基于最小势能原理的悬臂梁弯曲研究

Research on bending of the cantilever based on the principle of minimum potential energy

首先介绍了能量原理的有关概念,简述了最小势能原理,推导了梁的应变能公式。然后以悬臂梁为例,着重论证了最小势能原理等价于平衡微分方程和静力边界条件。再论述了基于最小势能原理的里兹法,应用于求梁的挠曲线的基本思想,最后用算例检验,得出了几条结论,这些结论可供相关工程研究人员参考。

This article has introduced the concept of energy principle, outlined the principle of minimum potential energy, deduced the strain energy formulation of beams, and put the emphasis on the principle of minimum potential energy is equivalent to the equilibrium differential equation and static boundary conditions in the case of cantilever beam, then discussed the basic idea that apply the Rayleigh-Ritz＇s method which based on the principle of minimum potential energy to work out the deflection beam line, finally, obtained several conclusions that can give reference for relative researchers through example testing.