Evaluation of stress intensity factors by the R-functions method

An attempt has been made to apply the novel R-functions method (RFM) to the linear elastic fracture mechanics (LEFM) problems. Essential feature of this method consists in a conversion of logical operations performed on sets (relevant to the sub-domains) into algebraic operations performed on elementary functions. The RFM is an analytical-numerical approach to the solution of the boundary value problems involving arbitrary domains that may be concave or/and multiconnected. The solution constructed by the R-functions method is realized in two phases. In the first one an analytical formula for the so-called general structure of solution (GSS) is designed in such a way that it satisfies the prescribed boundary conditions while a certain number of functions remains undetermined. In the second step a suitable numerical procedure is employed to evaluate these functions in order to satisfy the governing equation of the problem considered. The method was proved to be effective in elasticity problems, especially when fully computerized through the use of symbolic programming. The paper gives:

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some basic information about the R-functions method,

formulation of the RFM designed for applications to the LEFM problems,

general structure of the solution for 2D cracked bodies with relevant types of singularity and boundary conditions taken into account,

an outline of the numerical approach and some illustrative examples.

The present work may be considered as an encouraging first step, but further significant effort is required before the R-functions method of treating the problems of fracture mechanics becomes a useful and efficient mathematical tool.