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.

On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams

Abstract: In this work, a trigonometric refined beam theory for the bending, buckling and free vibration analysis of carbon nanotube-reinforced composite (CNTRC) beams resting on elastic foundation is developed. The significant feature of this model is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the Timoshenko beam (TBM) without including a shear correction factor. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are assessed by employing the rule of mixture. To examine accuracy of the present theory, several comparison studies are investigated. Furthermore, the effects of different parameters of the beam on the bending, buckling and free vibration responses of CNTRC beam are discussed.

Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method

Abstract: In this paper, an analytical method is developed to study the dynamic behavior of functionally imperfect Euler-Bernoulli and Timoshenko graded beams with differing boundary conditions, namely, hinged-hinged, clamped-clamped, clamped-hinged, and clamped-free. A transfer matrix method is used to obtain the natural frequency equations. The modified rule of mixture is used to describe the material properties of the functionally graded beams having porosities. The porosities are assumed to be evenly distributed over the beam cross-section. In this study, the effects of boundary conditions, material volume fraction index, slenderness ratio, beam theory, and porosity on natural frequency are determined. The present results are validated with results available in the literature.

A formulation and implementation of geometrically exact curved beam elements incorporating finite strains and finite rotations

Abstract: This paper deals with the formulation and implementation of the curved beam elements based on the geometrically exact curved/twisted beam theory assuming that the beam cross-section remains rigid. The summarized beam theory is used for the slender beams or rods. Along with the beam theory, some basic concepts associated with finite rotations and their parametrizations are briefly summarized. In terms of a non-vectorial parametrization of finite rotations under spatial descriptions, a formulation is given for the virtual work equations that leads to the load residual and tangential stiffness operators. Taking the advantage of the simplicity in formulation and clear classical meanings of both rotations and moments, the non-vectorial parametrization is applied to implement a four-noded 3-D curved beam element, in which the compound rotation is represented by the unit quaternion and the incremental rotation is parametrized using the incremental rotation vector. Only static problems are considered. Conventional Lagrangian interpolation functions are adopted to approximate both the reference curve and incremental rotation of the deformed beam. Reduced integration is used to overcome locking problems. The finite element equations are developed for static structural analyses, including deformations, stress resultants/couples, and linearized/nonlinear bifurcation buckling, as well as post-buckling analyses of arches subjected to different types of loads, such as self-weight, snow, and pressure (wind) loads. Several examples are used to test the formulation and its Fortran implementation.