Discretization error in the calculation of sensitivities by means of the finite element method (Spanish text)

Shape optimization processes for structural components require gradient (sensitivity) values for the magnitudes of interest evaluated with enough precision. In this sense an estimator for the discretization error in shape sensitivities evaluated by means of the finite element method has been developed. An analysis procedure based on this error estimator has also been proposed. This procedure allows for the evaluation of solutions with an error in sensitivities lower than that specified by the analyst.; The proposed error estimator can be considered as an extension of the Zienkiewicz-Zhu error estimator for its application to the estimation of the discretization error arising from shape sensitivity analysis, both at a global and at a local level.; The analysis of the discretization errors in sensitivities and in energy norm allowed for the development of an equation that relates both errors through a constant. The behavior of the error estimator in sensitivities has been shown to be similar to that of the error estimator in energy norm. This similar performance can be justified by the relationship between both errors.; This relationship has also been the key in the development of a numerical procedure used to quantify the quality of the techniques used to calculate the velocity field employed in sensitivity analysis. The proposed procedure showed that the domain triangulation method is the most appropriate method for the mesh generator utilized, out of those evaluated.; The study of the stress recovery methods based on the SPR technique that has been carried out, allowed the development of a technique of reduced computational cost named SPR-R. This modification of the SPR technique makes possible the evaluation of a recovered stress field that, in boundary nodes, exactly reproduces the imposed tractions. As a result, error estimation in energy norm has been substantially improved in elements located over the component boundary. The technique has also been applied to evaluate the recovered field of sensitivities of stresses with respect to design variables, which is included in the equation of the estimator of discretization error in sensitivities. Consequently the behavior of this estimator has also been improved over the contour elements.