Flat problem of the elastic environment reinforced with three families of fibres

Rectilinear reinforcing structures are used more often for research of tensely deformed state of flat constructions from fibrous composites. It has been shown in a number of works presented in Yu. V. Nemirovsky and V. D. Kurguzov (2003), Yu. V. Nemurovsky and V. D. Kurgozov (2004) and Yu. V. Nemirovsky and A. P. Yankovsky (2002), that use of complex curvilinear structures of reinforcing can results in effective designs taking into account the charge of armature rigidity and durability. In the given work the general approach on a presence of flat designs reinforcing structures which provide required reinforcing fibres effective work is considered. Resolving systems flat problem are constructed for possible combinations of three fibres families of reinforcing. These families can be not extensible and equal stretchable families of fibres. Use of algorithms of invariant solutions of partial differential equations construction has allowed constructing and investigating some model solutions.