International Journal of Impact Engineering 25 (2001) 537}552
Dynamic buckling of elastic}plastic beams including e!ects of
axial stress waves
UG lo Lepik
Institute of Applied Mathematics, Tartu University, Vanemuise 46, 51014 Tartu, Estonia
Received 22 March 2000; received in revised form 23 June 2000; accepted 14 November 2000
Buckling of axially compressed elastic}plastic beams is discussed. The load is applied instantaneously and
remains unaltered during the motion. The e!ect of stress waves travelling along the beam is taken into
account. It is assumed that the material of the beam has linear-strain hardening. A method of solution, based
on the Galerkin technique, is proposed; this method is applicable to an arbitrary number of degrees of
freedom. Numerical examples are presented. 2001 Elsevier Science Ltd. All rights reserved.
Keywords: Euler}Bernoulli beam; Dynamic buckling; Impulsive loading; Galerkin technique; Axial stress waves
Elastic}plastic buckling of beams under dynamic loads is an important problem in dynamics.
Usually, it is assumed that the beam is instantaneously brought to the state of uniform compressive
stress (the so-called uniform thrust theory, see e.g. ). This problem has been a subject of extensive
research; the results are presented in many text-books dealing with structural dynamics (see
If we want to examine the initial phase of buckling the e!ect of travelling axial waves must be
taken into account. This brings about an interaction of longitudinal and transverse waves. For
"nite-length beams a rather complicated state of stress is created because of re#ections of various
The e!ect of a travelling axial wave on the buckling of elastic beams was discussed by Sevin 
and Lindberg . Lindberg carried out also some camera observations of dynamic elastic
E-mail address: firstname.lastname@example.org (UG lo Lepik).
0734-743X/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.
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