A NEW ANALYTICAL SOLUTION FOR THE LOAD-DEFLECTION OF SQUARE MEMBRANES

Accurate models are essential for the determination of the elastic pro perties of thin films from load-deflection experiments, Although finit e element method (FEM) models have the potential to be very accurate, analytical models are desirable because of their simplicity, In this p aper we present a new analytical solution for the load-deflection of m embranes, Our solution yields the same relationship between the load a nd the deflection as the known analytical solution, However, the value s of two constants are up to 35% higher and correspond well with the r esults from FEM analysis, In addition, the new solution yields analyti cal forms of the bending lines, which agree well with experimental mea surements carried out with silicon nitride membranes, [136]