Curvilinear Displacement Transfer Functions for Deformed Shape Predictions of Curved Structures Using Distributed Surface Strains

Curvilinear Displacement Transfer Functions were formulated for deformed shape predictions of different curved structures using surface strains. The embedded curved beam (depth-wise cross section of a curved structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. The discrete approach enabled piecewise integrations of a curvature-strain differential equation for the embedded curved beam to yield closed-form Curvilinear Displacement Transfer Functions, which are written in terms of embedded curved-beam geometrical parameters and surface strains. By inputting the surface strain data, the Curvilinear Displacement Transfer Functions can transform surface strains into deflections along each embedded curved beam for mapping out the overall structural deformed shapes. The finite-element method was used to analytically generate the surface strains of the curved beams. The deformed shape prediction accuracies were then determined by comparing the theoretical deflections with the finite-element-generated deflections, which were used as yardsticks. By introducing the correction factors in simple mathematical forms, the Curvilinear Displacement Transfer Functions can be quite accurate for shape predictions of different curved-beam structures ranging from limit case of straight beam up to semicircular curved beam.