构造容许位移的转换边界法

本文提出了在复杂边界条件下构造容许位移的转换边界法.所谓转换边界法,就是首先根据叠加原理将实际系统转换为基本系统及附加边界力和附加边界位移,然后应用变分原理于基本系统,最后应用级数转换的办法求得实际系统的容许位移.本文还给出了边界条件变化的混合能量原理.这边界条件变化的混合能量原理和边界条件变化的势能原理和余能原理都是转换边界法的主要理论基础.应用转换边界法我们构造了复杂边界条件平面应力问题和弯曲问题矩形板的容许位移.由于转换边界法构造容许位移是遵循着变分原理和确定的程序进行的,因而克服了Rayleigh-Ritz法猜测、拼凑容许位移的困难.

The Method of Transformation of the Boundaries for Forming the Permissible Displacements

In this paper the method of transformation of the boundaries for structure the admissible displacements with various boundary conditions is presented. What is called the method of transformation of the boundaries is that, first we transform the actual system into the basic system and additional boundary forces and displacements on the basis of the superposition principle, then apply variational principles to the basic system, finally find the permissible displacement of the actual system by means of the method of transformation of the series.In this paper, we also give mixed energy principles under v iriation of boundary conditions. The mixed energy principles as the potential and complementary energy principles under variation of boundary conditions are all the chief theoretical fundamental of the method of transformation of the boundaries.Applying the method of transformation of the boundaries, we form the permissible displacements of rectangular plates of plane stress and bending problems with various edge conditions.Because the method of transformation of the boundaries is in progress to follow the variational principles and definite program to form permissible displacements, the difficulty in supposing and piecing together permissible displacements in the Rayleigh-Ritz method will be overcome.