Isogeometric structural shape optimization using automatic sensitivity analysis

Abstract

A method for isogeometric structural shape optimization using a multilevel approach and automated sensitivity analysis is presented in this work. The analysis mesh is obtained after carrying out successive refinements using the knot insertion and/or degree elevation algorithms, while retaining the coarse geometry for the domain design. Even though analytical sensitivities can be derived and implemented, they are prone to implementation errors and time consuming to derive. To circumvent the complication, we propose to use an automatic differentiation toolbox to perform the sensitivity analysis. This facilitates the computation of the gradients of the objective function with respect to the design variables defined over the coarse design domain with accuracy up to machine precision. Both forward and reverse modes of automatic differentiation are implemented. The accuracy, numerical efficiency and memory requirements are studied for analytical, numerical and automatic sensitivities in order to show the benefits and limitations of using automated gradients. Finally, numerical examples for two-dimensional and solid-shell shape optimization problems are presented to show the efficiency of the automatic sensitivities.