Optimal Continuous Strain-Type Sensors for Finite Deformations of Shell Structures

摘要

A continuously distributed strain-type sensor produces a signal proportional to the weighted integral of the local strains. In the geometrically linear setting this signal equals a desired kinematic entity, if the weight functions are chosen as a solution to a particular auxiliary problem of statics. In the present paper we study the design of such sensors for shell structures in a geometrically nonlinear regime using the modern variant of the theory of shells as material surfaces. In particular, we first suggest and numerically study the effect of the application of so-called nilpotent sensors, which produce a trivial signal in the geometrically linear range, to the determination of local buckling of shell structures. Using various sensors, one can estimate the location of the failure. Furthermore, we demonstrate the application of a recently suggested new general method to design strain-type sensors for measurements in the vicinity of a known pre-deformed state to shell structures.