In our previous work, we have shown that distributed strain-type sensors can be used to measure desired structural entities. A distributed strain-type sensor, whose distribution coincides with any statically admissible stress distribution due to quasi-static auxiliary forces, measures the work of these forces done on the original structural entities. Hence, a proper choice of the auxiliary forces results in the measurement of desired structural entities. In this article, we focus on the approximation of distributed sensors by sensor networks composed of sensor patches with constant intensity. The question is where to locate and how to assign weights to the patches such that the combined output of the network approximates the output of the distributed sensor. Our method is based on an integral statement characterizing the output of the distributed sensor and an integral statement for the output of the sensor network. As we cannot ensure the identity of the kernels of the integral statements, we develop methods ensuring the identity of the integral statements themselves. We develop the method for beam-type structures in detail. As a case study, we discuss a one-story frame structure and we seek to design sensor networks to measure desired structural entities; e.g., deflections or slopes.
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