Closed‐form solution of elastic circular membrane with initial stress under uniformly‐distributed loads: Extended Hencky solution

Source abstract

The well‐known Hencky solution is only applicable to the problem of deformation of the elastic circular membrane without initial stress under transverse uniformly‐distributed loads. The problem considered here is a more general case: an initial tensile or compressive stress has been present in the initially flat circular membrane before the membrane is subjected to the transverse loads. The closed‐form solution of the considered problem was presented and all the expressions obtained here for displacements, strains and stresses have the same form as those in the well‐known Hencky solution. The initial stress plays an important role in the determination of numerical value of the integral constant controlling membrane equation. The solution obtained here can be regressed into the well‐known Hencky solution when the initial stress is equal to zero, and it is therefore called extended Hencky solution.