MODELING OF FINITE INHOMOGENEITIES BY DISCRET SINGULARITIES

This work focuses on development of a mathematical apparatus that allows to perform an approximate description inhomogeneities finite sizes in continuous bodies by arranging the sources given sets smaller dimensions. The structure and properties source densities determine adequacy model. theory differential forms generalized functions underlies this study. boundary value problems with nonsmooth coefficients are formulated. solutions such is sought form weakly convergent series as alternative - equivalent recurrent set jumps. A feature approach ability consistently improve inhomogeneity. important because it qualitatively assess impact real characteristic accuracy model description. Reducing dimensions use efficient methods Green's function integral equations obtain semi-analytic solution for direct inverse problems. based number partial demonstrate proposed modeling inhomogeneities. defects oscillating elastic beam, arbitrary shape plate, fragile cracks two-dimensional body under static loading considered.