Numerical homogenization of active material finite-element cells
Article first published online: 1 OCT 2003
Copyright © 2003 John Wiley & Sons, Ltd.
Communications in Numerical Methods in Engineering
Volume 19, Issue 12, pages 977–989, December 2003
How to Cite
Buehler, M. J., Bettig, B. P. and Parker, G. G. (2003), Numerical homogenization of active material finite-element cells. Commun. Numer. Meth. Engng., 19: 977–989. doi: 10.1002/cnm.646
- Issue published online: 1 OCT 2003
- Article first published online: 1 OCT 2003
- Manuscript Accepted: 24 MAR 2003
- Manuscript Received: 3 MAR 2003
- Air Force Office of Scientific Research, Air Force Material Command, USAF. Grant Number: F49620-01-1-0152
- Aactive material;
- piezoelectric material;
- topology optimization
We present the homogenization of a parametrically defined periodic microstructure in which it is possible to separately control the volume fractions of conventional material, active material and void. The effective material properties from the homogenization reduce the necessary finite-element model complexity and also allow for topology optimization of smart structures or optimization of the microstructure itself. Homogenization equations for piezoelectric material including thermal effects are derived with a first-order asymptotic approach. The homogenization problem is solved numerically for discrete values of the design parameters. An interpolation technique is used to find analytical, continuously derivable functions for material properties of the design parameters. Consideration is given to planar microstructures and the treatment of microstructures consisting of dielectrically distinct materials. Copyright © 2003 John Wiley & Sons, Ltd.