EFFECTIVE-NUMERICAL METHOD FOR SOLVING THE PROBLEMS OF THE THEORY OF ELASTICITY IN FINITE DEFORMATIONS

Usually, when determining the safety margins and reliability of structures and their elements, it is sufficient to solve the boundary value problem of the theory of elasticity at small deformations. With the development of innovative technologies and the widespread use of composite materials, the calculation of materials at large deformations is required. The article formulates a twodimensional boundary value problem of the theory of elasticity in finite deformations for a rectangular region with different boundary conditions. The grid equations are compiled by the finite-difference method. To solve nonlinear grid equations, an effective iterative method is proposed based on the solution of finite-difference equations and boundary conditions with respect to the sought nodal values, taking into account nonlinear terms. The distribution of displacements and stresses in a given area is investigated and the numerical results are compared with the results obtained for boundary value problems of the theory of elasticity at small deformations.

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