Closed-Form Solution of a Peripherally Fixed Circular Membrane under Uniformly Distributed Transverse Loads and Deflection Restrictions

The problem of axisymmetric deformation of a peripherally fixed and uniformly loaded circular membrane under deflection restrictions (by a frictionless horizontal rigid plate) was analytically solved, where the assumption of constant membrane stress adopted in the existing work was given up, and a closed-form solution of this problem was presented for the first time. The numerical analysis shows that the closed-form solution presented here has higher calculation accuracy than the existing approximate solution.