A fast algorithm for solving nonlinear hypersingular integral equation
نویسندگان
چکیده
where 0 < ε < 1, and the unknown function g satisfies the boundary conditions g(±1) = 0. The integral has to be understood as the finite part of the strongly singular integral in the sense of Hadamard, who introduced this concept in relation to the Cauchy principal value. In fact, the toughness of brittle solids such as ceramics and cement-like materials can be increased considerably by the use of fibers which bridge microcracks and provide further resistance to fracture. The effect of presence of unbroken ligaments and fibers may be represented as distributed forces on the bridged portion of the crack. In [8] the physical problem about cracks of brittle solids is examined and the two following cases are studied:
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