Nomenclature aA.; / = bilinear form due to strain energy a 0 Vμ .; / = variation of aA.; / due to orientation change a 0 VA .; / = variation of aA.; / due to shape change cA.; / = bilinear form due to the damping dA.; / = bilinear form due to kinetic energy e.; / = bilinearmapping h = thickness of the design component `A./ = load linear form V = design velocity eld Vμ = orientation design velocity eld VA = shape design velocity eld y = eigenvector of structure Z = space of kinematically admissible displacements z = displacementvector 1A = sensitivity coef cient from central nite differencemethod 3 = eigenvalue of structure 3 0 = variation of 3 due to design change 3 0 Vμ = variation of 3 due to orientation change 3 0 VA = variation of 3 due to shape change = adjoint displacement vector 1⁄2 = mass density & = hysteretic damping coef cient A 0 = continuumdesign sensitivity coef cient ! = natural frequency of structure r = gradient operator
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Wang et al. (2002) studied this question.
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