binder, fibers, bending, plate of composite material, cracks, stress intensity factors, minimization of fracture parameters.

A thin elastic plate of an isotropic elastic medium (matrix) and allocated in it fibers (inclusions) of another elastic material at bending is considered. It is assumed that the material of the binder medium is weakened by doubly periodic system of through unequal length cracks collinear to axis and ordinate axes. The crack faces are free from external loads. Work resource of bending plate of composite material reinforced by unidirectional fibers depends on the stress distribution in the zones of interaction of its elements. Serviceability of the composite can be improved by changing the geometry of binder and fibers joint. The inverse problem of fracture mechanics to determine the optimal fibers shape providing the minimization of the stress intensity factors (moments) in the vicinity of crack tips, is solved. The criterion and solving method of the problem of fracture preventing for the composite under action of the given system of external bending loads are proposed. A closed system of equations, allowing to obtain the solution of optimal design problem for the composite depending on the geometrical and mechanical characteristics of the binder and fibers, is constructed. The obtained cross-section shape of the unidirectional fibers provides the increase of composite serviceability.

Mirsalimov Vagif, Dr. Sci. Phys. & Math., Prof., Azerbaijan Technical University; Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.

Askarov  Vusal,  Postgraduate  student,  Institute  of  Mathematics  and  Mechanics  of  NAS  of Azerbaijan, Baku, Azerbaijan.