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。
The omissions or multiplicities of energy items are hazardous to the completeness of the total potential energy of thin-walled members, which will cause the energy theory loosely or the incorrect values of critical load or critical moment. In order to propose complete total potential energy, the Vlasov＇s assumption of zero shear strain in middle surface is revised as zero linear shear strain in middle surface. The expression of the revised assumption is proposed and the linear shear strain of an arbitrary point in cross-section is deduced. The Vlasov＇s assumption can not be extended to non-linear shear strain and total strain range. The strain energy and the load potential energy are derived by the strain energy formula of elasticity theory, and the complete total potential energy is established. The results shown that：both the clear concept procedure and total potential energy are complete due to the linear shear strain energy; the load potential energy is derived strictly; the nonlinear shear strain energy is included accurately; and the nonlinear transverse strain energy is excluded.
出处
《工程力学》
EI
CSCD
北大核心
2017年第7期1-10,共10页
Engineering Mechanics
基金
国家自然科学基金项目(51308272)
关键词
弯扭屈曲
总势能的完备性
中面线性剪应变
应变能
荷载势能
flexural-torsional buckling
completeness of total potential energy
linear shear strain in middle-surface
strain energy
load energy
