Elastic-plastic deformation of
a three-layer rod on the elastic basis
E.I.Starovojtov, D.V.Leonenko,
A.V.Yarovaya
Three-layer elements of designs consisting of two bearing layers and
filler, have received significant distribution owing to the high durability at
rather small weight. In conditions of bending strain they appear to be the most
rational. Three-layer designs with an incompressible along thickness filler
including elastic-plastic are investigated before. Here the decision of a
problem on a bending of three-layer elastic-plastic rod laying on the elastic
basis, with compressible physically nonlinear filler is resulted.
The three-layer nonsymmetrical along thickness rod with compressible
filler is considered, external bearing layers are made from elastic-plastic
material, and filler - from nonlinear-elastic. For description of a kinematics
of a package following suppositions are accepted: in bearing layers Bernoulli
hypotheses are fulfilled, in rigid filler exact relations of the theory of
elasticity with linear approximation of transitions of its points from cross
coordinate z are valid. On contact boundaries conditions of a continuity
of transitions are used. Materials of bearing layers are incompressible in a
cross direction, reduction and small strains in filler are considered.
Thus, the problem about curving of the three-layer rod laying on the
elastic foundation is set and solved. As an example the influence of plastic
properties of materials of layers upon deformation of a rod is investigated at
the foundation with average rigidity. Convergence of a method of elastic solutions is investigated.
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