THEORETICAL STUDY OF NONLINEAR MEMBRANE PROBLEMS WITH APPLICATIONS TO AIR BAGS

The deformed configurations of air bags are obtained by potential energy minimization via the Ritz method. Air bags are modeled as nonlinear membranes undergoing finite elastic deformations. The formation is general for an arbitrary strain energy density function that describes the material of the air bag. However, the strain energy density for the potential energy functional minimized in the examples is based on the Mooney strain energy density. The deformed configuration of an air bag is assumed to be represented by a series of trigonometric functions with unknown coefficients. The unknown coefficients are determined by the Newton-Ralphson method for axisymmetric problems and Fletcher and Powell's method for non- axisymmetric problems. The slack variables are used to convert the inequality constraint into an equality constraint for nonaxisymmetric contact problems. The solution may justifiably be compared to a numerical integration of the corresponding equilibrium equations. The energy solution is in excellent agreement with previously published solutions for the inflation of a circular membrane and for the inflation of a rectangular membrane of neo-Hookean material. Solutions to several sample problems related to air bags are presented in this report.

  • Corporate Authors:

    Carnegie Institute of Technology

    Department of Mechanical Engineering
    Pittsburgh, PA  USA 
  • Publication Date: 1975-4

Media Info

  • Features: Figures; References; Tables;
  • Pagination: 164 p.

Subject/Index Terms

Filing Info

  • Accession Number: 00099291
  • Record Type: Publication
  • Source Agency: Highway Safety Research Institute
  • Report/Paper Numbers: DOT-HS-801540 Final Rpt.
  • Contract Numbers: DOT-HS-263-2470
  • Files: TRIS
  • Created Date: Sep 30 1975 12:00AM