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用奇异性理论研究轴向压缩以及由之引起的横截面积扩大对弹性压杆屈曲的影响。新模型得到的屈曲临界压力大于经典欧拉模型所给之值,且新模型显示,在无量纲特征长度的三个不同取值区间中,弹性杆的一阶屈曲模态表现为三种不同的形式:“超临界叉式分支”、“亚临界叉式分支”和“不存在”。而在经典欧拉模型中,弹性杆的一阶屈曲模态总表现为“超临界叉式分支”。根据新模型,定性评价了现有实验数据,并通过算例分析,解释了传统材料制作的杆件在较短时将发生屈服破坏而非亚临界叉式分支屈曲的现象。
The singularity theory is used to study the effect of axial compression and the resulting increase in cross-sectional area on the buckling of elastic compression bars. The critical pressure of buckling obtained by the new model is larger than the value given by the classical Euler model. The new model shows that the first order buckling mode of the elastic rod shows three different modes in three different intervals of dimensionless characteristic length Form: “Supercritical Fork Branch”, “Subcritical Fork Branch” and “Nonexistent”. In the classical Euler model, the first-order buckling mode of the elastic rod always shows “supercritical fork-type branch ”. According to the new model, the existing experimental data are qualitatively evaluated. The case analysis is given to explain the phenomenon that the rod made of traditional materials will yield buckle in short time but not the subcritical fork-type branch buckling.