Accession Number : ADP001034

Title :   Large Deformations and Stability of Axisymmetric Mooney Membranes - Finite Element Solutions,


Personal Author(s) : Johnson,Arthur R.

Report Date : FEB 1983

Pagination or Media Count : 20

Abstract : The nonlinear deformation of axisymmetric Mooney membranes are determined using the finite element method. A one-dimensional form of the potential energy is used. Element gradient and tangent stiffness matrices are computed directly from the potential energy and they are expressed as a sum of coefficients, that depend nonlinearly on the finite element interpolation functions. Numerical integration is used to obtain these element matrices which contain rational expressions of the nodal unknowns. Axisymmetric deformations of the inflated initially flat disk, the out-of-plane deformations of a disk with a circular rigid inclusion, the inflation of a torus with both circular and elliptical initial cross sections and the inflation and stretching of a cylinder are all determined. The torus solutions are carried out beyond the limit pressure yielding both stable and unstable solutions for one internal pressure. The effects of the order of numerical integration used to compute the gradient and tangent matrices and the effects of the order of the polynomial elements used on the convergence of the method with respect to mesh reduction are numerically computed using Richardson's method. (Author)

Descriptors :   *Finite element analysis, *Membranes, *Deformation, Rubber, Axisymmetric, Stability, Numerical integration, One dimensional, Potential energy, Matrices(Mathematics), Coefficients, Interpolation, Computations

Distribution Statement : APPROVED FOR PUBLIC RELEASE