Styahar A. Computer modeling of deformation of elastic bodies with thin inclusions using combined finite and boundary element method

In the thesis the approach for investigation of bodies with thin inclusions is proposed. Heterogeneous mathematical model of elastic body with thin inclusion is formulated. The stress-strain state of the matrix is described by the classical theory of elasticity. For the description of the stress-strain state of the thin inclusion the equations of Timoshenko shell theory are used. Perfect transmission conditions are hold on the interface. Existence and uniqueness of weak solution of the Steklov-Poincare equation are proved. Domain decomposition algorithm is formulated for the solution of the aforementioned problem and the convergence of this algorithm is proved. For the numerical solution in the massive part boundary element method is used with linear or quadratic basis functions. The approximate solution in the thin part is built using finite element method with approximating bubble functions. A priori error estimate is obtained for this approach. Numerical experiments illustrate the efficiency of the proposed algorithm.