Showing papers on "Timoshenko beam theory published in 1990"
TL;DR: In this paper, a co-rotational formulation for three-dimensional beams is presented, in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted "strain measures".
496 citations
TL;DR: In this paper, an approximate Galerkin solution to the one-dimensional cracked beam theory developed by Christides and Barr for the free bending motion of beams with pairs of symmetric open cracks is suggested.
214 citations
TL;DR: In this article, the vibration characteristics of uniform hanging beams under gravity were investigated and the governing differential equations for free vibrations of a vertically hanging Timoshenko beam subjected to its own weight were derived from Hamilton's principle.
66 citations
TL;DR: In this article, a two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity, and the model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the interior of the half-plane.
Abstract: A two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite half-plane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the interior of the half-plane. It is demonstrated that for composites of low volume fraction (<0.3), this decay mode furnishes values of buckling strain that are below the values predicted by the Rosen (1965) model. At a higher volume fraction the buckling mode corresponds to a half wavelength that is in violation of the usual assumptions of beam theory. Causes for deviations of the model prediction from existing experimental results are discussed.
66 citations
TL;DR: In this article, closed-form solutions for elastica with axial and shear deformations were derived using elliptic integrals, using the Timoshenko beam theory of finite displacements with finite strains.
63 citations
TL;DR: In this paper, the dynamic stability of a rotating shaft subjected to axial periodic forces varying with time is studied by the finite element method by using Timoshenko beam theory, and the transverse shear effect is included in the shape functions.
44 citations
TL;DR: In this paper, the lower natural frequencies of vibration of the structural system described the title have been determined and are presented for a significant range of values of the governing mechanical and geometric parameters for two types of configurations of structural interest: discontinuous variation of the thickness and continuous, linear variation.
44 citations
TL;DR: In this article, a simple beam theory analysis is presented for the determination of residual stress patterns in beams or plates using a strain gage technique, which is valid for a general stress distribution which need not be symmetric with respect to the neural axis.
Abstract: A simple beam theory analysis is presented for the determination of residual stress patterns in beams or plates using a strain gage technique. The analysis is valid for a general stress distribution which need not be symmetric with respect to the neural axis. The experimental approach consists of attaching a strain gage on the surface of a beam or a plate and then grinding off the other side. The recorded strain vs thickness ground off data can be used to determine the corresponding stress profile.
43 citations
TL;DR: In this article, a new concept of explanation of the shear locking phenomenon occurring in the Timoshenko beam is presented and the global expression of the equilibrium equation for a whole beam is considered.
40 citations
TL;DR: In this paper, the authors investigated the influence of various effects on mode localization in multi-span beams and found that, in addition to the ratio of imperfection to coupling stiffness, transverse support stiffness and Timoshenko beam effects greatly affect the tendency of a structure to exhibit localized modes.
Abstract: The influence of numerous effects on mode localization in multi-span beams is investigated. Finite-element methods are used to study localization as a function of: Timoshenko beam effects; beam end conditions; span length, mass, and stiffness imperfection; viscous damping; axial force; transverse support and rotational coupling stiffness; and modeling resolution. Three configurations are studied, commencing with two different two-span models, and culminating in a ten-span configuration resembling lattice-type large space structures. Results indicate that, in addition to the ratio of imperfection to coupling stiffness being an important localization parameter, transverse support stiffness and Timoshenko beam effects greatly affect the tendency of a structure to exhibit localized modes.
37 citations
TL;DR: In this paper, a rational and straight-forward method for developing equivalent continuum models of large beam-like periodic lattice structures based on energy equivalence is introduced, where the Extended Timoshenko bean model is chosen to take account of the effects due to couplings between extension, transverse shear and bending deformations.
Abstract: Subscripts A rational and straight-forward method is introduced for developing equivalent continuum models of large beam-like periodic lattice structures based on energy equivalence Extended Timoshenko bean model is chosen to take account of the effects due to couplings between extension, transverse shear and bending deformations The procedure for developing continuum models involves utilizing well-defined existing finite element matrices directly in caluclating strain and kinetic energies from which equivalent continuum structural and dynamic properties are induced The numerical results of free vibration analysis show that the method developed in this paper gives very reliable dynamic characteristics compared to other methods Nomenclature
TL;DR: In this paper, a cubic, isoparametric, curved, composite beam element is proposed using the co-rotational (CR) finite element formulation, which is incorporated with the small deflection beam theory.
TL;DR: In this article, the discretization of the Timoshenko beam problem by thep and theh-p versions of the finite element method is considered and optimal error estimates are established.
Abstract: In this paper the discretization of the Timoshenko Beam problem by thep and theh-p versions of the finite element method is considered. Optimal error estimates are established. The locking phenomenon disappears as the thickness of the beam decreases.
TL;DR: In the finite element calculations of problems in solid mechanics, the method of selected reduced integration (SRI) is frequently used to eliminate locking phenomena as mentioned in this paper, and often SRI is equivalent to the application of a mixed method.
Abstract: In the finite element calculations of problems in solid mechanics the method of selected reduced integration (SRI) is frequently used to eliminate locking phenomena. Often SRI is equivalent to the application of a mixed method. When multigrid methods are applied, the formulation as a mixed method is by far superior. This is shown by an analysis of the Timoshenko beam.
TL;DR: An experimental and theoretical study of free vibrations in an excised human tibia results in two simple tibia models, based on uniform beam theory with inclusion of shear deformations.
TL;DR: In this paper, a beam deformation model was proposed to describe the combined bending and twisting of anisotropic composite material open-section beams subjected to pure bending and transverse loading.
