变分法在薄壁杆件空间弹性失稳问题中新的应用

本文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所对应的失稳位移的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为复杂的空间失稳问题.

The New Application in the Problem of Spatial Elastic Stability of Thin-wall Bar

In the variational equation of destable potential energies, the potential energies of external forces by using additional moments of flexure and moments of torsion and their correspondent curvatures of destable displacement and increment of torsional angle are represented. Through partial integration method and with the application of displacements and natural boundary condition 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 method. In this way we can easily settle the problems of the thin-wall bar under forces and problems of spatial instability at the complex cross-section structure circumstance.