In this paper, a displacement-based, variationally consistent, two variable refined theory for shear deformable beams is presented. The beam is assumed to be of linearly elastic, homogeneous, isotropic material and has a uniform rectangular cross-section. In this theory, the beam axial displacement and beam transverse displacement consist of bending components and shearing components. The assum...

In this paper, a nonlocal foundation model is proposed to analyze the vibration and instability of a Y-shaped single-walled carbon nanotube (Y-SWCNT) conveying fluid. In order to achieve more accurate results, fourth order beam theory is utilized to obtain strain-displacement relations. For the first time, a nonlocal model is presented based on nonlocal elasticity and the effects of nonlocal fo...

Abstract This paper studies the boundary value problem for a fourth-order difference equation with three quasidifferences. The new existence criterion of at least one solution to issues considered is obtained using theory variational methods. main result illustrated in some examples.

* Correspondence: [email protected] Department of Mathematics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, P. R. China Full list of author information is available at the end of the article Abstract This article is concerned with the existence of nontrivial solutions for a non-positive fourth-order two-point boundary value problem (BVP) and the existence of positive solutions for a s...

We present new results on the existence of multiple positive solutions of a fourth-order differential equation subject to nonlocal and nonlinear boundary conditions that models a particular stationary state of an elastic beam with nonlinear controllers. Our results are based on classical fixed point index theory. We improve and complement previous results in the literature. This is illustrated ...

In the present study, the buckling analysis of single-walled carbon nanotubes (SWCNT) on the basis of a new refined beam theory is analyzed. The SWCNT is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new proposed beam theory has only one unknown variable which leads to one equation similar to Euler beam theory and is also free from any shear ...