Z. Erman et Rt. Fenner, 3-DIMENSIONAL DESIGN SENSITIVITY ANALYSIS USING A BOUNDARY INTEGRAL APPROACH, International journal for numerical methods in engineering, 40(4), 1997, pp. 637-654
A general shape design sensitivity analysis approach, different from t
raditional sensitivity methods is developed for three-dimensional elas
tostatic problems. The boundary integral design sensitivity formulatio
n is given in order to obtain traction, displacement and equivalent st
ress sensitivities which are required for design optimization. Those i
ntegral equations are derived analytically by differentiation with res
pect to the normal to the surface at design variable points. Subdivisi
on of boundary elements into sub-elements and rigid body translation m
ethods are employed to deal with singularities that occur during the n
umerical discretization of the domain. Four different examples are dem
onstrated to show the accuracy of the method. The boundary integral se
nsitivity results are compared with the finite difference sensitivity
results. Excellent agreement is achieved between the two methods.