Bodies with controllable constitutive laws: some mathematical issues for active optimisation

Maurizio Brocato

doi:10.1117/12.237074

26 April 1996 Bodies with controllable constitutive laws: some mathematical issues for active optimisation

Maurizio Brocato

Proceedings Volume 2779, 3rd International Conference on Intelligent Materials and 3rd European Conference on Smart Structures and Materials; (1996) https://doi.org/10.1117/12.237074
Event: 3rd International Conference on Intelligent Materials, 1996, Lyon, France

Abstract

The response of some bodies to strain can be modified by external fields; it thence appears that some of their mechanical processes can be controlled through an appropriate insertion of sensors-processors-actuators. Thus, we imagine a body where the stress response function depends also on a set of control fields, as would happen in a linear elastic body for which the Young's modulus E could be altered, within limits, by a fitting choice of an external field K: E equals E (K(x,t)). The changes are set to achieve a goal: an assigned functional must reach its extreme value. Consequently problems must be tackled of the type considered in the theory of distributed controls, but a basic issue is to be pointed out: here the controls may influence the terms under partial derivative in the equation of motion rather than those expressing external actions, thus possibly changing the kind of solution of the system (e.g. acting on the elastic coefficients of a vibrating rod all its fundamental modes do change both in frequency and shape). We refer to some tools already available in the literature and adapt some to a feasible circumstance.

Citation Download Citation

Maurizio Brocato "Bodies with controllable constitutive laws: some mathematical issues for active optimisation", Proc. SPIE 2779, 3rd International Conference on Intelligent Materials and 3rd European Conference on Smart Structures and Materials, (26 April 1996); https://doi.org/10.1117/12.237074

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