Variation Principles and Bounds for the Approximate Analysis of Plane Membranes Under Lateral Pressure

A first-order consistent approximation for the analysis of small deflections of membranes is given several variational formulations. Lower and upper bounds are derived for the volume enclosed by deformed and undeformed membranes. The power of the principles is discussed and their application is illustrated by some cases of practical interest. Explicit analytical results are given for linear elastic membranes having circular, elliptic, and rectangular contours.