SUMMARYA new computational tool is developed for the accurate detection and identification of cracks in structures, to be used in conjunction with non-destructive testing of specimens. It is based on the solution of an inverse problem. Based on some measurements, typically along part of the boundary of the structure, that describe the response of the structure to vibration in a chosen frequency or a combination of frequencies, the goal is to estimate whether the structure contains a crack, and if so, to find the parameters (location, size, orientation and shape) of the crack that produces a response closest to the given measurement data in some chosen norm. The inverse problem is solved using a genetic algorithm (GA). The GA optimization process requires the solution of a very large amount of forward problems. The latter are solved via the extended finite element method (XFEM). This enables one to employ the same regular mesh for all the forward problems. Performance of the method is demonstrated via a number of numerical examples involving a cracked flat membrane. Various computational aspects of the method are discussed, including the a priori estimation of the ill-posedness of the crack identification problem.

This paper considers a planar elastic composite fonned by identical inclusions of a smooth shape embedded periodically in a background. Both materials are taken to be homogeneous and linearly isotropic. The paper addresses two major topics related to such media: the problem of solving their stress states and the attendant problem of computing the composite effective parameters. At given averages, the local stresses/strains are calculated to high accuracy using the well-known Kolosov-Muskhelishvili potentials, which perform well in many situations. This paper's contribution to this approach is twofold. First, the author introduces a new representation of the potentials that incorporates the stress periodicity and given average fields in a simple manner. Second, the author formulates the initial boundary value problem in a nonintegral form that saves computational effort when solving the resultant system of algebraic equations.

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Conformal mappings provide an elegant formulation for planar elastostatic problems. Here, the mapping function coefficients are used in a new manner as design variables in the genetic-algorithm (GA) approach to find a piecewise smooth optimal shape of a single traction-free hole in an elastic plate that minimizes the local stresses under remote shear. This scheme is sufficiently fast and accurate to numerically show that the sought-for shape generates tangential stress of constant absolute value, equal to 30% less than the stress concentration factor (SCF) for the commonly used circular hole. The shape has four symmetrically located corners, and the stress changes sign while remaining finite as it rounds each corner. This is the same shape as the energy-minimizing contour identified in 1986 by the author and Cherkaev for the same load. Other nontrivial examples are given to demonstrate the potential of the approach.