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.

Nonlinear thermal dynamic buckling of FGM beams

Abstract: Based on the nonlinear dynamic analysis, dynamic buckling and imperfection sensitivity of the FGM Timoshenko beam subjected to sudden uniform temperature rise are studied. Initial geometric imperfection of the beam is also taken into account. It is assumed that during deformation the beam is resting over a conventional three-parameter elastic foundation with softening/hardening cubic non-linearity. The analysis is performed with considering temperature dependency assumption of each thermo-mechanical property of the FGM beam. The governing nonlinear dynamic equations are derived based on the generalized Hamilton principle. In the spatial approximation of the problem, a set of ordinary differential equations in time is obtained by the conventional multi-term Ritz method. These equations are converted into a set of algebraic equations by utilizing the Newmark family of time approximation scheme. The obtained non-linear algebraic equations are solved via the well known Newton–Raphson iterative scheme. The Budiansky–Roth criterion is used to detect the unbounded motion type of dynamic buckling. Results reveal that for beams with stable post-buckling equilibrium path, no dynamic buckling occurs according to the Budiansky–Roth criterion. However, dynamic buckling may occur for the FGM beams resting on sufficiently stiff softening elastic foundation due to their unstable post-buckling equilibrium paths.

Analysis of the Flexure Test for Laminated Composite Materials

Abstract: Equations applicable to a general class of symmetrically laminated beams are derived by considering a beam as a special case of a laminated plate. The beam bending stiffness thus becomes a function of all the bending stiffness coefficients of a laminated plate. The validity of this approach is verified by comparing theoretical results to flexure data on graphite/epoxy angle-ply and quasi-isotropic laminates. In addition, it is shown that flex strength on general composite laminates is extremely difficult to interpret, even though the stresses can be calculated from the modified beam theory. Discontinuities in the in-plane stresses at layer interfaces lead to a state of stress which is difficult to compare to standard laminate tensile coupons.

Consistent Modeling of Rotating Timoshenko Shafts Subject to Axial Loads

Abstract: The equations of motion of a flexible rotating shaft have been typically derived by introducing gyroscopic moments, in an inconsistent manner, as generalized work terms in a Lagrangian formulation or as external moments in a Newtonian approach. This paper presents the consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load. The coupling between flexural and torsional vibration due to mass eccentricity is not considered. In addition, a new approach for calculating correctly the effect of an axial load for a Timoshenko beam is presented based on the change in length of the centroidal line. It is found that the use of either a floating frame approach with the small strain assumption or a finite strain beam theory is necessary to obtain a consistent derivation of the terms corresponding to gyroscopic moments in the equations of motion. However, the virtual work of an axial load through the geometric shortening appears consistently in the formulation only when using a finite strain beam theory.

A Lagrangian Hencky-type non-linear model suitable for metamaterials design of shearable and extensible slender deformable bodies alternative to Timoshenko theory

Abstract: Among the most studied models in mathematical physics, Timoshenko beam is outstanding for its importance in technological applications. Therefore it has been extensively studied and many discretizations have been proposed to allow its use in the most disparate contexts. However, it seems to us that available discretization schemes present some drawbacks when considering large deformation regimes. We believe these drawbacks to be mainly related to the fact that they are formulated without keeping in mind the mechanical phenomena for describing which Timoshenko continuum model has been proposed. Therefore, aiming to analyze the deformation of complex plane frames and arches in elastic large displacements and deformation regimes, a novel intrinsically discrete Lagrangian model is here introduced whose phenomenological application range is similar to that for which Timoshenko beam has been conceived. While being largely inspired by the ideas outlined by Hencky in his renowned doctoral dissertation, the presented approach overcomes some specific limitations concerning the stretch and shear deformation effects. The proposed model is applied to get the solutions for some relevant benchmark tests, both in the case of arch and frame structures. It is proved that, also when shear deformation effects are of relevance, the enriched, yet simple, model and numerical computation scheme herein proposed can be profitably used for efficient structural analyses of non-linear mechanical systems in rather nonstandard situations.