Application of the method of successive approximation to the calculation of the average deflection of a circular plate. (English. Russian original) Zbl 0575.73061

Martynova, E. D.

Mosc. Univ. Mech. Bull. 39, No. 4, 1-5 (1984); translation from Vestn. Mosk. Univ., Ser. I 1984, No. 4, 43-45 (1984).

The author investigates the convergence of the process of successive approximation upon integration of the Kármán equations for a circular plate. It is shown that, under a uniformly distributed load, the convergence is uniform, and any two successive approximations yield estimates of upper and lower bounds for the exact solution of the nonlinear problem. The theoretical findings are confirmed by numerical calculations.

MSC:

74K20

Plates

Keywords:

average deflection; axisymmetric deformation; uniform transverse load; rigidly clamped edges; successive approximation; integration of the Kármán equations; circular plate; uniformly distributed load; convergence is uniform; estimates of upper and lower bounds for the exact solution; nonlinear problem