Deformation of orthotropick three-layer rectangular plate

Аuthors

Starovoytov E. I.^1*, Lokteva N. A.^2**, Starovoytovа E. E.¹

1. Belarusian State University of Transport, 34, Kirova srt., Gomel, 246653, Belarus
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: dstar@mail.by
**e-mail: nlok@rambler.ru

Abstract

Bending of elastic rectangular orthotropic three-layer plate with a hard core and the composite layers under the influence of local load is considered.
Statement of the problem is carried out in a rectangular coordinate system associated with the median plane of the aggregate. To describe the kinematics of the plate the hypothesis of broken normal are taken as follows: in the bearing layers Kirchhoff’s hypothesis are correct, in incompressible thickness filler the normal remains straight and does not change its length, but turns on some extra angle. On the contour of the plate it is assumed a presence of a rigid diaphragm, which prevents the relative layers shift. Deformations are small.
The equilibrium equations and force boundary conditions follow from the Lagrange principals of virtual work. As the fixing conditions the free bearing plate fixed on the contour of rigid tower is accepted. The plate is exposed to the following external loads: locally uniformly distributed load, concentrated force and concentrated moment.
The solution of the boundary value problem is carried out in a double trigonometric series. The projections of the load are expanded in trigonometric series. To find the displacement amplitudes a system of linear algebraic equations obtained from the differential equations of equilibrium in terms of displacements is used. The analytical solution is written out in the determinants.
Numerical parametric analysis of stress-strain state of the plate under the action of local loads has been carried out. Numerical results are obtained for the three-layer square orthotropic plate package, which consists of the following layers: support layers — high-strength carbon fiber epoxy binder, filler - polytetrafluoroethylene.
The action of surface loads such as load distribution on the entire outer surface of the plate and a force applied in the middle of the plate are considered. With equal resultant of forces data the movements from loads strapped on to the center of the plate are more. Differences in amount of displacement along different axes are explained by orthotropic of bearing layers materials.
The presented method of the three-layer rectangular orthotropic plates calculating allows to obtain sufficiently accurate parameters of the stress-strain state for engineering practice. Orthotropic materials of bearing layers are substantially affects the displacements and stresses in the plate.

Keywords:

three-layer circular plate, oscillations, local load, stress-strain behavior, composites

References

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