Zheng Xiao-jing, Zhou You-he. On Exact Solution of Karman’s Equations of Rigid Clamped Circular Plate and Shallow Spherical Shell under a Concentrated Load[J]. Applied Mathematics and Mechanics, 1987, 8(11): 997-1006.
Citation: Zheng Xiao-jing, Zhou You-he. On Exact Solution of Karman’s Equations of Rigid Clamped Circular Plate and Shallow Spherical Shell under a Concentrated Load[J]. Applied Mathematics and Mechanics, 1987, 8(11): 997-1006.

On Exact Solution of Karman’s Equations of Rigid Clamped Circular Plate and Shallow Spherical Shell under a Concentrated Load

  • Received Date: 1986-09-20
  • Publish Date: 1987-11-15
  • It is extremely difficult to obtain an exact solution of von Karmán's equations because the equations are nonlinear and coupled.So far many approximate methods have been used to solve the large deflection problems except that only a few exact solutions have been investigated but no strict proof on convergence is presented yet.In this paper,first of all,we reduce the von Kármán's equations to equivalent integral equations which are nonlinear,coupled and singular.Secondly the sequences of continuous function with general form are constructed using iterative technique.Based on the sequences to be uniformly convergent,we obtain analytical formula of exact solutions to von Karman's equations related to large deflection problems of circular plate and shallow spherical shell with clamped boundary subjected to a concentrated load at the centre.
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