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 <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>, 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 <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>. Only change in elastic modulus and Poisson’s ratio, with <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> 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.