Nonlinear Response of a Rectangular Membrane Sensing Element

The problem of large deflections is solved for a pressure sensing element in the form of a fixed-edge rectangular membrane with an aspect ratio of 1, 1.5, 2, or 3. Analytical formulas are derived for the deflection, allowing for midplane deformation. A manageable model is constructed for calculating the components of strain and stress. The results are found to be in good agreement with data obtained by the finite-element method. The magnitude of stress nonlinearity is calculated as a function of coordinates for each surface of the membrane.