TL;DR: In this paper, a PC program is presented for the preliminary design of composite beams based on composite mechanics and the finite element method (FEM), which allows accounting for shear effects on beam deflection.
TL;DR: In this article, a generalization of Timoshenko's beam theory by applying the asymptotic expansion method to a mixed variational formulation of the three dimensional linearized elasticity model is presented.
Abstract: In this work we obtain a generalization of Timoshenko's beam theory by applying the asymptotic expansion method to a mixed variational formulation of the three dimensional linearized elasticity model
TL;DR: In this paper, the dynamic stability of a Timoshenko beam with a thermal gradient lying on a variable Pasternak foundation and subjected to a pulsating axial force is studied.
TL;DR: A study of the natural vibration of a continuous Timoshenko curved beam on a Pasternak-type foundation is presented in this article, where the dynamic stiffness matrix of a curved member of constant section is derived and a two-span curved beam is given to illustrate the application of the proposed method and to show the effects of flexural and torsional rotary inertia, shear deformation, central angle of the arc, contact area between the beam and foundation, and the foundation constants on the natural frequencies of the beam.
TL;DR: In this paper, two tapered beam finite elements have been developed for rotor bearing analysis, and a linear approximation is used for the geometrical properties yielding closed form expressions for the element matrices.
TL;DR: In this article, the Timoshenko beam theory with corrections for the shear deformation and rotatory inertia effects is presented, and numerical results for various velocities of moving loads are given, and results are compared with response of Bernoulli-Euler beam theory.
Abstract: This letter presents the dynamic response of a simply supported beam excited by moving loads based on the Timoshenko beam theory with corrections for the shear‐deformation and rotatory inertia effects. Numerical results for various velocities of moving loads are given, and results are compared with response of a Bernoulli–Euler beam theory.
TL;DR: In this article, the optimal field-consistent assumed strain interpolation for the shear is derived and it is demonstrated that it has very high accuracy and is free from spurious force and moment oscillations.
Abstract: Curved beams in civil engineering applications call for out-of- plane bending and torsion under the action of out-of-plane transverse shear loads. The design of a quadratic displacement type curved beam element capable of representing shear deformation as in the Timoshenko beam theory will call for special attention to be-paid to the manner in which the shear strain is to be represented. Field-inconsistent representations of the out- of- plane transverse shear strain will result in a loss Gf efficiency and introduce spuriou oscillations in the bending moment, torsional moment and shear force. The optimal field-consistent assumed strain interpolation for the shear is derived here and it is demonstrated that it has very high accuracy and is free from spurious force and moment oscillations.
TL;DR: In this paper, the elastic Timoshenko beam theories and corresponding stiffness equations for finite rotation are solved to examine the effect of axial extension on the critical load of a column, and plays an important role in the buckling loads of higher modes.
TL;DR: In this paper, the beam theory for thin-walled composite beams, used extensively in the offshore industry in applications ranging from marine risers to platforms and frames, is presented.
Abstract: Presentation of the beam theory for thin-walled composite beams, used extensively in the offshore industry in applications ranging from marine risers to platforms and frames. This new theory, based on Timoshenko beam theory, can be incorporated into existing codes
01 Jan 1990
TL;DR: In this article, the development of both Kirchhoff and Timoshenko beam elements which are embedded in a continuously rotating frame is described, with emphasis on the consistent derivation of both the internal force vector and the tangent stiffness matrix.
Abstract: The paper describes the development of both Kirchhoff and Timoshenko beam elements which are embedded in a continuously rotating frame. Emphasis is placed on the consistent derivation of both the internal force vector and the tangent stiffness matrix.
TL;DR: In this paper, Modal shapes and natural frequency coefficients for a significant range of the mechanical and geometric parameters that come into play were determined for an exact solution of the title problem, and the beam dynamic characteristics agreed with values already available in the open literature.
TL;DR: In this paper, a solution of elementary beam theory and integrating polynomials in the thickness coordinate was used to generate kinematically-admissible strain fields and statically admissible strain field whose average approximates the actual 2D strain field in an orthotropic beam to within a relative mean square error of the order of magnitude of an arbitrary power of the ratio of the thickness of the beam to a characteristic wavelength.
Abstract: Starting with a solution of elementary beam theory and integrating polynomials in the thickness coordinate, we generate kinematically-admissible strain fields and statically-admissible strain fields whose average approximates the actual two-dimensional strain field in an orthotropic beam to within a relative mean square error of the order of magnitude of an arbitrary power of the ratio of the thickness of the beam to a characteristic wavelength of the elementary beam solution.
TL;DR: In this article, a finite element method using a Timoshenko beam model is used to study both the axial and lateral vibrations of a manipulator linkage system, and results for quasi-static and kineto-elastodynamic analyses are compared.
TL;DR: In this article, a two-dimensional transient thermal stress analysis of a laminated beam due to a partially distributed heat supply is presented, where the beam is composed of different materials in multilayers.
Abstract: This paper is concerned with a two-dimensional transient thermal stress analysis of a laminated beam due to a partially distributed heat supply. The beam is composed of different materials in multilayers. For the laminated composite beam we use the finite cosine transform and the Laplace transform for the temperature field and we adapt the elementary beam theory to the thermoelastic field. We then evaluate the temperature change, thermal stress distribution, and thermal deformation in a transient state. We apply the proposed theoretical method to the analysis of a beam with nonhomogeneous material properties, and examine the distributions of thermal stress and thermal deformation and the effect of relaxation of the stress distributions in a nonhomogeneous beam.