Abstract: The first order approximation theory o.f three dimensional elastic plates and its boundat T conditions presented hi the previous paper^[1] establishes six differential equations for the solutions o.f six undetermined functions u₀, u_a, A₍₀₎ and S_(2)a defined in the x, y platte. They can be divided into two groups, each constitutes three eqaations, to calculate u₀, S_(2)a, and u_a, A₍₀₎ respectiveh'. Their boundary conditions as well as these, equations are derived from the stationary conditions of variations of a functional for this problem based on the generalized variational principle. The solutions given by this theory are close to those given by the classical theory of thin plates as the ratio of thickness h to width a is small. For large ratiu, say h/a=0.3 a considerable difference arises between the two theories. It has not been made cleat" that in what range oJ the ratio such difference is reasonable to give more precise solutions, In order to solve this problem, we must study the second order approxhnation theory hi this paper. following the previous one, we shall establish the second order approximation theory by applying the stationary condition of variations of a functional for this problem based on the generalized variational principle to derive nine differential equations and the relate boundary conditions, which are used to calculate nine utidetermined functions u₀, u_a, A₍₀₎, S_(2)a, and S_(3)a. And the range of the validity of the first order approxhnation theol3, can be Jbund out by comparhtg the second order theory with the first order theory and the classical theory. It should be pohtted out here that the equations of the second order theot 3" can also be divided into two groups to be soh,ed separately, and the prncedure of solution is not too complicate to perform as nell. Here. we will use the same notations adopted in the previous paper, and not repeat their definitions.

Key words: three dimensional elastic plates, Kirchhoff-Love assumptions, second order approximation, dynamics of rigid body, drift of gyroscope, average method