An Upper Bound Solution for a Two-Layer Cylinder Subject to Compression and Twist

2007 ◽  
Vol 345-346 ◽  
pp. 37-40 ◽  
Author(s):  
Gow Yi Tzou ◽  
Sergei Alexandrov
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Additional Condition ◽  
Velocity Fields ◽  
Upper Bound Theorem ◽  
Predictive Capacity ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Bound Theorem ◽  
Formal Requirements

The choice of a kinematically admissible velocity field has a great effect on the predictive capacity of upper bound solutions. It is always advantageous, in addition to the formal requirements of the upper bound theorem, to select a class of velocity fields satisfying some additional conditions that follow from the exact formulation of the problem. In the case of maximum friction law, such an additional condition is that the real velocity field is singular in the vicinity of the friction surface. In the present paper this additional condition is incorporated in the class of kinematically admissible velocity fields chosen for a theoretical analysis of two - layer cylinders subject to compression and twist. An effect of the angular velocity of the die on process parameters is emphasized and discussed.

Upper Bound Solutions to Plane-Strain Extrusion Problems

1970 ◽  
Vol 92 (1) ◽  
pp. 158-164 ◽  
Author(s):  
P. C. T. Chen
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Material Properties ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Deformation Pattern ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Die Geometry ◽  
Bound Theorem

A method for selecting admissible velocity fields is presented for incompressible material. As illustrations, extrusion processes through three basic types of curved dies have been treated: cosine, elliptic, and hyperbolic. Upper-bound theorem is used in obtaining mean extrusion pressures and also in choosing the most suitable deformation pattern for extrusion through square dies. Effects of die geometry, friction, and material properties are discussed.

Direct Upper Bound Solution to Rectangular-to-Polygonal Extrusion Through Square Die

1999 ◽  
Vol 121 (2) ◽  
pp. 195-201 ◽  
Author(s):  
S. K. Sahoo ◽  
P. K. Kar ◽  
K. C. Singh
Keyword(s):  
Steady State ◽  
Velocity Field ◽  
Upper Bound ◽  
Velocity Fields ◽  
Extrusion Pressure ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Aspect Ratios

This paper is concerned with an attempt to find an upper bound solution for the problems of steady-state extrusion of asymmetric polygonal section bars through rough square dies. A class of kinematically admissible velocity fields is examined, reformulating the SERR technique, to get the velocity field that gives the lowest upper bound. This velocity field is utilized to compute the non-dimensional average extrusion pressure at various area reductions for different billet aspect ratios.

scholarly journals An Upper Bound Solution for the Compression of an Orthotropic Cylinder

Materials ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5253
Author(s):  
Lihui Lang ◽  
Sergei Alexandrov ◽  
Yun-Che Wang
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Yield Criterion ◽  
Limit Load ◽  
Compression Force ◽  
Orthotropic Cylinder ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Bound Theorem ◽  
Quick Estimate

The upper bound theorem is used in conjunction with Hill’s quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity field in the vicinity of the friction surface if the maximum friction law is adopted. The regime of sticking is also taken into consideration. The effect of this regime on the upper bound limit load is revealed. In particular, the kinematically admissible velocity field that includes the regime of sticking may result in a lower upper bound than that with no sticking. The boundary value problem is classified by a great number of geometric and material parameters. Therefore, a systematic parametric analysis of the effect of these parameters on the compression force is practically impossible. An advantage of the solution found is that it provides a quick estimate of this force for any given set of parameters.

An Upper Bound Solution for Upsetting of Two-Layer Cylinder

2006 ◽  
Vol 505-507 ◽  
pp. 1303-1308 ◽  
Author(s):  
Gow Yi Tzou ◽  
Sergei Alexandrov
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Limit Load ◽  
Equivalent Strain ◽  
Industrial Applications ◽  
Upper Bound Theorem ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Perfectly Plastic ◽  
Plastic Materials

An upper bound solution for axisymmetric upsetting of two-layer cylinder made of rigid perfectly plastic materials is provided. An important feature of the solution is that the kinematically admissible velocity field, in addition to the necessary requirements of the upper bound theorem, satisfies the frictional boundary condition in stresses, the maximum friction law. The latter is archived by introducing a singular velocity field such that the equivalent strain rate approaches infinity at the friction surface. The dependence of the upper bound limit load on geometric parameters and the ratio of the yield stresses of the two materials is analyzed. The solution can be used in industrial applications for evaluating the load required to deform two-layer cylinders.

