薄壁构件弯扭屈曲总势能的完备性分析

发布时间：2018-06-26 06:42

本文选题：弯扭屈曲 + 总势能的完备性　；参考：《工程力学》2017年07期

【摘要】：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。
[Abstract]:Omitting, multiple calculation or repeated calculation of potential energy terms will impair the completeness of the total potential energy of bending and torsional buckling of thin-walled members, which will lead to theoretical unrigour or critical load, and the calculation of critical moment is not accurate. In order to deduce the total potential energy of bending and torsional buckling of thin-walled members, the assumption that the mid-plane shear strain is zero is modified to that the midplane linear shear strain is zero and the expression is given in this paper. According to this expression, the linear shear strain and linear shear strain energy at any point on the cross section of thin-walled members are strictly derived, and it is pointed out that this assumption cannot be extended to nonlinear shear strain or total shear strain. Then the strain energy and external load potential energy are derived by using the strain energy formula of elastic theory, and the complete total 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 concept and logic of the total potential energy derived in this paper are clear, and the total potential energy is derived strictly from the linear shear strain energy and the external load potential energy. At the same time, the nonlinear shear strain energy is taken into account accurately and the nonlinear transverse strain energy is not included.
【作者单位】：兰州大学西部灾害与环境力学教育部重点实验室土木工程与力学学院;重庆大学土木工程学院;
【基金】：国家自然科学基金项目(51308272)
【分类号】：TU323

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