Abstract
The first order approximation theory of three dimensional elastic plates and its boundary conditions presented in the previous paper[1] establishes six differential equations for the solutions of six undetermined functions uo, ua, A(o) and S(2)a defined in the x, y plane. They can be divided into two groups, each constitutes three equations to calculate uo, S(2)a and ua, A(o) respectively. 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 ratio, say h/a=0.3 a considerable difference arises between the two theories. It has not been made clear that in what range of the ratio such difference is reasonable to give more precise solutions. In order, to solve this problem, we must study the second order approximation theory. In 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 undetermined functions uo ua, A(o), A(1), S(2)a and S(3)a. And the range of the validity of the first order approximation theory can be found out by comparing the second order theory with the first order theory and the classical theory. It should be pointed out here that the equations of, the second order theory can also be divided into two groups to be solved separately, and the procedure of solution is not too complicate to perform as well. Here, we will use the same notations adopted in the previous paper, and not repeat their definitions.
Similar content being viewed by others
References
Chien Wei-zang, Approximation theory of three dimensional elastic plates and its boundary conditions without using Kirchhoff-Love, assumptions,Applied Mathematics and Mechanics (English Ed.),16, 3 (1995), 203–224.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wei-zang, C. The second order approximation theory of three dimensional elastic plates and its boundary conditions without using kirchhoff-love assumptions. Appl Math Mech 16, 405–427 (1995). https://doi.org/10.1007/BF02459340
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02459340