Plane-strain indentation on a smooth foundation: A range of solutions for rigid-perfectly plastic strip

The computation of some slipline field solutions for asymmetric extrusion

“…b;el and dlcl, means that a sign change must be made in the usual formula; cf. equation (15) clel =Tlllu5 -PIC so that from (3) and (5) ~5 = TG:{(I -Q:Jplc + P:,P~C-P:,WU~I (6) Further, we know that 00; = PT+1u5, so that Oie; = Q$,PTd1u5 and Oiel = Q$lPT+lu5 -pic.…”

“…Equations (l), (6) and (7) provide three relations between ul, u3 and u5. Eliminating the latter two vectors between these three equations, we arrive finally at the following inhomogeneous equation for ul: WAul= BC (8) A = { P +~~~R~~ + (Q~,+,Q$, + Q$,P~~,~~:P:~~~~~,,.,~,,~~,'Q$,~~,, + Q~~,~Q $~~ (9) where and B ={-pi(I+Qu1+,P&) +~2 ( P 4 ,~, +Qv,+,Q$,) +Q3,P*4,T,,'(pi(I-Q~,)+p2P~,>} (10) Similarly, by working around the other half of the hodograph diagram from d2b;02 to the origin 0, we obtain two relations between u2, u4 and (r6 = Oek: …”

“…Equations (l), (6) and (7) provide three relations between ul, u3 and u5. Eliminating the latter two vectors between these three equations, we arrive finally at the following inhomogeneous equation for ul: WAul= BC…”