BIFURCATION BUCKLING OF SPHERICAL CAPS

Abstract

A nonlinear boundary value problem was considered for the axisymmetric buckling of thin spherical shells subjected to uniform external pressure. The uniformly compressed spherical state is a solution of this problem for all values of the pressure. It was proven, using Poincare's method, that for pressures sufficiently near each simple eigenvalue of the linearized shell buckling theory, there is another (buckled) solution of the nonlinear problem. A convergent perturbation expansion was used to analyze the buckled solutions near the eigenvalues. For a limited range of caps, it was proven that one or three buckled solutions bifurcate from the multiple (double) eigenvalues depending on their order. The existence of a lowest intermediate buckling was established and precise upper and lower bounds were given on its magnitude.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1964
Accession Number
AD0601176

Entities

People

  • Edward L. Reiss

Organizations

  • New York University

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Analytic Functions
  • Boundaries
  • Boundary Value Problems
  • Buckling
  • Differential Equations
  • Displacement
  • Eigenvalues
  • Eigenvectors
  • Energy
  • Equations
  • Geometry
  • Intervals
  • Military Research
  • New York
  • Nonlinear Differential Equations
  • Potential Energy
  • Shape

Readers

  • Calculus or Mathematical Analysis
  • Structural Dynamics.