The recently developed Derivative Boundary Integral Equation(DBIE) is used in the adjoin variable method for shape design sensitivity analysis of two-dimensional elasticity problems. The performance functional in the form of boundary integrals is considered. Following the derivation of shape design sensitivity in the usual Boundary Integral Equation(BIE) formulation, a new boundary integral identity is obtained. The resulting expression of the shape sensitivity has a form which is the same as the existing one in the usual BIE, but in the new derivative variables.
An elliptic hole problem in uniform tension at infinity is taken for numerical tests. First, the performance of the DBIE has been compared with that of the usual BIE. Contrary to the expectation that the tangential derivative must be better predicted, no appreciable improvement has been observed. There were cases even with nonrealistic oscillatory results when quadratic elements were used. Similarly, in the numerical sensitivity results, no general conclusion that the DBIE is better than the usual BIE could be made although there were several indication that the DBIE formulation is better performing than the other. The final conclusion for the comparative performance of the two formulation will only be possible after an elaborate and broad numerical study.