Buckling of structures under lateral load restraint has been found to differ from the conventional bifurcation problems and cannot be handled with conventional analysis. Towards a better understanding of this type of unconventional buckling problems, this work investigates the upheaval buckling of an elastica resting on a smooth surface and restrained by a lateral constant force. Analytical solutions for the Mode-1 and Mode-2 post-buckling responses and configurations of the elastica are established. Stability of the post-buckling configurations under force-control are investigated via the energy method. An energy barrier is found to exist and the buckling load depends on the restraining force and perturbation energy. The imperfection sensitivity of the system is different from the conventional buckling ones, and a characteristic imperfection is found to exist that can transform a snap-through instability into a bifurcation buckling. As a first attempt to address the problem of flange wrinkling under a constant blank-holding force during the cup-drawing process, the fundamental solutions are extended to study the wrinkling of a shrinking elastic annulus under a constant lateral restraining force. The post-wrinkling responses are established and an energy barrier is found to exist for each wrinkling mode. A characteristic imperfection is also found to exist for each mode, which eliminates the energy barrier and enables bifurcation wrinkling. The linear relationship between the critical restraining force that prevents the wrinkling of the elastic annulus and the imperfection amplitude is established, which is also verified by numerical simulations. This study contributes to a better understanding of load-restrained buckling problems and is expected to shed light on the elastoplastic buckling of plates and shells under lateral load restraints in general, and on the wrinkling of a thin sheet during cup-drawing in particular.

已经发现在横向载荷约束下结构的屈曲与传统的分叉问题不同，并且不能用传统的分析来处理。为了更好地理解此类非常规屈曲问题，这项工作研究了位于光滑表面上并受横向恒定力约束的弹性件的剧变屈曲。建立了模式 1 和模式 2 后屈曲响应和弹性​​体配置的解析解。通过能量方法研究受力控制下的后屈曲结构的稳定性。发现存在能量屏障，屈曲载荷取决于约束力和扰动能量。该系统的缺陷敏感性不同于常规屈曲系统，并且发现存在一种特征缺陷，可以将快速通过的不稳定性转变为分叉屈曲。作为解决拉拔过程中恒定压边力下法兰起皱问题的首次尝试，将基本解决方案扩展到研究在恒定横向约束力下收缩弹性环的起皱。建立起皱后反应，并发现每种起皱模式都存在能量屏障。还发现每种模式都存在特征缺陷，这消除了能量障碍并使分叉起皱成为可能。建立了防止弹性环褶皱的临界约束力与缺陷幅度之间的线性关系，这也通过数值模拟得到了验证。