This paper is a piece of research on the complex structure of functionally gradient materials, which is an applicable triangular cantilever plate structure locally fixed and supported by its round revolving axis. Combined with the generalized Euler equation and the generalized boundary conditions, Kantorovich method and the principle of the two independent variables generalized calculus of variations are adopted to establish the bending governing equation of plates to work out the solution. In comparison with the previous work on the problem, this paper, taking into account three generalized mechanical factors and FGM macro-or-mesoscopic heterogeneity, proposes a new concept of translating the issue of theoretical initial value into the problem of semi-analytical boundary value to obtain the refined solution and then researches the joint effect of grads stress fields. Thereby a refined version of Kantorovich macro-or-mesoscopic solution is developed.