Contactless Measurement of Stressed Deformed State of Structures Under Diagnosis

Abstract

The report containce a body of mathematics and corresponding software, descaned for personal computers, enabling to perfom a stressed states diagnosnics, based on using of values of displacement fields in fixed points obtained by scanning of a Doppler laser operated vibration meter. The said fields should be restore for the whole do main of definition on the base of discrete information. The said fields have predeterminated smoothness bacause the stress fields are obtained by diffirentiating of the displacement fields. The displacement fields are determined by framing of a cubically generalized splain being optained as a solution of a Poisson problem with Dirihlets boundary conditions and a specificially preset right — hant side of the equation the said problem has been decided by the potencial method. To solve it one has to frame a special computational apparatus for definition of singulur integrals. All this decrease the speed of algorythm response this. The method of solution of the Poisson problem worked out in this problem enables to increase the speed of algorythm response and runsas follow. Of the measurment is accuarate, then the Poissons prblem with a right — hand side, preset as a contiuons function and linear for every triangular division of the initial domain with undetermined coefficients, is brougth to dimensional problem with minimum energy using the FEM and properties of the splain extremity [2].