Refined semi-analytical design sensitivities

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. Their main drawback however, is their well-known inaccuracy problem for shape design sensitivities. It was found that the inaccuracies are especially unacceptable 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 method taking full advantage of analytical differentiation of rigid body modes. 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 presented in order to demonstrate the efficiency of the proposed method. It is concluded that the refined SA method possesses the advantages of the traditional SA method, whereas it does not exhibit its unacceptable inaccuracies.