Search

In this paper, buckling of a nanowire column subjected to self-weight and tip load is investigated. One end of the nanowire is free, while the other end is attached to a rotational spring support. Considering the equilibrium equations together with the Euler–Bernoulli beam theory, the governing differential equation describing the behavior of the column can be obtained. Effect of surface stress is also incorporated into the formulations in terms of transverse distributed loading. The differential equation has been solved analytically and the general solution can be presented in the terms of Bessel function of the first kind. Applying the boundary conditions, the characteristic equations influenced by surface stress and stiffness of the rotational spring at the support can be expressed and then the critical load can be determined using the Newton–Raphson iterative scheme. From the results, they reveal that the positive surface stress could strengthen the nanowire against the buckling. Fixity at the base is also influenced to the critical load where the increase of the stiffness of the spring results in the increase of critical load as well. [ABSTRACT FROM AUTHOR]

This paper investigates the behavior of a pre-stressed arch under a sliding load, where the initial configuration can be obtained from the buckling of a straight column. The shape of the pre-stressed arch can be varied by increasing the end shortening. Subsequently, a sliding load is applied at a certain height level. The orientation of the applied load maintains the right angle with respect to the tangential line of the arch. By moving the load horizontally, the behavior of the arch can be explored. The governing differential equations of the problem can be obtained by equilibrium equations, constitutive relation, and nonlinear geometric expressions. The exact closed-form solutions can be derived in terms of elliptic integrals of the first and second kinds. In this problem, the arch can be divided into two segments where each segment is a part of a buckled hinged-hinged column mounted on an inclined support. The shooting method is employed to solve the numerical solutions for comparing with the elliptic integral method. The stability of the pre-stressed arch is evaluated from vibration analysis, where the shooting method is again utilized for solving the natural frequencies in terms of a square function. A simple experiment is set up to explore the equilibrium shapes. Poly-carbonate sheet is utilized as the pre-stressed arch. From the results, it is found that the results obtained from elliptic integral method are in excellent agreement with those obtained from shooting method. The equilibrium shapes from the theoretical results can also compare with those from the experiment. The pre-stressed arch can lose its stability and snap into an upside-down (inverted) configuration depending on the ratio of rise to span-length and loading height. The instability of the arch is not only detected during the pushing of the sliding load but a pulling load can also cause unstable behavior of the arch. [ABSTRACT FROM AUTHOR]