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漏算、多算或重复计算势能项都会有损薄壁构件弯扭屈曲总势能的完备性,进而会造成理论不严谨或临界荷载、临界弯矩的计算值不准确。为推导完备的薄壁构件弯扭屈曲总势能,该文首先把符拉索夫的中面剪应变为零假定修正为中面线性剪应变为零并给出了表达式,依据该表达式严格推导了薄壁构件横截面上任意点的线性剪应变和线性剪应变能,指出了该假定不能推广到非线性剪应变或总剪应变。继而采用弹性理论的应变能公式分别推导了应变能和外荷载势能,得到了完备的弯扭屈曲总势能,并对现有的总势能的完备性进行了探讨。研究表明,该文的总势能推导过程概念明确、逻辑清晰,该文的总势能由于严格推导了线性剪应变能和外荷载势能,同时准确计入非线性剪应变能且不包含非线性横向应变能而更为完备。
Missing calculation, multiple calculation or double counting of potential energy items all will impair the completeness of the total potential energy of the bending and buckling of the thin-walled component, which in turn will cause the theory not rigorous or critical load, and the calculated critical bending moment is inaccurate. In order to deduce the total buckling and torsional buckling potential of a thin-walled component, this paper firstly modifies the mid-plane shear strain of null to the null hypothesis and modifies the mid-plane linear shear strain to zero and gives the expression. According to the expression The linear shear strain and linear shear strain at any point on the cross section of thin-walled members are derived. It is pointed out that this assumption can not be generalized to nonlinear or total shear strain. Then the strain energy and the external load potential energy are deduced by using the strain energy formula of elasticity theory, and the complete potential energy of bending and torsional buckling is obtained, and the completeness of the existing total potential energy is discussed. The results show that the general potential energy derivation process of the paper has a clear concept and a clear logic. The total potential energy of the paper derives the linear shear strain energy and the external load potential as well as accurately accounts for the nonlinear shear strain energy and does not include the nonlinear transverse strain Can be more complete.