THREE-DIMENSIONAL DESIGN SENSITIVITY ANALYSIS USING A BOUNDARY INTEGRAL APPROACH

A general shape design sensitivity analysis approach, di¤erent from traditional sensitivity methods is developed for three-dimensional elastostatic problems. The boundary integral design sensitivity formulation is given in order to obtain traction, displacement and equivalent stress sensitivities which are required for design optimization. Those integral equations are derived analytically by di¤erentiation with respect to the normal to the surface at design variable points. Subdivision of boundary elements into sub-elements and rigid body translation methods are employed to deal with singularities that occur during the numerical discretization of the domain. Four di¤erent examples are demonstrated to show the accuracy of the method. The boundary integral sensitivity results are compared with the Þnite di¤erence sensitivity results. Excellent agreement is achieved between the two methods.