces to classical quintic-in-w and quadratic-in-u element, with u, w, and ∂w/∂x as degrees of freedom. The element is totally devoid of membrane and shear locking phenomena. The formulation presents an efficient utilization of the nine generalized degrees of freedom available for the polynomial interpolation of field variables for a three-noded curved beam element. Numerical examples on static and free vibration analyses demonstrate the efficacy and locking-free property of the element. Copyright © 2001 John Wiley & Sons, Ltd.

Director‐based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates

Abstract: SUMMARY In the present work, a new director-based finite element formulation for geometrically exact beams is proposed. The new beam finite element exhibits drastically improved numerical performance when compared with the previously developed director-based formulations. This improvement is accomplished by adjusting the underlying variational beam formulation to the specific features of the director interpolation. In particular, the present approach does not rely on the assumption of an orthonormal director frame. The excellent performance of the new approach is illustrated with representative numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.

On torsion and shear of Saint-Venant beams

Abstract: Torsion and shear stress fields of a Saint-Venant beam and the relative location of shear and twist centres are investigated for sections of any degree of connectedness. The sliding-torsional compliance tensor of a Timoshenko beam is evaluated by an energy equivalence with Saint-Venant theory. Accordingly, the mutual sliding-torsional term is shown to depend linearly on the relative position of shear and twist centres and the standard definition of shear centre in a Timoshenko beam is found to be coincident with Saint-Venant twist centre. Coincidence of shear and twist centres is assessed for sections with vanishing Poisson ratio and for open, closed and multi-cell thin-walled cross sections. The eigenvalues of the shear factors tensor and the torsion factor are shown to be greater than unity, with the principal directions of shearing and bending compliances non necessarily coincident for non-symmetric cross sections. Numerical examples are developed to provide evidences of the location of the centres and of the principal shearing directions, for non-symmetric L-shaped cross sections with various thickness ratios.

Analysis of the vibration of an elastic beam supported on elastic soil using the differential transform method

Abstract: In this paper, a simulation method called the differential transform method (DTM) is employed to predict the vibration of an Euler–Bernoulli and Timoshenko beam (pipeline) resting on an elastic soil. The DTM is introduced briefly. DTM can easily be applied to linear or nonlinear problems and reduces the required computational effort. With this method exact solutions may be obtained without any need for cumbersome calculations and it is a useful tool for analytical and numerical solutions. To clarify and illustrate the features and capabilities of the presented method, various problems have been solved by using the technique and solutions have been compared with those obtained in the literature.