Mathematical modeling and numerical calculation of composite structures

The report is devoted to modeling the properties of composite materials. Two major approaches are considered: phenomenological and structural [1]. Within the framework of the first approach reinforced materials are modeled as homogeneous anisotropic medium with efficient physical and mechanical properties. In this case mechanical parameters of the material are determined basing on experimental data. In a structural approach, physical and mechanical parameters of the composite are expressed in terms of the parameters of its components and design of reinforcement that open up opportunities for improvement of the properties of composite structures. The mathematical relations describing the nonlinear elastic three-point bending of isotropic and reinforced beams with account of different strength and stiffness behavior in tension and compression are obtained. An algorithm for numerical solution of corresponding boundary-value problems is proposed and implemented. Results of numerical modeling have been compared to acquired data for polymer matrix and structural carbon fiber reinforced plastics.