The analytical-numerical method for solving boundary problems of the theory of elasticity and heat conductivity is developed for structural-heterogeneous media with inclusions of the spherical and cylindrical form (with an intermediate layer). Gradient models and as a special case classical models of the theory elasticity and heat conductivity are considered. The method is based on subdividing the initial area into simpler subdomain-blocks, and then representing the solution in each block as generalized Taylor or Loran expansions on fundamental systems of functions, which exactly satisfy the Helmholtz or Poisson equations. The advantage of this method is the opportunity of obtaining effective characteristics, and also local stress and temperature fields with a high guaranteed degree of accuracy.
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