Determination of a Drawing Die's Cone Angle at a Small Compression Ratio Based on the Upper Bound Theory

The value of a drawing die＇s cone angle has great influence on wire drawing. In order to determine the optimum value of a drawing die＇ s cone angle, the plastic deformation power Wi, shear deformation power Wi and friction power of contact surface Wf were calculated using the upper bound theory with a reasonable and movement permitted velocity field according to the related characteristics. Then the relation between half cone angle and unit drawing force was obtained and it was compared with the result with the spherical velocity field. The relative error of the two near the optimal value is only about 0. 26% through comparing with existing calculated results. Finally, in an ABAQUS environment the finite element modal of the wire rod with 12. 5 mm diameter in first drawing pass was established and the axial drawing force in different cone angles was obtained using the ABAQUS/Explicit explicit integration method. The finite element method （FEM） results verify the results using the upper bound theory and this indicated that the velocity field and the relation between half cone angle and unit drawing force reasonable.

Base stability analysis of braced deep excavation in undrained anisotropic clay with upper bound theory

It is imperative to evaluate factor of safety against basal heave failure in the design of braced deep excavation in soft clay.Based on previously published field monitoring data and finite element analyses of ground settlements of deep excavation in soft clay,an assumed plastic deformation mechanism proposed here gives upper bound solutions for base stability of braced deep excavations.The proposed kinematic mechanism is optimized by the mobile depth(profile wavelength).The method takes into account the influence of strength anisotropy under plane strain conditions,the embedment of the retaining wall,and the locations of the struts.The current method is validated by comparison with published numerical study of braced excavations in Boston blue clay and two other cases of excavation failure in Taipei.The results show that the upper bound solutions obtained from this presented method is more accurate as compared with the conventional methods for basal heave failure analyses.

Minimax principle on energy dissipation of incompressible shear flow

The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin＇s variational principle characterizes the upper bounds （maxi- mum） of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin＇s formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin＇s variational principle and Howard- Busse＇s statistical turbulence theory.