Some refining of classic theory of rectangular plates made from composite materials | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 8 > №1 / 2002 / Pages: 28-64

Some refining of classic theory of rectangular plates made from composite materials


We present the construction of three-dimensional theory of rectangular composite plates with no use of the Kirchhoff-Love hypotheses. The main attention we pay to the construction of three-dimensional equations for determining stress-strain state of boundary layer type, that is, stress-strain state in narrow boundary regions. In particular, we consider a problem of refining the stress-strain state in the region near the rigidity fixed edge of a plate (as a rule, fracture occurs in regions of such type). Considering a problem on boundary plane deformation, we arrive at a bi-harmonic problem with particular boundary conditions. To use the results obtained in the calculations based on numeric methods for design of composite structures, we employ the method of energy. This method allows us to reduce the system of partial difference equations to the system of ordinary differential equations along with corresponding boundary conditions. The variational procedure employed is similar to the Vlasov-Kantorovich procedure. We study the convergence of the solution obtained and construct functions approximating the solution through the thickness of the plate in the form of high-order polynomials. We study the influence of elasticity of fixed edges on the results by solving a problem of contact of a plate with an elastic isotropic half-space. The results obtained allow us simulate real boundary conditions accurately. Using the Flaman-Boussinesq solution as well as the influence function and taking into account an additional potential energy of the plate, we arrive at the modified boundary conditions. The calculations made demonstrate that the stress-strain state of plane boundary deformation influences drastically on the strength characteristics of an orthortopic composite plate. It is obtained that the presence of compliance of the edge supported leads to some decreasing of additional stresses in the plane boundary deformation.