Dyyak I. Numerical modeling of deformation processes on the basis of combining finite and boundary elements methods

The thesis is dedicated to the designing and investigation of combined hybrid numerical schemes of finite and boundary element methods for problems of mathematical physics. Numerical schemes of combining FEM and DBEM were designed and investigated for the mathematical heterogeneous "elastic body - Tymoshenko's plate" and for a physically heterogeneous problem with local zones of elastoplastic deformations. The algorithm for the direct boundary element method (DBEM) using the collocation method for the nonstationary heat conduction problem is developed. The solution of the problem of quasi-static thermoelasticity of DBEM by the Galerkin method is constructed with the use of a special procedure for calculating hypersingular integrals. A semi-analytical version of the FEM for the problems of the dynamic theory of the elasticity of spatial axisymmetric objects based on the eigenfunction expansion method have been developed and investigated. Using the Schwartz method, a heterogeneous scheme of FEM and UBEM was developed and investigated. Based on the DDM, heterogeneous numerical schemes for contact problems without friction and computational designs using homogenization theory have been suggeted and investigated. A new error estimator of the adaptive FEM scheme for elasticity theory problems is proposed and implemented. The results of the computational experiments using the developed software confirm the theoretical estimates obtained.