Application of upper bound theorem to processes of simultaneous deformation of viscoplastic and rigid perfectly plastic materials

2007 ◽  
Vol 14 (S1) ◽  
pp. 19-21
Author(s):  
Sergei Alexandrov ◽  
Robert Goldstein
Keyword(s):  
Upper Bound ◽  
Upper Bound Theorem ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Bound Theorem

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.

Pipe Flow of Plastic Materials

1980 ◽  
Vol 47 (3) ◽  
pp. 496-498 ◽  
Author(s):  
W. H. Yang
Keyword(s):  
Nonlinear Programming ◽  
Upper Bound ◽  
Pipe Flow ◽  
Food Processing ◽  
Nonlinear Programming Problem ◽  
Upper Bound Theorem ◽  
Cross Sectional ◽  
Plastic Materials ◽  
Bound Theorem ◽  
Sectional Shape

Plastic materials behave as both solids and fluids. When forced to move in a pipe, they flow as a solid plug with a slipping boundary. Depending on the cross-sectional shape of the pipe, the slipping boundary may not coincide with the inner boundary of the pipe. When such is the situation, there exist dead regions in the flow. This is undesirable when the material is time degradable as those encountered in the food processing and chemical industry. Two formulations of nonlinear programming problems governing the pipe flow are presented. They correspond, respectively, to the lower bound and upper bound theorems of plasticity. An efficient method is developed for the nonlinear programming problem formulated from the upper bound theorem. Application of the method to two examples are demonstrated.

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

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.

Hardening effect analysis in indentation processes by modular configuration of the upper bound theorem

2017 ◽  
Vol 10 (1) ◽  
pp. 59
Author(s):  
Carolina Bermudo Gamboa ◽  
Francisco De Sales Martín Fernández ◽  
Lorenzo Sevilla Hurtado
Keyword(s):  
Upper Bound ◽  
Upper Bound Theorem ◽  
Effect Analysis ◽  
Hardening Effect ◽  
Bound Theorem

scholarly journals Influence of Anisotropy and Nonhomogeneity on Stability Analysis of Fissured Slopes Subjected to Seismic Action

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhidan Liu ◽  
Jingwu Zhang ◽  
Weiping Chen ◽  
Di Wu
Keyword(s):  
Upper Bound ◽  
Mathematical Optimization ◽  
Optimization Procedure ◽  
Seismic Action ◽  
Anisotropy Coefficient ◽  
Upper Bound Theorem ◽  
Bound Theorem ◽  
Software Codes ◽  
The Stability ◽  
The Impact

Based on the upper bound theorem of limit analysis, this paper presents a procedure for assessment of the influence of the soil anisotropy and nonhomogeneity on the stability of fissured slopes subjected to seismic action. By means of a mathematical optimization procedure written in Matlab software codes, the stability factors NS and λcφ are derived with respect to the best upper bound solutions. A series of stability charts are obtained in this paper, and then the critical locations of cracks are determined for cracks of known depth. The results demonstrate a significant influence of the soil anisotropy and nonhomogeneity on the stability of the fissured slopes and the location distribution of the cracks. In addition, the procedures for getting the factor of safety are put forward. It is shown that a decrease in the nonhomogeneity coefficient n0 and an increase in the anisotropy coefficient k could lead to the fissured slopes becoming unsafe. Finally, this article also illustrates the variation in the safety factor of fissured slopes under the impact of three factors (Kh, H1/H, and λ).

The Upper‐Bound Theorem for Families of Boxes in ℝ d

Mathematika ◽  
2007 ◽  
Vol 54 (1-2) ◽  
pp. 25-34
Author(s):  
Jürgen Eckhoff
Keyword(s):  
Upper Bound ◽  
Upper Bound Theorem ◽  
Bound Theorem

Passive earth-pressure coefficients by upper-bound numerical limit analysis

2011 ◽  
Vol 48 (5) ◽  
pp. 767-780 ◽  
Author(s):  
Armando N. Antão ◽  
Teresa G. Santana ◽  
Mário Vicente da Silva ◽  
Nuno M. da Costa Guerra
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Earth Pressure ◽  
Wall Friction ◽  
Passive Earth Pressure ◽  
Upper Bound Theorem ◽  
Pressure Coefficients ◽  
Bound Theorem

A three-dimensional (3D) numerical implementation of the limit analysis upper-bound theorem is used to determine passive horizontal earth-pressure coefficients. An extension technique allowing determination of the 3D passive earth pressures for any width-to-height ratios greater than 7 is presented. The horizontal passive earth-pressure coefficients are presented and compared with solutions published previously. Results of the ratio between the 3D and two-dimensional horizontal passive earth-pressure coefficients are shown and found to be almost independent of the soil-to-wall friction ratio. A simple equation is proposed for calculating this passive earth-pressure ratio.

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