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Showing papers on "Timoshenko beam theory published in 1995"


Journal ArticleDOI
TL;DR: In this article, a hierarchical displacement interpolation was proposed for the beam theory of Reissner, which is capable of eliminating both shear and membrane locking phenomena in the finite element beam theory.

302 citations


Journal ArticleDOI
TL;DR: In this paper, the authors pre-sents the deflection and stress resultants of single-span Timoshenko beams, with general loading and boundary conditions, in terms of the corresponding Euler-Bernoulli beam solutions.
Abstract: The Timoshenko beam theory is an extension of the Euler-Bernoulli beam theory to allow for the effect of transverse shear deformation. This more refined beam theory relaxes the normality assumption of plane sections that remain plane and normal to the deformed centerline. The relaxation takes the form of allowing an additional rotation to the bending slope, and thus admits a nonzero shear strain. This paper pre-sents the deflection and stress resultants of single-span Timoshenko beams, with general loading and boundary conditions, in terms of the corresponding Euler-Bernoulli beam solutions. These exact relationships allow engineering designers to readily obtain the bending solutions of Timoshenko beams from the familiar Euler-Bernoulli solutions without having to perform the more complicated flexural–shear-deformation analysis.

137 citations


Journal ArticleDOI
TL;DR: In this article, a finite strain continuum theory is presented for unidirectional fiber reinforced composites under in-plane loading, and the constitutive response is expressed in terms of couple stress theory, and deduced from a unit cell of a linear elastic Timoshenko beam embedded in a non-linear elastic-plastic matrix.
Abstract: A finite strain continuum theory is presented for unidirectional fibre reinforced composites under in-plane loading. The constitutive response is expressed in terms of couple stress theory, and is deduced from a unit cell of a linear elastic Timoshenko beam embedded in a non-linear elastic-plastic matrix. The continuum theory is implemented within a finite element framework and is used to analyse compressive failure of polymer matrix composites by fibre microbuckling. It is assumed that microbuckling initiates from an imperfection in the form of a finite elliptical region of fibre waviness. The calculations show that the compressive strength decreases with increasing imperfection spatial size from the elastic bifurcation value of Rosen (1965, Fibre Composite Materials, pp. 37–75, American Society Metals Seminar) to the imperfection-sensitive infinite band strength given by Fleck et al. [1995, J. Appl. Mech. 62, 329–337.].

120 citations


Journal ArticleDOI
TL;DR: In this article, an analytical model for load-displacement curves of concrete beams is presented, where the fracture is modeled by a fictitious crack in an elastic layer around the midsection of the beam.
Abstract: An analytical model for load-displacement curves of concrete beams is presented. The load-displacement curve is obtained by combining two simple models. The fracture is modeled by a fictitious crack in an elastic layer around the midsection of the beam. Outside the elastic layer the deformations are modeled by beam theory. The state of stress in the elastic layer is assumed to depend bilinearly on local elongation corresponding to a linear softening relation for the fictitious crack. Results from the analytical model are compared with results from a more detailed model based on numerical methods for different beam sizes. The analytical model is shown to be in agreement with the numerical results if the thickness of the elastic layer is taken as half the beam depth. It is shown that the point on the load-displacement curve where the fictitious crack starts to develop and the point where the real crack starts to grow correspond to the same bending moment. Closed-form solutions for the maximum size of the fracture zone and the minimum slope on the load-displacement curve are given.

114 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a finite element formulation for static analysis of linear elastic spatial frame structures and apply exact non-linear kinematic relationships of the space finite-strain beam theory, assuming the Bernoulli hypothesis and neglecting the warping deformations of the cross-section.

108 citations


01 Apr 1995
TL;DR: In this paper, a positive definite preconditioner is constructed for saddle point problems with penalty term and it is proved that the condition number of the preconditionaled system can be made independent of the discretization and the penalty parameters.
Abstract: Iterative methods are considered for saddle point problems with penalty term A positive definite preconditioner is constructed and it is proved that the condition number of the preconditioned system can be made independent of the discretization and the penalty parameters Examples include the pure displacement problem in linear elasticity, the Timoshenko beam, and the Mindlin-Reissner plate Key words: Saddle point problems, penalty term, nearly incompressible materials, Timoshenko, Mindlin-Reissner, preconditioned conjugate residual method, multilevel, domain decomposition Please note: This report is a revised version of tr676

103 citations


Journal ArticleDOI
TL;DR: In this paper, the free vibration frequencies of Timoshenko beams on two-parameter elastic foundations were examined and two variants of the equation of motion were deduced, in which the second foundation parameter is a function of the total rotation of the beam or a function due to bending only, respectively.

100 citations


Journal ArticleDOI
TL;DR: In this article, the linear flexural stiffness, incremental stiffness, mass, and consistent force matrices for a simple two-node Timoshenko beam element are developed based upon Hamilton's principle, where interdependent cubic and quadratic polynomials are used for the transverse and rotational displacements, respectively.

