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The paper presents a solution to physically nonlinear problems of the theory of elasticity for continuous isotropic bodies. The presented solution method is a synthesis of the boundary state method and the small parameter method. As a result of the expansion of the desired characteristics of the stress-strain state into power series, it becomes necessary to solve a number of linear problems in the theory of elasticity. The latter is provided by the boundary state method. The solution of problems and assessment of the accuracy of the results.

THE SOLUTION OF PROBLEMS OF THE THEORY OF ELASTICITY FOR AN ISOTROPIC PHYSICALLY NONLINEAR MATERIAL.