Multiscale analytical sensitivity analysis for composite materials

We describe a methodology aimed at determining the sensitivity of the global structural behaviour, such deformation or vibration modes with respect to the local characteristics such as material constants of microconstituents. An analytical gradient computation, which involves the direct di erentiation of the multiple scale strong forms with respect to the design parameters is developed. Comparison of the multiple scale sensitivity analysis (MASA) to the central nite di erence (CFD) approximation in terms of accuracy and computation e ciency is carried out. We demonstrate the robustness of the MASA approach compared to the CFD approximation, which has been found to be highly sensitive to the choice of the step size, whose optimal value is problem dependent