Relaxed approach to structural optimization

Robert V. Kohn

doi:10.1117/12.148424

22 July 1993 Relaxed approach to structural optimization

Robert V. Kohn

Proceedings Volume 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures; (1993) https://doi.org/10.1117/12.148424
Event: 1993 North American Conference on Smart Structures and Materials, 1993, Albuquerque, NM, United States

Abstract

Consider a material whose physical properties are controllable, with two possible states. Suppose further that the control can be applied in a distributed manner, e.g. by laying down a very fine grid and specifying the state of each cell independently. Can we design 'smart structures' by adjusting the control to optimize some performance criterion? This problem is difficult because the set of possible controls is discrete. There is a natural way to make it continuous, however, known as the 'relaxed approach.' Physically, it amounts to the introduction of composite materials as structural components. Mathematically, it amounts to the introduction of fluttering controls. It has evolved over the past 15 years, through the combined effort of many individuals. This is a review paper. The goal is not to present new mathematical results, but rather to publicize the technique of relaxation. Perhaps some readers will known of new problems where this technique could be used to advantage.

Citation Download Citation

Robert V. Kohn "Relaxed approach to structural optimization", Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); https://doi.org/10.1117/12.148424

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