Search

This study is the first of its kind to apply an analytical technique to offer an accurate solution for the static buckling and static bending of functionally graded (FG) sandwich nanobeams, in which the core layer is an auxetic honeycomb. One notable aspect of this work is the use of third-order shear deformation theory for the computations. It is worth noting that the displacement field of the nanobeam is contingent upon a single parameter. This approach enables the resolution of stability and static bending issues encountered in nanobeams including auxetic honeycomb cores, while also providing a realistic depiction of the beam's mechanical behavior. The two surface layers are composed of different materials, each of which has mechanical characteristics that change in accordance with the exponential function law. The precise solution described in this work is very adaptable and may be used to investigate the mechanical behavior of beams with different boundary constraints, taking into consideration the effect of the nonlocal parameter. When the angle α of the cell varies, the honeycomb core's mechanical characteristics, such as Poisson's coefficient and elastic modulus E , vary continually. This results in static bending and buckling responses that are distinct from those of other auxetics. This study also found it intriguing that the wall angle α has a value of around 90° and that sandwich nanobeams have the highest load capacity. In addition, numerical calculations have been performed to demonstrate the influence of certain geometrical parameters, materials, and boundary constraints on the critical buckling load and maximum deflection of the nanobeam. • This study is the first of its kind to apply an analytical technique for the static buckling and static bending of FG sandwich nanobeams, in which the core layer is an auxetic honeycomb. • This study offers calculation findings demonstrating the effect of geometrical factors, materials, and boundary conditions on the ultimate load response and maximum displacement of FG sandwich nanobeams. • It is discovered that a certain value for the wall angles of the core layer cell yields the highest possible performance from this beam. [ABSTRACT FROM AUTHOR]

In this paper we have discussed the frictional buckling behavior of a slender rod constrained in a horizontal cylinder. Buckling and post-buckling behaviors including the onset of helical buckling and subsequent axial force transfer are interpreted in a new way. Helical buckling and concomitant low force transfer efficiency which would prevent further axial extended reach is important to engineering structures, such as coiled tubing operations in petroleum industry. By means of the beam-column method, new governing differential equation of frictional buckling are derived to predict critical buckling force. We also investigate the transfer efficiency of axial force quantifying the effect of axial friction on rod lockup phenomenon in post-buckling analyses by perturbation solution. The coupling effect between axial force and friction is solved for the first time in this paper. The bending moment at the lock-up limit which would cause the rod to rupture is also analyzed. Finally, we have compared the proposed model with experimental results to verify its validity. Through these analyses, we have provided another interpretation to the existing experiment and numerical simulation results of frictional buckling. The derived results are simple and convenient for a problem in industrial practice. • New buckling differential equations of frictionally, cylindrically restrained rod are derived. • Critical buckling loads of frictional buckling are solved from the new buckling equations. • Analytical solutions about axial force transfer efficiency are derived by perturbation solution. • Good agreement is found between the theory and experimental results. [ABSTRACT FROM AUTHOR]

Analytical formulations and solutions for the stability analysis of simply supported Functionally Graded Material (FGM) sandwich plates hitherto not reported in the literature based on two higher-order refined computational models available in the literature are presented. These computational models are based on Taylor's series expansion of the displacements in the thickness coordinate and incorporate the realistic parabolic distribution of transverse strains through the plate thickness. One of them with twelve degrees-of-freedom considers the effects of both transverse shear and normal strain/stress while the other with nine degrees-of-freedom includes only the effect of transverse shear deformation. In addition another higher-order model and the first-order model developed by other investigators and available in the literature are also considered for the evaluation purpose. For mathematical modeling purposes, the Poisson's ratio of the material is considered as constant whereas Young's modulus is assumed to vary through the thickness according to the power law function. The governing equations of equilibrium for buckling analysis are obtained using the Principle of Minimum Potential Energy (PMPE). Solutions are obtained in closed form using Navier's technique by solving the eigenvalue problem. The comparison of the present results with the available elasticity solutions and the results computed independently using the first-order and another higher-order theory available in the literature shows that the higher-order refined theory with 12 degrees-of-freedom predicts the critical buckling load more accurately than all other theories considered in this paper. After establishing the accuracy of prediction, extensive numerical results for FGM sandwich plates using all the models are presented which will serve as a benchmark for future investigations. [ABSTRACT FROM AUTHOR]

This paper provides a review of models and solutions for the buckling and postbuckling of beams available from the 50s of the last century to date. Beams with axially unrestrained (movable) ends and restrained (immovable) ends are covered. In each class, the formulation of the nonlinear buckling problem for the buckling loads and the postbuckling states is discussed and the underlying assumptions are highlighted. For relatively large-amplitude buckling of beams with movable ends, approximate analytical solutions up to the third order are presented and compared with the exact solutions expressed in terms of elliptic integrals. For beams with immovable ends, buckling involves midplane stretching that makes the nonlinear buckling problem takes the same form of the standard eigenvalue problem and, hence, exact solutions are affordable. This review combines the research outcomes on buckled beams from two scientific viewpoints: the structural dynamics and the nonlinear vibration viewpoints, respectively. Moreover, it presents in one place the formulation and the exact solutions for the buckling of beams to serve as an on-demand resource for researchers concerned with the buckling and postbuckling of beams. • Presents a comprehensive review on the modeling of buckling and postbuckling of thin elastic beams. • Beams with sliding ends and immovable ends are considered. • Exact solution for the buckling loads and postbuckling amplitude are presented. • The review covers the period since the 50s of the last century to date. [ABSTRACT FROM AUTHOR]

The paper is concerned with the solution to the buckling problem of a plate having two opposite edges free and subjected to a uniform compressive load applied to another two fully clamped edges. At first glance, the problem might look simple, resembling the buckling of a compressed strip-beam. However, this is not the case. The buckled plate bends between the free edges as opposed to the beam buckling mode. The situation even more complicated when the plate material is not isotropic since the bending depends not only on the plate's aspect ratio but also on the elastic properties of the material. In this work, an analytical solution for such a buckling problem formulated for an orthotropic composite plate and based on the combined Kantorovich and generalised Galerkin methods is presented, and a compact analytical formula for the critical load is derived. The solution was verified by comparison with the finite element analysis. • Solution to the buckling problem of an orthotropic CCFF plate subjected to a uniaxial compressive load is presented. • The problem solved using the combined Kantorovich and generalised Galerkin methods. • A compact analytical formula for the critical load is derived. • The results were successfully verified by the finite element analyses. [ABSTRACT FROM AUTHOR]