An inverse homogenization design method for stress control in composites.

摘要

This thesis addresses the problem of optimal design of microstructure in composite materials. The work involves new developments in homogenization theory and numerical analysis. A computational design method for grading the microstructure in composite materials for the control of local stress in the vicinity of stress concentrations is developed. The method is based upon new rigorous multiscale stress criteria connecting the macroscopic or homogenized stress to local stress fluctuations at the scale of the microstructure. These methods are applied to three different types of design problems. The first treats the problem of optimal distribution of fibers with circular cross section inside a long shaft subject to torsion loading. The second treats the same problem but now the shaft cross section is filled with locally layered material. The third one treats the problem of composite design for a flange fixed at one end and loaded at the other end.