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研究的梯度功能材料复合结构,为一个有着实际应用背景的由圆转轴局部固支的三角形悬臂板结构,采用Kantorovich解法及二类独立变量广义变分原理建立板的弯曲控制方程,并结合广义Euler方程和广义自然边界条件求解.与以往问题大不相同的是,考虑了3个广义力学因素和FGM宏细观非均质性,提出了理论初值问题化为半解析边值问题精化求解的新概念,研究了梯度应力场的参加效应.由此,拓展为Kantorovich宏细观精化新解法.
The gradient functional material composite structure studied is a triangular cantilever plate structure partially supported by a rotating shaft with a practical application background. The bending governing equations of the plate are established by using the Kantorovich method and two types of independent variables generalized variational principle. Combined with the generalized Euler Equations and generalized natural boundary conditions.With the very different from the past, considering the three generalized mechanics factors and the macroscopic heterogeneity of the FGM, we put forward that the theoretic initial value problem can be refined to the semi-analytical boundary value problem The new concept of Kantorovich is studied, and the participation effect of gradient stress field is studied.