High Order Nonlinear Finite Element Analysis of the Axisymmetric Rubber Membrane.

Abstract

The nonlinear deformations of axisymmetric membranes made of Mooney material are determined using the finite element method. The analysis is constructed in a form that can be easily extended to other nonquadratic energy functionals encountered in finite elasticity. The axisymmetric deformations analysed are the in-plane expansion of a disk with a hole, the inflation of an initially flat circular disk, the out-of-plane deformation of a disk with an inclusion caused by moving the inclusion along the axis of symmetry, and the inflation of a torus with both circular and elliptical cross sections. Stability of the solutions obtained is verified by computing the eigenspectrum of the potential energy's Hessian. Convergence rates with respect to mesh reduction are numerically determined for the displacement field and the strain energy. Quadratic three node Lagrange elements are used for all problems except the torus for which cubic Hermite elements are also used. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1979
Accession Number
ADA137195

Entities

People

  • Alexander D. Johnson
  • I. Fried

Organizations

  • Boston University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Applied Mechanics
  • Axisymmetric
  • Boundary Value Problems
  • Cartesian Coordinates
  • Computers
  • Constitutive Equations
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Geometry
  • Mechanics
  • Numerical Analysis
  • Numerical Integration
  • Potential Energy

Fields of Study

  • Physics

Readers

  • Approximation Theory.
  • Operations Research
  • Structural Health Monitoring of Composite Structures.