Microstructure-sensitive design of a compliant beam

We show that mechanical design can be conducted where consideration of poly crystalline microstructure as a continuous design variable is facilitated b y use of a spectral representation space. Design of a compliant fixed-guide d beam is used as a case study to illustrate the main tenets of the new app roach, called microstructure-sensitive design (MSD). Selection of the mecha nical framework for the design (e.g., mechanical constitutive model) dictat es the dimensionality of the pertinent representation. Microstructure is co nsidered to be comprised of basic elements that belong to the material Set. For the compliant beam problem, these are uni-axial distribution functions . The universe of pertinent microstructures is found to be the convex hull of the material set, and is named the material hull. Design performance, in terms of specified design objectives and constraints, is represented by on e or more surfaces (often hyperplanes) of finite dimension that intersect t he material hull. Thus, the full range of microstructure, and concomitant d esign performance, can be exploited for any material class. Optimal placeme nt of the salient iso-property surfaces within the material hull dictates t he optimal set of microstructures for the problem. Extensions of MSD to hig hly constrained design problems of higher dimension is also described. (C) 2001 Elsevier Science Ltd. All rights reserved.