Closed-form solution of well-known Hencky problem without small-rotation-angle assumption

In this paper, the well‐known Hencky problem, the large deflection problem of axisymmetric deformation of uniformly loaded circular membranes, was resolved, where the small‐rotation‐angle assumption usually adopted in membrane problems was given up. The presented closed‐form solution has a higher accuracy than well‐known Hencky solution, a better understanding of the non‐linear behavior of the considered problem could thus be reached. The presented numerical example shows that, the important integral constant controlling differential equations should change along with the increase of the applied transverse loads, but in well‐known Hencky solution it becomes a constant due to the adopted small‐rotation‐angle assumption, resulting in the calculation error to increase, especially when the applied transverse loads is relatively large the well‐known Hencky solution will no longer apply. The presented closed‐form solution has a higher accuracy than well‐known Hencky solution, a better understanding of the non‐linear behavior of the considered problem could thus be reached. The presented numerical example shows that, the important integral constant controlling differential equations should change along with the increase of the applied transverse loads, but in well‐known Hencky solution it becomes a constant due to the adopted small‐rotation‐angle assumption, resulting in the calculation error to increase, especially when the applied transverse loads is relatively large the well‐known Hencky solution will no longer apply.