Vasiliev T. Analysis of stress-strain state in mixed boundary value problems for bending of finite length cylindrical bodies

The dissertation is devoted to research of stress-strain state of isotropic and trans-versely isotropic finite length cylindrical bodies in mixed boundary value problems. By means of the spectral theory of non self-adjoint differential operators in case of doubled point’s spectrum it was offered the procedure to obtain elementary solutions for homogeneous assistant problems for layer and infinite cylinder. The homogeneous bases were got for basic homogeneous assistant problems. The components of displacement vector were taken in series by elementary solutions. To build the solution were used methods of reducing the system of functional equations to infinite system of linear algebraic equations. The last one were solved both the method of simple reduction and the method of improved reduction (by use of asymptotic theory). The analysis of stress-strain state in mixed boundary value problems for bending of finite length cylindrical bodies was provided in wide interval of changing of physical and geometrical parameters. The principal possibility of using different kinds of homogeneous solutions was discussed. The practical estimates for boundaries of the theory of thin plates were given. For power of singularity on corner line of isotropic and transversely isotropic cylinder was established transcendental equations. The convergence of series for dis-placements and stresses was investigated. On basis of asymptotic theory the algorithm of improvement of convergence for series of stresses was provided. The intensity factors were obtained by means of the theory of residuals.