Abstract
Theory of Generalized J-integral(GJ-integral) by the author(1985) is applicable to elliptic boundary value problems, which relate to shape sensitivity analysis of potential energies. GJ-integral catch the movement of singular points, for examples, boundary, the interface in mixed boundary value problems, the edge of cracks in fracture problems. In this paper, the summary of GJ-integral theory is written. In transmission problem, the singularities also appear, however theory is not directly applicable by discontinuity of coefficients in partial differential equations. New attempt to transmission problems and its numerical calculation by FEM are done in the case-diva∇u=f in Ω . Here a=a1Χ1+a2(1-Χ1)with smooth functions a1,a2 > 0, using the characteristic function Χ1 of Ω1 ⊂⊂ Ω .
