Optimization of stresses in a local region for the maximization of sensitivity and minimization of cross—sensitivity of piezoresistive sensors

Based on the analysis of a typical configuration of piezoresistive sensors, the intensity and uniformity of stresses produced by measurand force in the piezoresistive elements are identified as the parameters that affect the sensitivity of a sensor, and stresses produced by perturbation forces in the piezoresistive elements are identified as the parameters that affect the cross-sensitivity of a sensor. To maximize sensitivity and minimize cross-sensitivity, a shape and topology optimization problem is formulated to tailor the stresses in a local region where the piezoresistive elements are placed. In the optimization, the measurand force and perturbation forces are considered separately as two load cases. The optimization problem is solved via the level set based method. Numerical examples in two dimensions are investigated.