非线性弹性材料压杆临界力的计算方法

压杆的稳定是一个经典的力学问题，而通常讨论的压杆大多都是假定为理想弹性材料，而非线性弹性压杆的临界力求解问题鲜有论文论述，从压杆稳定理论的完整性以及各种材料的真实应力应变曲线看，有必要对这类问题进行讨论。本文首先指出了非线性弹性材料轴心压杆求解临界荷载时存在的困难，利用压杆在受压下的普遍中性平衡方程式，讨论了临界荷载的一般求解方法。为简化一般求解方法，首先讨论了材料可能出现的各种非线性应力应变曲线，提出了非线性弹性压杆屈曲时截面上应力分布的简化处理原则，并分析指出按简化方法求解的临界荷载是实际临界荷载的上限值，最后提出了临界荷载求解的简化修正方法。

Calculation of Critical Force for Compression Bar of Nonlinear Elasticity Stuff

Columns stability is a classic mechanical problem,and the most discussed bar are assumed to be an ideal elastic material,and few papers discuss non-linear flexible bar,but from the integrity of the stability,it is necessary to discuss the stability of the non-linear flexible bar.This paper pointed out the difficulties to obtain the critical load of the non-linear elastic material axis compression bar,and discussed the general method for the critical load of bar from the general neutral balance formula under pressure.To simplify the general method of solving,this paper discussed the various non-linear stress-strain curves of flexible material,and simplified the distribution of stress at the section when the non-linear flexible bar buckling,so that obtained the critical load is the up limited,at last amendment the expression of the critical force.