High-performance methods for investigation stress concentration in shells using mathematical models of their deformation mechanics and reduction of the boundary problem to the problem with initial conditions

The problem is solved using well-known differential equations of mechanics to specify deformation of shells and supporting frames. The equations are represented in the matrix form. The convergent-series-type formula is obtained and used for solving the matrix differential equations. Calculation algorithm is based on coupling several short shells to provide stability of the numerical procedure. Boundary conditions and external loads are taken into account when the system of algebraic equation is solved. Decision of the boundary problem is obtained under condition that the independent variable is within the stress concentrations vicinity. The obtained theorem proves: the obtained numerical decision of the boundary problem is in the stress concentration vicinity may be taken as the initial condition of the Cochi problem and used for investigation of the stress concentration problem with the apriori established error.