Some generalization of the theory of bending of anisotropic plates

Bogdan Krušić ; France Brešar

Theoretical and applied mechanics, Tome 8 (1982) no. 1, p. 77 .

Résumé

In this paper, the problem of the bending of an anisotropic plate is serious with the method introduced in 1938 by Lahnicki [2]. In his discussion, he started from Kirchhoff's theory of thin plates and for the complete description of the stress-deformation state, he needed two analytical functions. We generalized the solution by assuming that the displacements $u,v,w$ are expressed in the form of polynomials with respect to the variable $Z$ (equation 1.4). These polynomials naturally represent the beginning of the corresponding Taylor series. It turns out that the number of functions used to express the stress-strain state of the plate depends on the degree of the polynomials. In our application ($N=3$), we obtained six such functions. We have constructed odd boundary value problems to determine these six functions and as a simple example we have solved the half plane problem.