Способ обработки результатов магнитной дефектоскопии для достоверного обнаружения опасных дефектов сплошности в реальном времени

The inverse problems of magnetostatics for defects of a continuum can be formulated in various ways. It is possible to set a task of definition of defects with high precision and permission,or it is possible to limit the task to detection of several types of defects («dangerous» defects) with good probability. At the same time «small» defects will be passed by the computer program. The problem of minimization of functional for both experimental and computational magnetic field differences is the main problem for the solution of any inverse problem, both in on – line (real time), and in off - line modes. Computational method of calculations in real time of the simplified inverse problem, without accumulation of experimental databases is considered.

RESEARCH OF THE TENSELY-DEFORMED STATE OF ELEMENTS OF MOBILE HEAT STORAGE

Worked out methodology of determination of the tensely-deformed state of elements of mobile heat storage of capacity type, that works in the real terms of temperature and power stress on allows to estimate influence of potential energy on resilient deformation that influences on reliability of construction and to give recommendations on planning of tank (capacities) of accumulator. For determination possibly of possible tension of construction of accumulator kinematics maximum terms were certain. As a tank of accumulator shows a soba the difficult geometrical system, the mathematical model of calculation of coefficient of polynomial and decision of task of minimization of functional was improved for determination of tension for Міzеs taking into account the real geometry of equipment. Conducted quantitative estimation of the tensely-deformed state of the union coupling, corps and bottom of thermal accumulator and the resource of work of these constructions is appraised. Thus admissible tension folds 225 МРа.

Modeling the plane radiation structures consisting of discrete elements

Modeling the radiation pattern (RP) of plane arrays has been carried out using the strict electrodynamical solution of the respective direct problem that allows obtaining the representation of RP in the explicit operator form. The system of integral equations of the Hallen type is used for the determination of the current distribution in the apertures of radiators. The optimal excitation coefficients in apertures are determined while minimization of functional presenting the mean-square deviation of the given and synthesized amplitude RPs. The additional terms in the functions are applied for the minimization of radiation in a near zone of array and limitation on the values of excitation coefficients. The computational results demonstrate the quick convergence of the proposed iterative procedure and the ability to synthesize the prescribed amplitude RPs of the various types.

THE OSCILLATIONS OF ROD CONSTRUCTIONS WITH TAKING INTO ACCOUNT THE ENERGY DISSIPATION

The paper presents a solution of the problem of beam oscillation with the energy dissipation. In studying of the dissipation of the internal energy in the materials the one of the complicated problems is the problem when the material is acting by a variable load. If the frequency of the exciting loads has definite ratios with the eigenfrequency of oscillations, the level of dynamic loads is sharply increases. If the dependence of the logarithmic decrement of the amplitude at the free vibrations, it can be used to calculate the resonant vibrations. When we solving problems for rod constructions the greatest interest has the spectrum of the natural frequencies and corresponding mode shapes. It is proposed to use a two-node finite element in the case of plane bending vibrations of the rod. In this case, the nodal unknowns are deflections and turning angles the nodes. For the approximation of displacements we use a third-order polynomial. To find the spectrum eigenfrequencies and mode shapes is suggested to use a method of increasing stiffness, which is based on the minimization of functional of the Rayleigh type. The method coordinate wise descent is applied to solve the problem of minimizing the functional, which is one of the methods of nonlinear programming. We present numerical algorithm for solving the dynamics of rod structures.

Minimization of Functional Majorant in a Posteriori Error Analysis Based on H(div) Multigrid-Preconditioned CG Method

We consider a Poisson boundary value problem and its functional a posteriori error estimate derived by S. Repin in 1999. The estimate majorizes the H1 seminorm of the error of the discrete solution computed by FEM method and contains a free ux variable from the H(div) space. In order to keep the estimate sharp, a procedure for the minimization of the majorant term with respect to the ux variable is introduced, computing the free ux variable from a global linear system of equations. Since the linear system is symmetric and positive definite, few iterations of a conjugate gradient method with a geometrical multigrid preconditioner are applied. Numerical techniques are demonstated on one benchmark example with a smooth solution on a unit square domain including the computation of the approximate value of the constant in Friedrichs' inequality.