Study of the plane problem for a physically nonlinear elastic solid by methods of the theory of functions of one complex Variable

Successful application of methods of complex analysis in linear elasticity problems, initiated by Kolosov, Muskhelishvili, Vekua, and their students, serves as a basis for similar studies in the field of analytical-numerical approximations to solutions of boundary value problems and various nonlinear equations of mathematical physics. In the present paper, we suggest a method for solving plane boundary-value problems for a special class of physically nonlinear elastic solids in the case of small strains. This general method, which can be used for a wide class of domains, is illustrated by the example of a square domain with boundary conditions given in stresses. These methods can also easily be used for boundary conditions of other types.