Topic
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.
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TL;DR: In this article, the static behavior of composite beams with arbitrary lay-ups using various refined shear deformation theories is presented, which do not require shear correction factor, account for parabolical variation of shear strains and consequently shear stresses through the depth of the beam, and have strong similarity with Euler-Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions.
97 citations
TL;DR: In this article, a non-local Euler beam model with axial prestress is established based on the theory of nonlocal elasticity, which can be applied to modeling and characterization of size-dependent mechanical properties of micro- or nanobeam-based devices.
Abstract: In this article, a nonlocal Euler beam model with axial prestress is established based on the theory of nonlocal elasticity. Frequency equations and modal shape functions of beam structures with axial compressive or tensile prestresses under some typical boundary conditions are derived based on the model. The corresponding dynamic properties are presented and discussed in detail, which are shown to be very different from those predicted by classic elasticity theory. The theoretical model and results presented in this article can be considered as modifications of their counterparts based on classical continuum theory and can be applied to modeling and characterization of size-dependent mechanical properties of micro- or nanobeam-based devices.
97 citations
TL;DR: In this article, the effects of shear deformation, rotary inertia and the length of load distribution on the vibration of the Timoshenko beam have been analyzed for the case of uniform partially distributed moving masses.
97 citations
TL;DR: In this article, the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets were investigated.
Abstract: This paper investigates the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets within the framework of Timoshenko beam theory. The material properties of FG-CNTRCs are assumed to vary in the thickness direction, and are estimated through a micromechanical model. The governing equations and boundary conditions are derived by using Hamilton's principle and discretized by employing the differential quadrature (DQ) method to obtain the natural frequency and critical buckling load of the sandwich beam. A detailed parametric study is conducted to study the effects of carbon nanotube volume fraction, core-to-face sheet thickness ratio, slenderness ratio, and end supports on the free vibration characteristics and buckling behavior of sandwich beams with FG-CNTRC face sheets. The vibration behavior of the sandwich beam under an initial axial force is also discussed. Numerical results for sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets are also provided for comparison.
97 citations
Journal Article•
TL;DR: In this paper, the effect of various material distributions on the displacements and the stresses of the beam is examined, and numerical results indicate that stress distributions in FG beams are very different from those in isotropic beams.
Abstract: Static analysis of a functionally graded (FG) simply-supported beam subjected to a uniformly distributed load has been investigated by using Ritz method within the framework of Timoshenko and the higher order shear deformation beam theories. The material properties of the beam vary continuously in the thickness direction according to the power-law form. Trial functions denoting the transverse, the axial deflections and the rotation of the cross-sections of the beam are expressed in trigonometric functions. In this study, the effect of various material distributions on the displacements and the stresses of the beam are examined. Numerical results indicate that stress distributions in FG beams are very different from those in isotropic beams
97 citations