MATHEMATICAL MODELING OF МЕСHANICAL MACROPROPERTIES MATERIALS REINFORCED BY PERIODIC LATTICE
Used method of cellular functions, which allows to determine the mechanical macrocharacteristics materials periodically reinforced by lattice. The method is based on the asymptotic decomposition of the spatial problem of elasticity, without building models and the introduction of additional hypotheses. Mechanical macrocharacteristics defined as integrals of cellular functions. Valium family are the solution of boundary value problems posed on the unit cell with periodic boundary conditions. A unit cell is a periodic one period, in a plane mechanical properties of the composite function. In the results of the presented calculated numerically, depending on the values of mechanical macrocharacteristics the thickness of the reinforcing by lattice, for two types of reinforcement: a tetragonal lattice, hexagonal lattice. Demonstrated the non-linearity of this relationship, as well as a significant difference mechanical macrocharacteristics for two types of reinforcement. A comparison macrocharacteristics calculated by the method of cellular functions with the results presented in the works of YV Nemirovski.