89 citations


Journal ArticleDOI
TL;DR: In this article, an analytic solution for free and forced vibrations of stepped Timoshenko beams is presented and used for the approximate analysis of generally non-uniform Timoshenko beam, where the frequency equation is expressed in terms of some initial parameters at one end of the beam; while in the case of forced vibrations, the solution may be obtained by solving a set of algebraic equations with only two unknowns.

88 citations


Journal ArticleDOI
TL;DR: In this paper, the quasi-static and dynamic responses of a linear viscoelastic beam are solved numerically by using the hybrid Laplace transform/finite element method.
Abstract: The quasi-static and dynamic responses of a linear viscoelastic beam are solved numerically by using the hybrid Laplace transform/finite element method In the analysis, the Timoshenko beam theory, which includes the transverse shear and rotatory inertia effect and conventional beam theory, are used to solve this problem The temperature field is assumed to be constant and homogeneous and that the relaxation modulus has the form of the Prony series In the hybrid method, the Laplace transform with respect to time is applied to the coupled equations and the finite element model is developed by applying Hamilton's variational principle without any integral transformation The numerical results of quasi-static and dynamic responses for the models of Maxwell fluid and three parameter solid types are presented and discussed

81 citations


Journal ArticleDOI
TL;DR: In this article, the Bresse-Timoshenko beam theory was applied in the computation of the eigenvalues of the equations of motion governing in-plane and out-of-plane vibration of circular arches.

Journal ArticleDOI
TL;DR: In this paper, a three-layered beam theory has been given in which the continuity of displacements and the transverse shear stresses has been satisfied at the interfaces, and the final displacement parameters of the problem are only those corresponding to the base layer.

Journal ArticleDOI
TL;DR: In this article, a full Lagrangian version and an Eulerian-Lagrangian formulation of the beam deformation problem are proposed, where a Galerkin projection is applied to discretize the resulting governing partial differential equations.

Journal ArticleDOI
TL;DR: In this paper, simple two-noded and three-nodes general curved beam elements have been formulated on the basis of assumed strain fields and Timoshenko's beam theory, and it is shown that these elements give better convergent characteristics than the modified isoparametric curve elements that have been shown in existing studies.

Journal ArticleDOI
TL;DR: In this article, the dynamic response of a rotating shaft subject to axial force and moving loads is analyzed by using Timoshenko beam theory and the assumed mode method and the deformations of the shaft are expressed in terms of an inertial reference frame.

Journal ArticleDOI
TL;DR: An efficient formulation for dynamic analysis of planar Timoshenko's beam with finite rotations is presented in this paper, where both an inertial frame and a rotating frame are introduced to simplify computational manipulation.

Journal ArticleDOI
TL;DR: In this paper, a finite element is formulated for the torsion problems of thin-walled beams, based on Benscoter's beam theory, which is valid for open and also closed cross-sections.

Journal ArticleDOI
TL;DR: In this paper, a stiffness matrix for a beam element with shear effect on an elastic foundation is developed using the differential-equation approach for plane-frame analysis and small-displacement theory and linear linear programming.
Abstract: A stiffness matrix for a beam element with shear effect on an elastic foundation is developed using the differential-equation approach for plane-frame analysis. Small-displacement theory and linear...

Journal ArticleDOI
Dong-Min Lee1, In Lee1
TL;DR: In this article, the analysis of vibration characteristics of anisotropic stiffened plates with eccentric stiffeners has been performed using the finite element method based on the shear deformable plate theory.

Journal ArticleDOI
TL;DR: In this article, the authors derived the equation of motion which governs the lateral vibration of a spinning pretwisted beam and applied the Galerkin method to obtain the associated finite element equations of motion.

Journal ArticleDOI
Seong Min Jeon1, Maeng Hyo Cho1, In Lee1
TL;DR: In this article, the static and dynamic behavior of composite box beams is investigated using a large deflection beam theory, and the finite element equations of motion for beams undergoing arbitrary large displacements and rotations, but small strains, are obtained from Hamilton's principle.

Journal ArticleDOI
TL;DR: In this paper, a modified beam theory analysis is presented for the ENF specimen, which is used to evaluate the mode II delamination fracture toughness of fiber reinforced composite materials, and the analysis combines the solution of a beam on a generalized elastic foundation to incorporate the effect of crack tip deformation, and a Timoshenko Beam Theory solution of ENF to incorporate transverse shear on the predicted energy release rates.
Abstract: A new modified beam theory analysis is presented for the ENF specimen, which is used to evaluate the mode II delamination fracture toughness of fiber reinforced composite materials. The analysis combines the solution of a beam on a generalized elastic foundation to incorporate the effect of crack tip deformation, and a Timoshenko Beam Theory solution of the ENF to incorporate transverse shear on the predicted energy release rates. A distinctive feature of this approach is that crack tip deformation and shear deformations are treated separately and explicitly in accounting for deviations from simple beam theory. Two unknown parameters are introduced, however, that must be determined by comparison with finite element solutions. The resulting solution nevertheless demonstrates considerable accuracy over a wide range of material properties (e.g., axial to shear modulus ratios) and crack lengths. In addition, the current analysis compares very favorably with other analyses of the ENF that incorporate the effec...

