Showing papers on "Timoshenko beam theory published in 1986"
TL;DR: In this article, a response function is derived for an infinite, uniform, one-dimensional structure which is subjected to an array of harmonic forces or moments, spaced equidistantly, and which have a constant phase or ratio between any adjacent pair.
188 citations
TL;DR: In this article, material conservation and balance laws of elementary beam theory have been derived and applied to beams with discontinuities in the stiffness results in a surprisingly simple formula to calculate stress intensity factors of cracked beams.
Abstract: Material conservation and balance laws of elementary beam theory have been derived. The application to beams with discontinuities in the stiffness results in a surprisingly simple formula to calculate stress intensity factors of cracked beams.
67 citations
TL;DR: In this article, the dynamics and stability of short tubes conveying fluid is examined by means of Timoshenko beam theory for the tube and a three-dimensional fluid-mechanical model for the fluid flow, rather than the plug-flow model utilized heretofore.
50 citations
TL;DR: In this paper, the steady state response of an axially moving strip subjected to a constant lateral force fixed in space is studied on the basis of a thick beam theory which takes into account the effects of rotatory inertia, shear deformation and the second-order term in the normal stress due to the rotation of the strip.
49 citations
TL;DR: In this paper, the stability problem of densely distributed oscillators moving along a Timoshenko beam on an elastic foundation is considered and the forward speed of the moving subsystem is assumed to be constant.
Abstract: The stability problem of densely distributed oscillators moving along a Timoshenko beam on an elastic foundation is considered The forward speed of the moving subsystem is assumed to be constant The friction at the contact line between the beam and the oscillator set is neglected A qualitatively new instability region is found It is pointed out that the critical velocity for some system parameters takes smaller values than the velocity of shear waves or the velocity of longitudinal waves
47 citations
TL;DR: In this article, a shear flexible quadratic isoparametric beam element with two degrees of freedom per node is examined from the point of view of the consistency of the constrained strain fields that arise in the thin-beam limits.
Abstract: A shear flexible (i.e. Timoshenko) quadratic isoparametric beam element with two degrees of freedom per node is critically examined from the point of view of the consistency of the constrained strain fields that arise in the thin-beam limits. The errors, in terms of convergence of displacement fields and violent oscillations of stress fields, that emerge when exactly integrated elements are used are predicted a priori and confirmed with numerical experiments. The rationale behind the use of optimal stress sampling at Gaussian points is also derived directly from these arguments.
47 citations
46 citations
TL;DR: In this paper, the effects of rotational speed and root flexibilities on the static buckling loads and on the regions of dynamic instability of a Timoshenko beam are investigated by finite element method.
46 citations
39 citations
TL;DR: In this paper, a global-local approach was proposed to solve dynamic problems involving truss beams, where a continuum Timoshenko beam was used to model sections of truss beam wherever possible and accurate.
Abstract: A global-local approach was proposed to solve dynamic problems involving truss beams. A continuum Timoshenko beam was used to model sections of truss beams wherever possible and accurate. Near applied loads the continuum model was not adequate and detailed truss finite elements (discrete model) were employed. This approach was also proven efficient for an odd-shaped truss structure connected to a truss beam. Between the continuum model and the discrete model, compatibility conditions were derived.
35 citations
TL;DR: In this paper, a classical elasticity solution for the stress and displacement fields in loaded orthotropic beams is presented and the corresponding stress equations, derived from a stress function which satisfies the orthotropic analogue of the biharmonic equation, are written as Fourier series.
01 Apr 1986
TL;DR: A finite element based, nonlinear model is presented in this paper for revolute jointed spatial manipulators and the resulting methodology is shown to identify the effects of the nonlinear interactions on the dynamic positioning characteristics of the manipulator.
Abstract: A finite element based, nonlinear model is presented in this paper for revolute jointed spatial manipulators. The model allows for the nonlinear coupling effects between the nonlinear gross motions of the manipulator links and their elastic deformations. The governing equations of motion are derived including the effects of rotatory inertia, shear deformation, and the effects of the gross non-linear motion of each of the links. A simple and efficient finite element has been developed for the manipulator links using Timoshenko Beam Theory. The resulting methodology is shown to identify the effects of the nonlinear interactions on the dynamic positioning characteristics of the manipulator.
TL;DR: In this paper, a solution exacte for les frequences propres de vibration de poutres libres is proposed, comme base de comparaison de la theorie des Poutres de Timoshenko and d'une approximation de contraintes planes developpee ici.
