Accession Number : AD0284010

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

Corporate Author : STANFORD UNIV CALIF

Personal Author(s) : GOODIER,J.N. ; RAMSEY,H.

Report Date : JUL 1962

Pagination or Media Count : 1

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)

Descriptors :   *BEAMS (ELECTROMAGNETIC), *BEAMS (STRUCTURAL), *BUCKLING, *ELASTIC PROPERTIES, *SHEAR STRESSES, *STRESSES, DEFORMATION, GREEN'S FUNCTION, INTEGRAL TRANSFORMS, LOAD DISTRIBUTION, LOADING, PARTIAL DIFFERENTIAL EQUATIONS, TORSION BARS

Distribution Statement : APPROVED FOR PUBLIC RELEASE