Journal ArticleDOI
TL;DR: In this paper, the effects of a viscoelastic adhesive layer on the dynamic response and structural damping of sandwich structures were studied by employing a newly developed sandwich beam theory.
Abstract: The effects of a viscoelastic adhesive layer on the dynamic response and structural damping of sandwich structures are studied by employing a newly developed sandwich beam theory. The two face layers are considered as ordinary beams (Euler beams) with both axial and bending resistance. The core material is considered to be viscoelastic. A newly developed high-order displacement field assumption is used in order to achieve a more accurate kinematics of the flexible viscoelastic core than would be possible under the classical assumptions for sandwich beams. Imperfect interface conditions between faces and core are defined as linear relations between longitudinal displacement discontinuities and the transverse shear stress at the adhesive layer. The viscoelastic properties of the adhesive layer and the core material are assumed in a complex modulus formula that is a function of frequency for a given temperature. The linear equations of motion that describe the vibration of the sandwich finite beam a...


Journal ArticleDOI
TL;DR: In this paper, a nonlinear elastic foundation model was developed to predict the mixed-mode (modes I and II) delamination failure of laminated composites, based on the linear elastic two-dimensional asymptotic solution of the strain field ahead of the crack tip and appropriate nonlinear constitutive laws.
Abstract: A nonlinear elastic foundation model has been developed to predict the mixed-mode (modes I and II) delamination failure of laminated composites. Two types of nonlinear elastic foundations were used to represent pure mode I and pure mode II components of the material failure ahead of the crack tip. One is a tension spring foundation for mode I component and the other is a shear spring foundation to represent the mode II component. Each spring foundation was characterized based on the linear elastic two-dimensional asymptotic solution of the strain field ahead of the crack tip and appropriate nonlinear constitutive laws. To predict the onset of crack propagation, the model employed an energy criterion as a failure condition derived from experimental trends of mixed-mode failure of laminated composites. Mode I, mode II, and mixed-mode fracture tests were performed to investigate the validity of the current model. A finite element was developed and incorporated into a computer code to simulate laboratory fracture tests, utilizing Timoshenko's first-order shear beam theory and a nonlinear constitutive law. The current model predicted the experimental results of load vs displacement curves closely. It also exhibited a satisfactory mode separation capability and was able to predict mode mixture results available in the literature.

Journal ArticleDOI
TL;DR: In this paper, a co-rotational finite element formulation for the dynamic analysis of a planar curved Euler beam is presented, where the Euler-Bernoulli hypothesis and the initial curvature are properly considered for the kinematics of a curved beam.

Journal ArticleDOI
TL;DR: In this paper, the free vibration, dynamic response, and static buckling of a layered beam is studied, which is composed of two identical parallel beams with a viscoelastic-material layer in between.
Abstract: The studies of the free vibration, dynamic response, and static buckling of a layered beam are presented. This layered beam is composed of two identical parallel beams with a viscoelastic-material layer in between. The boundary conditions of these two parallel beams (called the upper and lower beams in the present paper) can be different. The dynamic shape functions and the dynamic-stiffness matrix of such a layered beam are established directly based on the theory of an axially loaded damped Timoshenko beam on a viscoelastic foundation by superposition scheme. The dynamic interactions between these two parallel beams and the viscoelastic layer of a layered beam are emphasized. A simple layered-beam example is included for demonstrations and discussions.

Journal ArticleDOI
TL;DR: In this paper, two sets of exact natural frequency and mode shape formulae for an axially loaded Timoshenko uniform single-span beam carrying elastically supported end masses are derived.

Journal ArticleDOI
TL;DR: In this paper, the exact vibration frequencies for variable cross-section beams are found using the dynamic stiffness matrix approach, and compared with known results of beams with various taper ratios.
Abstract: The Timoshenko beam model incorporates the effect of shear deformations and rotary inertia in the vibration response of beams. For constant cross-section beams it was shown that the effect is dependent on the aspect ratio of the beams, and for beams with large ratio the effect is small. In this work exact vibration frequencies for variable cross-section beams are found using the dynamic stiffness matrix approach. An example is given and compared with known results of beams with various taper ratios.

Journal ArticleDOI
TL;DR: In this article, a curvature-based beam element with six degrees of freedom and two-, three-, four, four, and five-node Timoshenko straight beam elements with four, five, six and seven degree of freedom, respectively, are proposed to eliminate stiffness locking when applied to the dynamic analysis of the beams.