Author(s)

J. Steinberg

Abstract

Integral equation formulation for a singular biharmonic problem J. Steinberg Department of Mathematics, Technion, 32000 Haifa, Israel Introduction We consider a model problem of linear fracture mechanics (mode I) which is formulated as a pure Dirichlet problem with the biharmonic equation for the Airy stress function. On the boundary which includes a straight slit the values of the function and of its normal derivative are prescribed and vanish on the slit, see fig. 2 below. The condition that the gradient of the solution should be bounded makes the problem a well-posed one. Fig. 1 illustrates the physical problem and because of symmetry it is formulated for the upper half of the rectangular plate as in fig 2. Several properties of the solution u are known, see[6], and are summarized as fol- lows: (a) According to the symmetry principle for biharmonic functions, u can be continued analytically on a second sheet, which linked cross-wise along the slit with the physical domain of fi

Keywords