Microstructure-sensitive design of a compliant beam

TLDR: In this article, the authors considered polycrystalline microstructure as a continuous design variable and used a spectral representation space for the design of a compliant fixed-guided beam.

Abstract: We show that mechanical design can be conducted where consideration of polycrystalline microstructure as a continuous design variable is facilitated by use of a spectral representation space. Design of a compliant fixed-guided beam is used as a case study to illustrate the main tenets of the new approach, called microstructure-sensitive design (MSD). Selection of the mechanical framework for the design (e.g., mechanical constitutive model) dictates the dimensionality of the pertinent representation. Microstructure is considered 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 one or more surfaces (often hyperplanes) of finite dimension that intersect the material hull. Thus, the full range of microstructure, and concomitant design performance, can be exploited for any material class. Optimal placement of the salient iso-property surfaces within the material hull dictates the optimal set of microstructures for the problem. Extensions of MSD to highly constrained design problems of higher dimension is also described.

Figures

Fig. 1. Schematic of the compliant 4xed-guided beam.

Fig. 3. Depiction of the material hull M in a three-dimensional subspace.

Fig. 5. Depiction of the optimal solution set (yellow line segment), formed by the intersection of iso-property planes for the primary objective and constraint (gray) and the secondary constraint (brown) with the material hull (blue). Yellow points indicate the microstructure of rolled Ni (left) and rolled+recrystallized Ni (right).

Fig. 2. Depiction of the material set Mc in a three-dimensional subspace.

Table 2 Ratio of predicted maximum and minimum beam lengths and their associated axial-distributions for selected cubic phases (〈u vw〉min is the axial-distribution associated with Lmin and 〈u vw〉max is the axial-distribution associated with Lmax :)

Table 3 List of Q coeIcients for relation (32) for selected cubic phases (units of 1011 dyn=cm2)