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薄壁构件的总势能方程在结构稳定分析和工程设计中具有十分重要的地位和意义,是进行结构稳定计算的基础和钢结构设计规范中制定相关设计公式的依据。多年来薄壁构件的总势能方程一直存在着多种形式,一些设计规范依据的总势能方程也不尽相同。该文采用典型的薄壁构件纵向位移表达式,从理性力学的角度,对薄壁构件的总势能方程进行了严格的推导,得到了应用较多、具有代表性的几种表达式,对产生总势能方程不同形式的原因进行了理论上的剖析,该文认为主要是推导者所采用的基本假定不同、采用的构件纵向位移表达式不同、推导方法上的差异以及工程梁理论本身不完善所造成的;理论的分析证明了经典理论下薄壁构件的总势能方程是最为准确合理的表达式。
The total potential energy equation of thin-walled components plays an important role in structural stability analysis and engineering design. It is the basis of structural stability calculation and the basis for formulating relevant design formulas in the code of design of steel structures. For many years, the total potential energy equation of thin-walled components has been in many forms, and some of the design equations are based on the total potential energy equation is not the same. In this paper, a typical expression of longitudinal displacement of thin-walled members is adopted. From the perspective of rational mechanics, the total potential energy equation of thin-walled members is strictly deduced. Several expressions, which are mostly used and representative, are obtained. The total potential energy equation of different forms of the reasons for the theoretical analysis of the article that the main assumption is that the basic assumptions used by different members of the longitudinal displacement of the expression of differences in the derivation of differences in the theory and engineering beam theory itself is imperfect The theoretical analysis proves that the total potential energy equation of the thin-walled member under the classical theory is the most accurate and reasonable expression.