Problems solution based on parameter differentiation method

Criterion of hyperelastic soft shell deforming nonlinear problem numerical solution continuation uniqueness assessment is suggested in the work. The criterion can be used when carrying out calculations. It is based on investigation of properties of Jacobi matrix of linear algebraic equations system which is formed when using parameter differentiation method. This method allows reducing nonlinear boundary value problem solution to a couple of quasilinear boundary value and nonlinear initial problems and applying initial parameters method of solving linear boundary value problems. For assessment of solution continuation uniqueness in each point of integration interval one needs controlling magnitudes of resolving differential equation system right-hand sides vector components, as well as calculating determinant and rank of Jacobi matrix of algebraic equations system formed as a result of initial parameters method using, and expanded Jacobi matrix rank calculation. For testing suggested criterion the problem of neohookean material hemisphere static inflation by uniformly applied pressure is considered. Solution of this problem as certain values of numerical algorithm parameters leads to various calculation difficulties – calculation stability loss, big errors of calculation results, non-uniqueness of solution which reason requires additional investigations. It is shown that in the points, where mentioned difficulties are met, determinateness conditions for the function of right-hand sides of differential equation system formulated within the framework of the suggested criterion are broken.