SUMMARYThe 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 ÿeld 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.
SUMMARYThe present paper focuses on the evaluation of the shape sensitivities of the limit and bifurcation loads of geometrically non-linear structures. The analytical approach is applied for isoparametric elements, leading to exact results for a given mesh. Since this approach is di cult to apply to other element types, the semi-analytical method has been widely used for shape sensitivity computation. This method combines ease of implementation with computational e ciency, but presents severe accuracy problems. Thus, a general procedure to improve the semi-analytical sensitivities of the non-linear critical loads is presented. The numerical examples show that this procedure leads to sensitivities with su cient accuracy for shape optimization applications.
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