Fedotov V.P.  

Physical models and the mathematical modeling of the coupled processes in an engineering system

The phenomenological equation between stresses, strains, temperature, concentration of alloying elements, magnetic; characteristics are necessary for analyze a strength of engineering structures. But the retrieval measured data for these equations is labor-consuming when operating of the object in an aggressive environment. Often it is not possible. The subsequent presentation is based on the assumption about the inability to obtain the physical and mechanical properties and the introduction of the concepts of sustainability. the destruction of the resource of the technical object within a closed system, since they are directly related to the nature of the exchange with the environment. The reciprocity relationships for coupled problems are formulated in the framework of open nonequilibrium systems on the basis of Onsager's approach.

The modified boundary element method for solution elliptic, parabolic, hyperbolic problems of to improve the speed and accuracy of calculations is offered. The modification is based on the integral equivalent differential boundary value problem, on an analytical integration and differentiation of the influence functions for the three types of problems and on the parallelization at all stages of solving problems at the level of the algorithm. The integration is done once for each of the types of problems, resulting in a compact easy-to-program formula is offered. The method is illustrated by the solution on the test problems of heat conduction, diffusion, elastoplasticity, vibration plates.

The work was supported by RFBR grant 13-01-12003.