Applied Mathematics and Mechanics

, Volume 8, Issue 11, pp 1057–1068

# On exact solution of kármán's equations of rigid clamped circular plate and shallow spherical shell under a concentrated load

• Zheng Xiao-jing
• Zhou You-he
Article

## Abstract

It is extremely difficult to obtain an exact solution of von Kármán'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 ised 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 Kármán'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.

## Keywords

Exact Solution Circular Plate Iterative Solution Perturbation Parameter Concentrate Load
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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