变分法在薄壁杆件空间弹性失稳问题中的研究  

The Research in the Problem of Spatial Elastic Instability Thin-wall Bar

作　　者：葛晓明[1] 朱聘儒[1] 

机构地区：[1]苏州科技学院城建系,江苏苏州215011

出　　处：《科技通报》2002年第6期457-462,共6页Bulletin of Science and Technology

基　　金：建设部科研基金资助项目 ( 99- 0 31- 3)

摘　　要：在薄壁杆件空间弹性失稳势能的变分方程中 ,应用附加弯矩与扭矩及其对应的失稳位移曲率与扭率的增量来表达其外力失稳势能 .该微分方程通过分部积分法应用位移及应力自然边界条件 ,得出各阶微分方程的迦辽金法的方程组来进行计算 ,从而简便地解决了薄壁杆件受力及截面结构均较复杂的空间失稳问题 .In the variational equation of unstable potential energies, the potential energies of external forces by using additional moments of flexure and moments of torsion and their correspondent curvatures of unstable displacement and increment of torsional angle are represented. Through partial integration method and with the application of displacement and natural boundary conditions for stress, we can get all order differential equations from variational equation of potential energy for spatial elastic instability. The one among them that we compute with is the spatial combination equation systems of Fanepkii method. In this way the problems of the thin wall bar under forces and problems of spatial instability at the complex cross section structure circumstance can be easily solved.

关 键 词：变分法 薄壁杆件 对应变换 失稳势能 变分方程 空间弹性失稳 迦辽金法 

分 类 号：TU320.1[建筑科学—结构工程]