Shellability and the Upper Bound Theorem

1995 ◽  
pp. 231-290
Author(s):  
Günter M. Ziegler
Keyword(s):  
Upper Bound ◽  
Upper Bound Theorem ◽  
Bound Theorem

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.

An Analytical Approach to the Problem of Core Fracture During Extrusion of Bimetal Rods

1985 ◽  
Vol 107 (3) ◽  
pp. 247-253 ◽  
Author(s):  
B. Avitzur ◽  
R. Wu ◽  
S. Talbert ◽  
Y. T. Chou
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Analytical Approach ◽  
Upper Bound Theorem ◽  
Numerical Computations ◽  
Bound Theorem

The process of core fracture in bimetals during extrusion was reexamined. The new analysis, based on the upper-bound theorem in limit analysis, eliminated the lengthy numerical computations employed in the previous work [1]. The criterion for core fracture was derived and discussed.

Direct Upper-Bound Solution and Finite Element Approach to Round-To-Square Drawing

1985 ◽  
Vol 107 (3) ◽  
pp. 254-260 ◽  
Author(s):  
C. R. Boe¨r ◽  
W. D. Webster
Keyword(s):  
Finite Element ◽  
Upper Bound ◽  
Wire Drawing ◽  
Upper Bound Theorem ◽  
Finite Element Approach ◽  
Advantages And Disadvantages ◽  
Modeling Techniques ◽  
Solution Methods ◽  
Element Approach ◽  
Bound Theorem

The paper presents a direct comparison between two modeling techniques of metal forming processes, in the present case wire drawing. The two methods have the same basic approach in using the Upper-Bound Theorem but the solution methods are fundamentally different. One method is a direct analytical solution requiring the knowledge of a kinematically admissible velocity field, the other method uses a finite element approach and calculation of the velocities at the nodes of the mesh. Both methods minimize the power required. The theoretical fundamentals of the two methods, the solution approaches and the results are presented and compared. The advantages and disadvantages of both methods are also analysed.

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