Efficient structural optimization routines require availability of gradient
information. Semi-analytical (SA) design sensitivities are rather popular,
as they combine ease of implementation with computational efficiency. Thei
r main drawback however, is their well-known inaccuracy problem for shape d
esign sensitivities. It was found that the inaccuracies are especially unac
ceptable for slender structures and become more pronounced when relatively
large rigid body motions can be identified for individual finite elements.
Based on these observations, the authors recently developed a refined SA me
thod taking full advantage of analytical differentiation of rigid body mode
s. The present article presents a sound and unified formulation of refined
semi-analytical (RSA) design sensitivities for linear, linearized buckling,
geometrically nonlinear and limit point analyses. Numerical results are pr
esented in order to demonstrate the efficiency of the proposed method. It i
s concluded that the refined SA method possesses the advantages of the trad
itional SA method, whereas it does not exhibit its unacceptable inaccuracie
s. (C) 2000 Elsevier Science Ltd. All rights reserved.