МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ МЕХАНИЧЕСКИХ СВОЙСТВ КОМПОЗИЦИОННЫХ МАТЕРИАЛОВ ПРИ НАРУШЕНИИ СПЛОШНОСТИ

Abstract

Urgency of the research. Composite materials are widely use in airplane construction, providing for high strength, stiffness, fatigue and weight characteristics.Target setting. Products made of composite material can lose continuity in the process of service under the effect of loads. In these conditions it is necessary to determine the dependence of mechanical properties of the material on the design and technology factors.Actual scientific researches and issues analysis Most authors of the works in the field of modeling properties of composite materials, their operation characteristics use various mathematical methods which are not connected with experiments, in so doing they do not concern the problem on the obtained model adequacy.Uninvestigated parts of general matters defining. It is difficult to study properties of the composite materials by theoretical analysis. It is proposed to use the experimental statistical approach with attraction of the experiment design theory and regression analysis.The research objective. This work objective is mathematical modeling of the effect of design-technological factors of manufacturing products of composite materials on their mechanical properties under continuity violation under the impulse loads.The statement of basic materials. The authors use the extended conception of the obtained model orthogonality: the experiment design, the model structure and structural elements of the model are orthogonal to each other. The regular plan 23×43//32 was chosen for the experiment performance. The effect of 6 factors on the ultimate strength and elasticity modulus of composite materials was modeled. The models obtained are stable, adequate and informative.Conclusions. The use of the conception of experiment design and formalized production of the model structure under modeling mechanical properties of the composite materials has completely confirmed high efficiency of such methodological approach and allowed constructing the mathematical models fit for the practical application. The obtained models permit us to perform the comprehensive analysis of the effect of studied factors on the modeled functions, optimize the factors’ values by the accepted criterion, predict properties and solve other problems.