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

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)

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1983
Accession Number
ADP001034

Entities

People

  • Arthur R. Johnson

Organizations

  • United States Army Soldier Systems Center

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Axisymmetric
  • Coefficients
  • Convergence
  • Energy
  • Finite Element Analysis
  • Inclusions
  • Internal Pressure
  • Interpolation
  • Maryland
  • Mathematical Analysis
  • Mathematics
  • Membranes
  • Numerical Analysis
  • Numerical Integration
  • Potential Energy

Readers

  • Electrical Engineering
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Wave Propagation and Nonlinear Chaotic Dynamics.