Abstract: On utilise une solution exacte pour les frequences propres de vibration de poutres libres, comme base de comparaison de la theorie des poutres de Timoshenko et d'une approximation de contraintes planes developpee ici
TL;DR: In this paper, a general computer program is described which analyses any cross-section with open or closed parts, and solutions are readily available for open sections and regular single cell closed sections.
TL;DR: In this paper, the global damping for the continuum beam is explicitly expressed in terms of the damping coefficients of individual truss members, and the gradient method is used for parameter estimations in conjunction with the Timoshenko beam model.
Abstract: Truss beams with members having viscous damping are modeled as continuum Timoshenko beams. Procedures for deriving the equivalent beam stiffnesses and damping are presented. The global damping for the continuum beam is explicitly expressed in terms of the damping coefficients of the individual truss members. The continuum beam model is used to study transient vibration problems and the solutions are compared well with the full scale finite element solutions. The gradient method is used for parameter estimations in conjunction with the Timoshenko beam model. It is shown that the Timoshenko beam model can be easily updated with measured data and the updated model can yield very accurate transient solutions.
TL;DR: In this article, the residual stresses in a bonded tile/substrate structure were analyzed using both analytical and finite element methods, and the response of the calculated stress states to changes in various model dimensions and material parameters was studied parametrically.
TL;DR: In this paper, the authors considered the problem of optimally controlling the deflections and velocities of a damped Timoshenko beam subject to various types of boundary conditions by means of a distributed applied force and moment.
Abstract: The present paper considers the problem of optimally controlling the deflections and/or velocities of a damped Timoshenko beam subject to various types of boundary conditions by means of a distributed applied force and moment An analytic solution is obtained by employing a maximum principle
TL;DR: In this article, a finite difference technique is applied to the strains and curvatures obtained from MSC/NASTRAN thin plate solutions to determine their derivatives, which are then incorporated into classical thin plate theory to calculate interlaminar shear stresses.
TL;DR: In this article, an analysis of the elastic-plastic load-carrying behavior of thin-walled spatial beam structures is presented based on a beam theory valid for large displacements and rotations, which admits arbitrary cross-sections, curved axes, initial imperfections, a general material description, and fully accounts for the influence of warping constraints as well as the stress-history dependence of the shear moduli.
Abstract: An analysis of the elastic–plastic load-carrying behaviour of thin-walled spatial beam structures is presented. It is based on a beam theory valid for large displacements and rotations, which admits arbitrary cross-sections, curved axes, initial imperfections, a general material description, and which fully accounts for the influence of warping constraints as well as the stress-history dependence of the elastic–plastic shear moduli. An incremental updated Lagrangian viewpoint is adopted in the derivation of the basic beam equations from a generalized variational principle, and in the numerical solution procedure the displacement–finite element approach is followed. The associated tangential stiffness matrices are obtained by direct numerical integration of the governing incremental differential equations rather than through the use of shape functions in connection with a virtual work principle. Applications of the theory are given in which the influence of the loading configuration, material parameters, geometric nonlinearities and warping constraints on the load-carrying behaviour and on the bifurcation and ultimate loads of thin-walled beam structures is explored.
TL;DR: In this paper, four large glulam beams with notches on the tension side were tested for strength and stiffness, and the results corroborate the substantial analytic effect of size predicted by fracture mechanics for notched beams.
Abstract: Four large glulam beams with notches on the tension side were tested for strength and stiffness. Using either bending net section beam theory or shear formula to calculate crack propagation critical load is very unconservative. A linear elastic fracture mechanics approach, taking into account the high tension stresses perpendicular to grain and shear stresses at the notch reentrant corner, conservatively predicts the critical load. The data corroborate the substantial analytic effect of size predicted by fracture mechanics for notched beams. Results quantify the observed behavior of bending of beams with notches on the tension side. The strength reduction is so severe for large beams that substituting a beam having the net depth of the notched beam is preferable. Removing material would remove the stress concentrator and would increase the strength up to net section theory prediction at the notch location. Using an effective notch length (actual notch length + notch depth added to each end of the notch) and variable moment of inertia, beam theory accurately predicts the notch beam deflection under load.
TL;DR: In this paper, the response of a transversely isotropic beam of finite length to a frictionless cylindrical and flat indenter is studied using a global-local technique, which accounts for the local behavior near the indenter and the global beam behavior.
