Pabyrivskyy V. Construction solutions of space boundary problems of the elastic theory by the method of holomorphic functions of two complex variables

The thesis is dedicated a formulation of problems three dimensional elasticity theory with use of a method holomorphic function of two complex variables and development on this basis of a technique construction decisions of base boundary problems. The scalar and vector harmonic functions have been taken as a basis of general solution representation when formulating boundary problems of three dimensional elasticity theory. Having generalized Cauchy-Riemann conditions on this ground, vector of displacement and stress tensor for complex conjugate problem is represented via scalar and vector holomorphic function of two complex variables. Respective boundary conditions are formulated and additional integral conditions of stress tensor’s principal moment equality to zero on the solid’s side surface are refined. The methodology of basic states for complex stress tensor via representation of scalar and vector holomorphic functions in terms of uniform polynomials of respective order with respect to complex variables is proposed.