超静定细长弹性杆在面内温度载荷作用下的稳定性问题

基于材料力学的基本理论，得到了梁发生纵横弯曲时的挠曲线近似微分方程，通过讨论非零解的存在性，研究了具有三个支座的超静定细长弹性杆在面内温度载荷作用下的稳定性问题，得到了三支座弹性杆的发生屈曲的控制方程，通过数值计算给出了临界载荷随中间支座位置变化的关系，以及中间支座为弹性支座时，其弹性系数同临界载荷的关系，研究表明：对于两端铰支的梁，中间支座位于梁长的正中时，临界载荷最大，梁的稳定性最好；而中间支座的弹性系数愈大，梁的稳定性愈好。

Stability of statically indeterminate slender elastic bar subjected to temperature load

Based upon the fundamental theory of material mechanics, an approximate differential equation of bar deflection was obtained as it bended. Discussing the existence of nonzero solution, the stability of a statically indeterminate slender elastic bar subjected to temperature load was studied. The control equation of elastic bar with three supports was obtained when its buckling happened. Using the numerical method, the relationship of critical load to the position of median support as well as to the elasticity factor were given for elastic support. It was found by investigation that the stability of the bar was the best when the median support was near the middle of the bar and the elasticity factor of median support was bigger.