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.

Modeling and analysis of microtubules based on a modified couple stress theory

Abstract: Based on a modified couple stress theory, a new Timoshenko beam model is established to address the size effect of microtubules (MTs) in this paper. The bending equation and the buckling equation are derived from the minimum total potential energy principle. Results obtained from the present model show that length dependence of MTs is related not only to shear effect but also to size effect, and the size effect is coupled in the shear effect, which means that the phenomenon of length dependence will disappear when the shear effect is neglected. Moreover, when very long MTs are considered, the persistence lengths are related to the internal material length scale parameter, which is different from the conclusions obtained from the classical and previous nonlocal beam models. The effect of the internal material length scale parameter on the buckling wavelength, the buckling growth rate and the buckling amplitude of the MTs is also discussed in this paper, and a comparison between present and previous results is presented.

A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler–Bernoulli beams

Abstract: We present a finite element discrete model for pantographic lattices, based on a continuous Euler–Bernoulli beam for modeling the fibers composing the pantographic sheet. This model takes into account large displacements, rotations and deformations; the Euler–Bernoulli beam is described by using nonlinear interpolation functions, a Green–Lagrange strain for elongation and a curvature depending on elongation. On the basis of the introduced discrete model of a pantographic lattice, we perform some numerical simulations. We then compare the obtained results to an experimental BIAS extension test on a pantograph printed with polyamide PA2200. The pantographic structures involved in the numerical as well as in the experimental investigations are not proper fabrics: They are composed by just a few fibers for theoretically allowing the use of the Euler–Bernoulli beam theory in the description of the fibers. We compare the experiments to numerical simulations in which we allow the fibers to elastically slide one with respect to the other in correspondence of the interconnecting pivot. We present as result a very good agreement between the numerical simulation, based on the introduced model, and the experimental measures.