TOPOLOGY OPTIMIZATION OF SHEETS IN CONTACT BY A SUBGRADIENT METHOD

We consider the solution of finite element discretized optimum sheet problems by an iterative algorithm. The problem is that of maximizing the stiffness of a sheet subject to constraints on the admissible designs and unilateral contact conditions on the displacements. The model allows for zero design volumes, and thus constitutes a true topology optimization problem. We propose and evaluate a subgradient optimization algorithm for a reformulation into a non-differentiable, convex minimization problem in the displacement variables. The convergence of the method and its low computational complexity are established. An optimal design is derived through a simple averaging scheme which combines the solutions to the linear design problems solved within the subgradient method. To illustrate the efficiency of the algorithm and investigate the properties of the optimal designs, thealgorithm is numerically tested on some medium- and large-scale problems. © 1997 by John Wiley & Sons, Ltd.     

Structural Characterization of Phase Separation in Fe-Cr: A Current Comparison of Experimental Methods

Self-assembly due to phase separation within a miscibility gap is important in numerous material systems and applications. A system of particular interest is the binary alloy system Fe-Cr, since it is both a suitable model material and the base system for the stainless steel alloy category, suffering from low-temperature embrittlement due to phase separation. Structural characterization of the minute nano-scale concentration fluctuations during early phase separation has for a long time been considered a major challenge within material characterization. However, recent developments present new opportunities in this field. Here, we present an overview of the current capabilities and limitations of different techniques. A set of Fe-Cr alloys were investigated using small-angle neutron scattering (SANS), atom probe tomography, and analytical transmission electron microscopy. The complementarity of the characterization techniques is clear, and combinatorial studies can provide complete quantitative structure information during phase separation in Fe-Cr alloys. Furthermore, we argue that SANS provides a unique in-situ access to the nanostructure, and that direct comparisons between SANS and phase-field modeling, solving the non-linear Cahn Hilliard equation with proper physical input, should be pursued.