PROBLEMS OF RELATED ELASTIC AND VISCOELASTIC BUCKLING IN ONE AND TWO DIMENSIONS

Abstract

The following viscoelastic buckling problems are investigated: (1) the buckling of a simplysupported viscoelastic column under a thrust varying arbitrarily with time; (2) the viscoelastic beam-column with time-dependent transverse load; (3) the torsion of a viscoelastic bar of thin-walled open section in the presence of axial stress, under a time-varying torsional moment; (4) the buckling of a compressed viscoelastic bar on a viscoelastic foundation. Pinned ends are considered, and then free ends which can deflect and rotate. For free ends, buckling is localized near the ends and proceeds at a faster rate than for any mode when the ends are pinned; and (5) the buckling of a viscoelastic frame. Essential singularities arise in the Laplace transform of the deflection. Inversion of the Laplace transform is effected by first representing the transform by its singular parts according to the Mittag-Leffler theorem, in terms of a new variable. The correspondence between elastic and viscoelastic buckling led to an investigation of the stability of the free surface of a compressed semi-infinite elastic medium, as a preliminary to viscoelastic stability in two dimensions. An elastic solution is obtained by means of Green and Zerna's formulation of perturbation from finite strain, and compared with an earlier result of Biot. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1962
Accession Number
AD0284010

Entities

People

  • H. Ramsey
  • J.n. Goodier

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Buckling
  • Deflection
  • Failure (Mechanics)
  • Inversion
  • Mathematical Analysis
  • Mathematics
  • Mechanical Phenomena
  • Perturbations
  • Transverse

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Structural Dynamics.