Multi-Functional Topology Optimization of Piezoresistive Nanocomposite Beams

This paper presents an analysis of optimization for multifunctional nanocomposites. A carbon nanotubeepoxy composite is optimized for maximum resistance change and minimum strain energy. Analysis uses a finite element method and includes the coupled physics of mechanics, electrostatics, and piezoresistivity. The problem is solved first for minimum strain energy, then two resistance maximization problems are solved. For all optimization, sensitivities are obtained analytically. After solving the individual problems a weighted sum approach is used in the multi-objective optimization of both minimizing the strain energy and maximizing the resistance change. Comments are made as to the effect of the topology optimization method as a design tool, on the shape of the optimized cross sections, and on the possible extensions on using the coupled physics topology optimization algorithm.