Shape reconstruction of membranes from strain measurements

What is it about?

This work presents a method to reconstruct the shape, i.e. the displacement, and the loads, i.e. the pressure applied to a membrane, starting from strain measurements. The method assumes that strain measurements are available, but does not require any knowledge of the mechanical properties of the membrane. The results are validated using experiments in which strains were estimated using Digital Image Correlation, an optical method. In practical applications, strains could also be measured by other means, like embedded strain gauges, optical fibers, or more.

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Why is it important?

Addressing this problem in membranes, i.e. in extremely thin structural elements, whose transverse stiffness is provided only by in-plane tension, is very difficult. This is especially true when transverse displacement is so large that tension departs significantly from the value of the undeformed structure, i.e. when no transverse loads are applied. In fact, in those cases common methods, based on constant reference prestress and thus intrinsically linearized, fail or overpredict the transverse displacement. In our work, a dedicated incremental and iterative numerical technique had to be developed to address the fact that, in the neighborhood of the undeformed solution, the problem formulated with usual least-squares methods is ill-conditioned.

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