SOLUTION OF THREE-DIMENSIONAL BOUNDARY VALUE PROBLEMS OF THE NONLINEAR THEORY OF ELASTICITY USING THE METHODS OF MULTI-DIMENSIONAL COMPLEX ANALYSIS
A new analytical-numeric method for the solution of 3D boundary value problems of nonlinear elasticity theory of Murnagan''s model is considered. Murnagan''s model allows to account for finite deformations of the material. The method suggested is based on the application of complex analysis methods in combination with standard numerical optimization techniques. The method is used to numerically solve the problems on uniaxial tension and simple torsion of a finite cylinder with symmetrical side recess.