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An inverse procedure for identification of loads applied to a fractured component using a meshfree method

An efficient iterative inverse procedure is proposed for the identification of the distribution of loads that has led to a specific crack propagation path in a fractured component. This procedure determines the load applied to a part of the boundary based on the captured crack propagation path. The aim of this work, which is the first time to be presented, is important from the perspective of failure analysis, especially in the cases where it is not possible to directly measure the applied loading conditions. The inverse analysis requires the direct fracture mechanics problem to be solved for various boundary loading conditions. For each of the forward problems the meshfree radial point interpolation method, which is augmented with the background decomposition method for evaluation of domain integrals is employed. Using meshfree methods makes it possible to deal with the numerous direct problems, which appear in the formulation of the inverse problem, easily, accurately, and efficiently. The inverse problem of identification of the load distribution is formulated as an optimization problem. For solving the global minimization problem, a stochastic optimization method is used, in which the damped Gauss–Newton method is utilized as the local search algorithm. Through two example problems it is shown that the presented approach can be used effectively for the load identification of a component which has fractured along a specific path.