Post-buckling phenomena of slender rods have attracted great attention for both theoretical and engineering aspects. In this study, we explored the post-buckling behavior of a slender rod with two hinged ends under its self-weight. We first established the potential energy functional of the system, and then derived the governing differential equations according to the principle of least potential energy. We further addressed the physical meaning of the Lagrange multiplier by analyzing the force equilibrium. A computer code of shooting method was developed by using the commercial software MathCAD, which has proved efficient in computing the post-buckling configurations of the rod. We finally discussed the buckling of an oil sucker rod adopting our numerical results, which will be beneficial to the engineering design.
Nanowire stiction is a crucial bottleneck for the development of M/NEMS devices.We present a model of a nano-beam stuck to the substrate in consideration of both surface elasticity and residual surface stress.The critical detachment length can be derived from the transversality condition using the variational method.The effects of the surface parameters on the adhesion of the nano-beam are discussed in detail.These analyses provide some suggestions for engineers in the design and fabrication of more accurate M/NEMS instruments.
In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube (CNT) ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thoroughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materials, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.
