Abstract:
An algorithm for the numerical solution of the equilibrium problem of a two-dimensional elastic body containing two thin elastic inclusions is developed. The inclusions are modeled within the framework of the theory of Timoshenko beams and intersect at right angle at an internal point of one of them, forming a T-shaped structure in an elastic body. One of the inclusions delaminates from the elastic matrix, forming a crack. On the crack faces, as part of the domain boundary, boundary conditions of the inequality form are specified. The presence of this type of boundary conditions leads to nonlinearity of the problem and formulation in the form of a variational inequality. To develop an algorithm for the numerical solution of the problem, an approximate problem of finding the saddle point of the Lagrangian is formulated. The convergence of solutions of the approximate problem to the solution of the original problem is proven. An iterative Uzawa-type algorithm is constructed and its convergence is shown. Examples of numerical implementation are given.
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