Topology Optimization of Multifunctional Nanocomposite Structures

Abstract

This thesis presents the design of multifunctional structures through the optimal placement of nanomaterial additives. Varying the concentration of Carbon Nanotubes (CNTs) in a polymer matrix affects its local effective properties, including mechanical stiffness, electrical conductivity, and piezoresistivity. These local properties in turn drive global multifunctional performance objectives. A topology optimization algorithm determines the optimal distribution of CNTs within an epoxy matrix in an effort to design a set of structures that are capable of performing some combination of mechanical, electrical, or peizoresistive functions. A Pareto-Based Restart Method is introduced and may be used within a multi-start gradient based optimization to obtain well defined multiobjective Pareto Fronts. A linear design variable filter is used to limit the influence of checkerboarding. The algorithm is presented and applied to the design of beam cross-sections and 2D plane stress structures. It is shown that tailoring the location of even a small amount of CNT (as low as 2 percent and as high as 10 percent, by volume) can have significant impact on stiffness, electrical conductivity, and strain-sensing performance. Stiffness is maximized by placing high concentrations of CNT in locations that either maximize the bending rigidity or minimize stress concentrations. Electrical conductivity is maximized by the formation of highly conductive paths between electrodes. Strain-sensing is maximized via location of percolation volume fractions of CNTs in high strain areas, manipulation of the strain field to increase the strain magnitude in these areas, and by avoiding negative contributions of piezoresistivity from areas with differing net signed strains. It is shown that the location of the electrodes can affect sensing performance. A surrogate model for simultaneous optimization of electrode and topology is introduced and used to optimize a 2D plane stress structure. This results in a significant increase in sensing performance when compared to the fixed-electrode topology optimization.