On the Resolution of Hypersurface Singularities (original) (raw)

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Structured Singular Value of Symmetric Matrix and Its Lower Bound

Robust stability and performance analysis are reduced to the computation of a structured singular value problem. However its computation is a difficult task and forms a bottleneck of the analysis because it is based on the numerical optimization. We show that this computational burden can be reduced in the case where the matrix under consideration is symmetric. In this case, the computation is equivalent to the maximization of spectral radius over (S+w-1)-parameters, where S is the number of the repeated scalar blocks and w is the total size of full blocks.

Intensity of Singular Stress at the End of a Fiber under Pull-Out Force

Key Engineering Materials, 2007

In this study, singular stress fields at the ends of fibers are discussed by the use of models of rectangular and cylindrical inclusions in a semi-infinite body under pull-out forceļ¼ŽThe body force method is used to formulate those problems as a system of singular integral equations where the unknown functions are densities of the body forces distributed in a semi-infinite body having the same elastic constants as those of the matrix and inclusions.Then generalized stress intensity factors at the corner of rectangular and cylindrical inclusions are systematically calculated with varying the elastic ratio, length, and spacing of the location from edge to inner of the body. The effects of elastic modulus ratio and aspect ratio of inclusion upon the stress intensity factors are discussed.

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