On the application of a limiting process to the dynamic relaxation analysis of circular membranes, circular plates and spherical shells

Abstract Two efficient techniques in the dynamic relaxation (DR) iteration procedure are described: (1) a limiting process technique for the governing equations expressed in polar or spherical coordinates and (2) a new DR-formulation for the time-step proposed by Mikami. The former technique overcomes the mathematical singularity at the coordinate origin without the use of interlacing finite difference meshes. The latter solution technique allows all variables to be evaluated at the same time without the use of fictitious densities. The validity of the use of these two techniques has been demonstrated through the numerical results for the problems of large deflection of axisymmetric circular membranes, large deflection of axisymmetric circular plates, and small deflection of axisymmetric spherical shells.

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