Analysis of Rectangular Orthotropic Membranes for Mechanical Properties Identification through Load-Displacement Data

In this paper, an innovative procedure is introduced for the identification of the mechanical properties of orthotropic membranes based on load-displacement data. To this end, novel functional forms of the displacement components for rectangular membranes are appropriately introduced. Unknown coefficients of these displacement functions are determined, minimizing the total potential energy of the membrane. The energy method is then combined with an optimization procedure to estimate the elastic constants of the membranes in a straightforward manner. Specifically, a genetic algorithm is used to minimize a properly defined objective function directly related to the sought mechanical properties and computed based on known load-displacement data of the membrane under uniformly distributed load. Numerous applications are reported to demonstrate the efficiency and accuracy of the proposed identification procedure in capturing properties of the membranes. Further, several numerical applications are presented to show the reliability of the proposed displacement field functions by comparing results with finite-element model data, as well as analytical solutions when available. Notably, considering the increasing use of membrane elements in many engineering applications, results suggest that the proposed procedure may represent an accurate and appealing alternative approach for determining membrane mechanical properties, whose characteristics are still difficult to estimate using commonly employed techniques.