Adaptive sensing of kinematic entities in the vicinity of a time-dependent geometrically nonlinear pre-deformed state

A continuously distributed strain-type sensor can be designed to produce a signal proportional to a desired kinematic entity in the geometrically linear range. The corresponding spatial distribution of the sensor is found as a solution to an auxiliary problem of statics. For a geometrically nonlinear setting we suggest a new general method to design continuous strain-type sensors for measurements in the vicinity of a known pre-deformed state. This method is formulated for a general three-dimensional continuum, and a numerical implementation for rod structures is presented. The efficiency is first demonstrated for a nonlinear static deformation of a spatial rod structure; the modern approach to numerical modeling of rods with no shear deformation is utilized. Another example of in-plane vibrations of a rod demonstrates the benefit of the adaptive recomputation of the sensor distribution accounting for the actual time-dependent pre-deformation.