Improvement of semi-analytical design sensitivities of non-linear structures using equilibrium relations

The accuracy problem of the semi-analytical method for shape design sensitivity analysis has been reported for linear and non-linear structures. The source of error is the numerical di erentiation of the element internal force vector, which is inherent to the semi-analytical approach. Such errors occur for structures whose displacement eld is characterized by large rigid body rotations of individual elements. This paper presents a method for the improvement of semi-analytical sensitivities. The method is based on the element free body equilibrium conditions, and on the exact di erentiation of the rigid body modes. The method is e cient, simple to code, and can be applied to linear and non-linear structures. The numerical examples show that this approach eliminates the abnormal errors that occur in the conventional semi-analytical method