求解位移方程的能量原理

本文在Castigliano原理的基础上推广了单位虚载荷法.据此,用力法直接导出了梁、板和壳一类结构的挠曲面的一般方程.我们导出了具有非齐次位移边界条件的矩形薄板和考虑横向切变形影响的矩形厚板的挠曲面方程.同时给出了相应直梁的挠曲轴方程.推广了互等定理的应用.计算了三个简例.

Energy Theorems for Solving Equations of Deflections

In this paper the unit-dummy-load method is generalized on the basis of Castigliano's Theorem. On these grounds the general eguations of deflection surfaces of the structures, such as a kind of beams,plates and shells, are directly derived by the force method.We derived the eguations of the deflection surfaces of the rectangular thin plates and thick plates considering the effect of transverse shearing deformations with the inhomogeneous displacement boundary conditions. At the same time we give the equations of deflection axes of the corresponding straight beams.The applications of the reciprocal theorem are also generalized.Three simple calculated examples are given.