On evaluation of shape sensitivities of non-linear critical loads

The 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