受弧形邊界拘束之彈性樑的變形及穩定性分析

Abstract

本文中我們考慮在底部平面兩端夾持(clamped-clamped)的彈性樑(elastica)在受到頂部牆面側向壓縮後的變形及穩定性。我們考慮三種頂部牆面:分別為凹面(concave)、凸面(convex)及平面(plane)。首先建立受壓縮彈性樑的變形軌跡圖，接著由振動法決定各式變形的穩定性。當頂部牆面以半靜態方式(quasi-statically)壓縮時，我們架設實驗驗證理論上預測的變形演變。當頂部牆面為平面時，free fold(與牆面發生點接觸前的變形)恰接觸到牆面時，壓縮外力會減少到零。當頂部牆面不再是平面時，此現象就不見得存在。當頂部牆面不再是平面，線接觸變形的多樣性會受到破壞。當頂部牆面為凹面時，頂面不會發生二次挫曲，反而是底部平面兩端的線接觸持續變長。當頂部牆面為凸面不會發生頂部線接觸。

In this paper we consider the deformation and stability of a clamped-clamped elastica resting on a bottom plane and pressed by a top wall laterally. Three types of top walls are considered; they are concave, convex, and plane surfaces. Deformation maps of the pressed elastica are first constructed. The stability of various deformation patterns is determined via a vibration method. The theoretical predictions on the deformation evolution when the top wall presses quasi-statically are verified experimentally. In the case of plane top wall, the external pressing force reduces to zero whenever the free fold of a previous deformation starts to touch the wall. In the case when the top wall is not a plane, this is in general no longer true. The multiplicity of line-contact deformations in the case of plane top wall is destroyed when the top wall is curved. No secondary buckling will occur when the top wall is concave. Instead, line contact on the sides of the bottom plane will develop. In the case when the top wall is convex, no line contact on the top wall is possible.