考虑压缩效应的简支弹性杆受压屈曲的理论分析

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：#x0201c;超临界叉式分支#x0201d;、#x0201c;亚临界叉式分支#x0201d;和#x0201c;不存在#x0201d;。而在经典欧拉模型中，弹性杆的一阶屈曲模态总表现为#x0201c;超临界叉式分支#x0201d;。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。

Theoretic Analysis on the Buckling of a simply supported Compressible Elastic Rod under the Axial PressurE

An improved scheme is proposed by using the singularity theory to study the effect of compressibility of an elastic rod on its critical loads of buckling modes. It is indicated that the critical load of the first buckling mode calculated by the improved scheme is increased compared with that calculated by the classical Euler scheme. For the first buckling mode of an elastic rod, Euler scheme predicts that it's always the supercritical fork bifurcation, but the improved scheme shows the existence of different bifurcations (supercritical fork bifurcation, subcritical fork bifurcation and no buckling mode) in accordance with different value ranges of the rod dimensionless characteristic length. The conformity of the improved scheme to test results is evaluated qualitatively. Besides, it is explained by the analysis of an example based on the improved scheme that why rods with shorter lengths made from traditional materials always occur yield failure rather than buckling of subcritical fork bifurcation.