Mathematical Apparatus for Selection of Optimal Parameters of Technical, Technological Systems and Materials Based on Vector Optimization

We presented Mathematical apparatus of the choice of optimum parameters of technical, technological systems and materials on the basis of vector optimization. We have considered the formulation and solution of three types of tasks presented below. First, the problem of selecting the optimal parameters of technical systems depending on the functional characteristics of the system. Secondly, the problem of selecting the optimal parameters of the process depending on the technological characteristics of the process. Third, the problem of choosing the optimal structure of the material depending on the functional characteristics of this material. The statement of all problems is made in the form of vector problems of mathematical (nonlinear) programming. The theory and the principle of optimality of the solution of vector tasks it is explained in work of https://rdcu.be/bhZ8i. The implementation of the methodology is shown on a numerical example of the choice of optimum parameters of the technical, technological systems and materials. On the basis of mathematical methods of solution of vector problems we developed the software in the MATLAB system. The numerical example includes: input data (requirement specification) for modeling;transformation of mathematical models with uncertainty to the model under certainty;acceptance of an optimal solution with equivalent criteria (the solution of numerical model);acceptance of an optimal solution with the given priority of criterion.

EXPERIMENTAL MEASUREMENT OF MAGNETIC FIELD IN A NOVEL FLOW CONTROL OF MOLD

In order to know the distribution of magnetic field in a novel flow control of mold (NFC Mold) and to provide the experimental data for the electromagnetic structure design and the analysis of flow control in continuous casting mold, the magnetic field in a NFC Mold were measured by Tesla meter of Model CT-3. The method of vector synthesis was adopted in the measurement of magnetic fields. The results showed that the magnetic field in the NFC Mold was composed of two main magnetic areas that were symmetrical. Although there was leaking magnetic flux between the lower surface of the upper pole and the upper surface of the lower pole on the sides, it was restrained by the main magnetic fields effectively. Therefore the NFC Mold was more preferably satisfied to be used in controlling the molten steel flow in continuous casting mold.

Static response of a layered magneto-electro-elastic half-space structure under circular surface loading

A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic（MEE） structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coeficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coeficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading,are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.