The Linear Elastic Wedge Under a Tip Couple at the Critical Angle. Where Is the Paradox?

Abstract The classical problem of a two-dimensional infinite linear elastic wedge, with opening angle $2\alpha $ 2 α , subjected to the action concentrated couple at its tip, was considered by Carothers. solution, which presents quadratic singularity in stress field, suffers spurious behavior critical $\alpha = \alpha ^{*} \simeq \, 0.715 \,\pi = ∗ ≃ 0.715 π when grows unboundedly within body. This inconsistency is usually referred as “wedge paradox”. Here, relying on rather intuitive arguments, we present representation for field wedge captures other states characterized singularity. first obtained considering an auxiliary problem, ideally split into three wedges under tip couples, whose values are determined compatibility conditions terms and displacement common lines. Remarkably, find that state varies continuously ; =\alpha ^{*}$ does not vanish, although has zero resultant moment resultant. An alternative derivation solution relies upon notion nuclei strain, suggests that, angle, applied dipoles without point. We conclude it form Carothers’ cannot account all vertex. paradox naturally disappears proposed representation.