Mathematical and Numerical Calculation of the Interlayer Slip of a Two-Layer Glued Beam

This study analyses the spatial variation of the deflection, rotation, and slip at the interface of two-layer bamboo scrimber-concrete composite beam simply supported under uniform transverse load on its entire length. The Timoshenko model is considered, and the equations are solved using the analytical methods and direct numerical simulation based on finite differences schemes and a Fortran code. The results obtained show that it is a good agreement between the results from the mathematical calculation and those obtained from the numerical simulation.

Stress-Based FEM in the Problem of Bending of Euler–Bernoulli and Timoshenko Beams Resting on Elastic Foundation

The stress-based finite element method is proposed to solve the static bending problem for the Euler–Bernoulli and Timoshenko models of an elastic beam. Two types of elements—with five and six degrees of freedom—are proposed. The elaborated elements reproduce the exact solution in the case of the piece-wise constant distributed loading. The proposed elements do not exhibit the shear locking phenomenon for the Timoshenko model. The influence of an elastic foundation of the Winkler type is also taken into consideration. The foundation response is approximated by the piece-wise constant and piece-wise linear functions in the cases of the five-degrees-of-freedom and six-degrees-of-freedom elements, respectively. An a posteriori estimation of the approximate solution error is found using the hypercircle method with the addition of the standard displacement-based finite element solution.

Static and Dynamic Responses of Micro-Structured Beams

In this study, we developed a one-dimensional Timoshenko beam model, embedded in a 3D space for static and dynamic analyses of beam-like structures. These are grid cylinders, that is, micro-structured bodies, made of a periodic and specifically designed three-dimensional assembly of beams. Derivation is performed in the framework of the direct 1D approach, while the constitutive law is determined by a homogenization procedure based on an energy equivalence between a cell of the periodic model and a segment of the solid beam. Warping of the cross-section, caused by shear and torsion, is approximatively taken into account by the concept of a shear factor, namely, a corrective factor for the constitutive coefficients of the equivalent beam. The inertial properties of the Timoshenko model are analytically identified under the hypothesis, and the masses are lumped at the joints. Linear static and dynamic responses of some micro-structured beams, taken as case studies, are analyzed, and a comparison between the results given by the Timoshenko model and those obtained by Finite-Element analyses on 3D frames is made. In this framework, the effectiveness of the equivalent model and its limits of applicability are highlighted.

Critical Comparison of Bresse–Timoshenko Beam Theories for Parametric Instability in the Presence of Pulsating Load

In this paper, we investigate parametric instability of Bresse–Timoshenko columns subjected to periodic pulsating compressive loads. The results are derived from three theories, namely the Bernoulli–Euler model for thin beams and two versions of the Bresse–Timoshenko model valid for thick beams: The truncated Bresse–Timoshenko model and the Bresse–Timoshenko model based on slope inertia. The truncated Bresse–Timoshenko model has been derived from asymptotic analysis, whereas the Bresse–Timoshenko model based on slope inertia is an alternative shear beam model supported by variational arguments. These models both take into account the rotary inertia and the shear effect. Simple supported boundary conditions are considered, so that the time-dependent deflection solution can be decomposed into trigonometric spatial functions. The instability domain in the load–frequency space is analytically characterized from a Meissner-type parametric equation. For small slenderness ratio, these last two Bresse–Timoshenko models coincide but for much higher slenderness ratio, the parametric instability regions in the load–frequency space shift to the left and widen them as compared to the Bernoulli–Euler model. The importance of these effects differs between the models.

A Molecular Dynamic Study on Nonlinear Vibration Behaviors of Fe Nanowires

In this paper, vibration behaviors of Fe nanowires are investigated by using the large-scale molecular dynamics (MD) simulations. It is observed that the vibration frequency of nanowires rises slightly and nonlinearly with the increase of initial actuation amplitude. Based on the atomic arrangement, a discrete spring-mass model is developed. Its nonlinear elastic relation is used to explain this phenomenon. In addition, Fe nanowires with different lengths and heights show different vibration properties in this work. The ratio between the length ([Formula: see text]) and the height ([Formula: see text]) of nanowires has a significant influence on vibration behaviors. The vibration properties of nanowires can be explained by the Euler–Bernoulli model when the ratio is relatively large, while they can be illustrated by the Timoshenko model when the ratio is relatively small.

Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction. The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.