A Theoretical Study of Circular Orthotropic Membrane Under Concentrated Load: The Relation of Load and Deflection

In this study, the deformation of circular orthotropic membranes subjected to a central concentrated force is investigated. An orthotropic membrane equation indicating load-deflection behavior based on Föppl-von Kármán membrane theory is obtained and the numerical solutions are gotten by using MATLAB. A variable k, which is the most influential parameter on the load-deflection behavior, is proposed. In isotropic membrane, the change of material parameters mainly influences the deflection of membranes subjected to a concentrated force; however, when studying for orthotropic membrane, the shape of membrane after deformation can be controlled by changing the value of xk. Only change in elastic modulus and Poisson's ratio, with k constant, mainly influence the deflection of curves, instead of the shape of curves. Then, four numerical simulations by ABAQUS are conducted and the membrane element M3D4R is used to set up a finite-element model. By comparing these simulation results with the solutions from orthotropic membrane equation, it is shown that the orthotropic membrane equation gives a good estimation of load-deflection behavior.