K. Ijima et al., EQUILIBRIUM SHAPE-ANALYSIS OF SINGLE-LAYER STRUCTURE BY MEASURE POTENTIAL FUNCTION, Structural engineering and mechanics, 5(6), 1997, pp. 775-784
A unified theory is presented for the shape analysis of curved surface
with a single layer structure composed by frame, membrane or shell. T
he shapes produced by the theory have no shear stress in elements, and
the stress states in the whole shape are as uniform as possible under
an ordinary load. The theory starts from defining an element potentia
l function expressed by the measurement of the element length or the e
lement area. Therefore, the shape analysis can produce various forms a
ccording to the definition of the potential function, and each of thos
e form or the cable net form with the potential function of the second
power of element length is simply gotten by the linear analysis. The
form in tensile stress is mechanically equal to an isotropic tension f
orm.