scholarly journals Upper Bound Solution of Safety Factor for Shallow Tunnels Face Using a Nonlinear Failure Criterion and Shear Strength Reduction Technique

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Fu Huang ◽  
Zai-lan Li ◽  
Tong-hua Ling
Keyword(s):  
Safety Factor ◽  
Upper Bound ◽  
Reduction Technique ◽  
Nonlinear Failure Criterion ◽  
Upper Bound Theorem ◽  
Tunnel Face ◽  
Bound Solution ◽  
Strength Reduction Technique ◽  
Bound Theorem ◽  
The Stability

A method to evaluate the stability of tunnel face is proposed in the framework of upper bound theorem. The safety factor which is widely applied in slope stability analysis is introduced to estimate the stability of tunnel face using the upper bound theorem of limit analysis in conjunction with a strength reduction technique. Considering almost all geomaterials following a nonlinear failure criterion, a generalized tangential technique is used to calculate the external work and internal energy dissipation in the kinematically admissible velocity field. The upper bound solution of safety factor is obtained by optimization calculation. To evaluate the validity of the method proposed in this paper, the safety factor is compared with those calculated by limit equilibrium method. The comparison shows the solutions derived from these two methods match each other well, which shows the method proposed in this paper can be considered as effective.

A Generalized Velocity Field for Plane Strain Extrusion Through Arbitrarily Curved Dies

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
H. Haghighat ◽  
P. Amjadian
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Angular Velocity ◽  
Plane Strain ◽  
Upper Bound ◽  
Velocity Fields ◽  
Finite Element Code ◽  
Admissible Velocity ◽  
Paper Plane ◽  
Good Agreement

In this paper, plane strain extrusion through arbitrarily curved dies is investigated analytically, numerically, and experimentally. Two kinematically admissible velocity fields based on assuming proportional angles, angular velocity field, and proportional distances from the midline in the deformation zone, sine velocity field, are developed for use in upper bound models. The relative average extrusion pressures for the two velocity fields are compared to each other and also with the velocity field of a reference for extrusion through a curved die. The results demonstrate that the angular velocity field is the best. Then, by using the developed analytical model, optimum die lengths which minimize the extrusion loads are determined for a streamlined die and also for a wedge shaped die. The corresponding results for those two die shapes are also determined by using the finite element code and by doing some experiments and are compared with upper bound results. These comparisons show a good agreement.

Plane Strain Forging—A Lower Upper Bound Approach

1975 ◽  
Vol 97 (1) ◽  
pp. 119-124 ◽  
Author(s):  
V. Nagpal ◽  
W. R. Clough
Keyword(s):  
Velocity Field ◽  
Process Parameters ◽  
Upper Bound ◽  
Dead Zone ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Admissible Velocity ◽  
Special Cases ◽  
Rectangular Strip ◽  
General Velocity

A general kinematically admissible velocity field applicable to forging of a rectangular strip of a incompressible material is presented. Generalized shape of any dead zone, if assumed, can be obtained in terms of process parameters from this velocity field. Two different upper bound solutions for average forging pressure are obtained from simple velocity fields which are special cases of proposed general velocity field. Numerical results of the solutions show improvement over previous upper bound solutions published in literature over a certain range of process parameters.

Selection of the Optimal Distribution for the Upper Bound Theorem in Indentation Processes

2014 ◽  
Vol 797 ◽  
pp. 117-122 ◽  
Author(s):  
Carolina Bermudo ◽  
F. Martín ◽  
Lorenzo Sevilla
Keyword(s):  
Upper Bound ◽  
Geometric Distribution ◽  
Optimal Choice ◽  
Optimal Distribution ◽  
Upper Bound Theorem ◽  
Modular Model ◽  
Bound Theorem ◽  
Rigid Zones ◽  
Dimensionless Relation ◽  
Selection Of

It has been established, in previous studies, the best adaptation and solution for the implementation of the modular model, being the current choice based on the minimization of the p/2k dimensionless relation obtained for each one of the model, analyzed under the same boundary conditions and efforts. Among the different cases covered, this paper shows the study for the optimal choice of the geometric distribution of zones. The Upper Bound Theorem (UBT) by its Triangular Rigid Zones (TRZ) consideration, under modular distribution, is applied to indentation processes. To extend the application of the model, cases of different thicknesses are considered

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