Numerical homogenization of active material finite-element cells

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.

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