TL;DR: A finite displacemtment theory for an arbitrary plane curved Timoshenko beam, in which an elastic constitutive relation is defined not by tensor components of stress and strain but by other physical components, was developed in this article.
Abstract: A finite displacemtment theory is developed for an arbitrary plane curved Timoshenko beam, in which an elastic constitutive relation is defined not by tensor components of stress and strain but by other physical components. This selection of components makes the governing equation simple and easy to handle. The nonlinear stiffness equation, with the use of nodal positions and the appropriate selection of local coordinates, is formulated for an elastic plane straight beam element. Three numerical examples of plane beam problems, involving geometrical nonlinearity, are employed as illustrative examples.
TL;DR: In this article, the effects of axial motion and joint mass with its rotational inertia on the flexural eigenfrequencies of a uniform Timoshenko two-bar frame are investigated.
Abstract: SUMMARY The equations of free lateral vibrations of a uniform Timoshenko two-bar frame including the effects of axial motion and joint mass with its rotational inertia are presented. The influence on the flexural eigenfrequencies of the axial motion alone or in combination with other parameters is fully assessed and thoroughly discussed. These parameters are: the translational and rotational inertia of the joint mass, the transverse shear deformation and rotatory inertia, the length, stiffness and slenderness ratios of the two bars of the frame. The variety of numerical results presented herein leads to the important finding that for framed structures the effect of axial inertia on the flexural eigenfrequencies alone or in combination with the foregoing parameters may be considerable. In particular, if the joint mass should be accounted for, the foregoing effect cannot be ignored, since it leads, in general, to considerable errors even for frames with relatively slender bars. INTRODUCTION The influence of longitudinal motion
TL;DR: In this paper, a method based on the variational principles in conjunction with the finite difference technique is used to examine the free vibrational characteristics of Timoshenko beams and shafts.
TL;DR: In this article, the problem of determining the optimal linear taper of a narrow rectangular beam that maximizes the critical buckling load subject to a volume constraint is addressed, and the solution to the problem is obtained by two independent approaches.
TL;DR: In this article, the basic equations for the beam-type vibration of rotating cylindrical shells are derived by the Timoshenko beam theory and the frequency analysis is presented for three kinds of boundary conditions.
Abstract: The basic equations for the beam-type vibration of rotating cylindrical shell are derived by the Timoshenko beam theory. The frequency analysis is presented for three kinds of boundary conditions and the validity of this model is examined by comparing the results with those based on the cylindrical shell theory. It is found that as for the natural frequencies of non-rotation, and rotation cylindrical shells and for the critical speeds reasonable results can be obtained by solving the problem on the basis of the Timoshenko beam theory.
TL;DR: In this article, random vibration analysis of flexible rotor-bearing systems subjected to six-component nonstationary earthquake ground accelerations is carried out, where the rotor system consists of several rigid disks and a flexible shaft that is modelled as a Timoshenko beam.
TL;DR: In this paper, an alternative theory, using concepts that are simple and familiar to the structural engineer, is developed, which neglects Poisson's ratio and employs, for flexural stresses at the center, large displacement harmonic decomposition truncated after the first term.
Abstract: Available methods of strength analysis of glass plates provide conflicting estimates of the reliability of glass plates under known loading. The most realistic theory is unfortunately also the most complex and yields a paradoxical result: Some glass plates can support higher uniform pressure when they are made longer, wider, and thinner. An alternative theory, using concepts that are simple and familiar to the structural engineer, is therefore developed. The theory neglects Poisson’s ratio and employs, for flexural stresses at the center, large displacement harmonic decomposition truncated after the first term. Membrane stresses at the center are calculated from second-order theory and deep beam analysis. The loading component carried by this stress system is subtracted from the applied uniform loading to define a loading around the edges. The maximum stresses from this loading are calculated by elementary beam theory. This theory is calibrated to agree with recent tests. It provides a simple explanation for the paradoxical result of complex theory.
TL;DR: In this article, the Timoshenko beam theory is used to compare experimental and analytical results in a steel frame subjected to a harmonic excitation, and the very good agreement between the experimental and the theoretical results proves the usefulness of this exact method over other methods as the finite elements.
TL;DR: In this paper, the Stodola iteration equations are theoretically established by allowing the progressive evaluation of the coefficients of the equivalent mass matrix for the transverse vibration of a uniform Timoshenko beam segment.