构造弹性力学位移函数的机械化算法

The Mechanical Method of Constructing the Displacement Functions in Elasticity

本文证明线性算子方程组Ａｕ＝ｆ的一般解为ｕ＝Ｃｖ＋ｅ，其中ｖ满足方程组Ｄｖ＝ｇ，Ｄ是对角矩阵。以Ｈｉｌｂｅｒｔ零点定理的构造性证明为基础，给出了Ｃ，Ｄ，ｅ的机械化求示。用此方法可以给出各种弹性力学位移函数的机械化算法。

In this paper, we have proven the general solution to the equations of linear operators Au=f as u=Cv+e,where v satisfies the equation Dv=g and D is a diagonal matrix,Basing on the constructive proof of Hilbert Nullstellensatz,we have given the mechanical method of constructing C,D and e,and some of the me-chanical algorithm displacement functions in elasticity are given by this method also.