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

scholarly journals The Upper Bound Theorem in Forging Processes: Model of Triangular Rigid Zones on Parts with Horizontal Symmetry

2020 ◽  
Vol 11 (1) ◽  
pp. 336
Author(s):  
Francisco Martín ◽  
María Jesús Martín ◽  
María José Cano
Keyword(s):  
Plastic Deformation ◽  
Upper Bound ◽  
Center Of Mass ◽  
Modular Approach ◽  
Strain Condition ◽  
Upper Bound Theorem ◽  
Horizontal Symmetry ◽  
Bound Theorem ◽  
Double Symmetry ◽  
Rigid Zones

This paper presents the analytical method capacity of the upper bound theorem, under modular approach, to extend its application possibilities. Traditionally, this method has been applied in forging processes, considering plane strain condition and parts with double symmetry configuration. However, in this study, the double symmetry is eliminated by means of a fluency plane whose position comes from the center of mass calculated. The study of the load required to ensure the plastic deformation will be focus on the profile of the part, independently on both sides of the fluence plane, modifying the number and the shape of the modules that form the two halves in which the part is defined. This way, it is possible to calculate the necessary load to cause the plastic deformation, whatever its geometric profile.

scholarly journals Adaptive Model to Apply the Upper-Bound Theorem in Plain Strain Forging

2012 ◽  
Vol 217-219 ◽  
pp. 2113-2116 ◽  
Author(s):  
F. Martín ◽  
L. Sevilla ◽  
A. Camacho ◽  
A. Sanz
Keyword(s):  
Upper Bound ◽  
Metal Forming ◽  
Deformation Process ◽  
Deformation Energy ◽  
Adaptive Model ◽  
Upper Bound Theorem ◽  
Upper Limit ◽  
Bound Theorem ◽  
Plain Strain ◽  
Rigid Zones

Present work applies the Upper-Bound Theorem (UBT) with Triangular Rigid Blocks (TRB) to metal forming compression processes like plane strain forge, offering an upper limit to required deformation energy. This analytical method, usually used by means of simplified models, is developed here incorporating different effects that impact in evolution of deformation process like shape factor and friction. By means of a new adaptive model, the shape and size of the rigid zones used for the UBT application are optimized according to the ratio of the width and the height of workpiece.

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).

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