Modeling of piezoelectric sensors adhesively bonded on trusses using a mathematical programming approach

In this study, piezoelectric sensors design adhesively bonded on truss elements is treated in the framework of mathematical programming. A numerical formulation based on the strength capacity of set structure, adhesive and piezoelectric sensor is proposed. Inside the formulations maximum strength capacity of the adhesive is considered as a limit value in the design. Two formulations are established to obtain the maximum strength of the set; the first one is built on the basis of finite differences and the other one on a formulation of finite elements both based on an admissible static field. The lower bound method applied to limit analysis is extended in this research to analyze trusses with sensors including the adhesive interface. Four examples are designed to assess the numerical methodologies in which the results are compared with other known data. The main contribution of this work is focused on finding the maximum coupling load that a piezoelectric sensor can read before being debonded based on the minimum size constraint of the sensor.