| Abstract: | The constitutive law of elastoplastic material being
simplified to three-line model (elastic-linear softening plastic-residual
ideal plastic model), and the material obeying Tresca yield criteria and
associated flow rule, the analytical solutions of thick-walled cylinder
subject to internal pressure $p$ were derived in the paper. The result shows
that the yield stress in the softening plastic region is the inverse square
of radial coordinate $r$.
Firstly, the pressure $p$ was taken as generalized force, the displacement $u$
taken as generalized displacement, and the thick-walled cylinder taken as a
whole system. On the basis of the solutions the stability problem of
thick-walled cylinder was then discussed. The $p$-$u$ curve of balance path was
drawn, on which each point denotes a balance state. The slope of the tangent
line for each point can be considered the stiffness of thick-walled
cylinder. The extreme value of generalized force is the critical point on
the curve, and the critical point separates the curve into two sections: the
section before the critical point is stable, and the stiffness is positive;
the section after the point is unstable, and the stiffness is negative. When
the generalized force reaches the critical point, the displacement increases
quickly and the system loses its stability, while ideal plastic thick-walled
cylinder loses its stability only when the plastic region penetrates through
the whole cylinder. Therefore, the failure mechanism is completely
different: the former belongs to extreme value point destabilization, and
the latter belongs to strength failure. That is to say, the bearing capacity
has different mechanical meanings. |
