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.
In this study,we considered the wetting phenomenon on a general substrate from a new viewpoint of continuum mechanics.The analyses first show how the Wenzel and the Cassie models deviate the practical results in some special substrates,and then elucidate the mechanism of the triple contact line(TCL) moving.Based upon variational theory of the total free functional dealing with the movable boundary condition,we show that the macroscopic contact angle(MCA) expression is the corresponding transversality condition.It manifests that the MCA depends only on the chemical and geometric property at the TCL,and is not affected by the gravity of the droplet and the contact area beneath the liquid.Our continuum model also shows the exploration of the pinning effect on a sharp wedge or the interface between two different phases.This investigation will help designing super-hydrophobic materials for novel micro-fluidic devices.
