Regional stress in a noncircular cylinder.

Several mathematical formulas are presented for estimating regional average circumferential stress and shear stress in a thick-wall, noncircular cylinder with a plane of symmetry. The formulas require images of exterior and interior chamber silhouettes plus surface pressures. The formulas are primarily intended for application to the left ventricle in the short axis plane near the base (where the meridional radius of curvature is normally much larger than the circumferential radius of curvature) and to blood vessels. The formulas predict stresses in a variety of chambers to within 3% of finite element values determined from a large-scale structural analysis computer program called ANSYS.