Papers by Keyword: Upper Bound Theorem

Abstract: The article represents theoretical analysis of friction influence on the process of formation experimental blank with several radial wedge-type branches having different constituent convergence angles. The authors show that with the correlation between volumes of material what are extruded into the branches it is possible to define the friction coefficient for set conditions of forging. Such approach allows suggesting the methodology for exact definition of friction coefficient for forged blank with a large area of contact surface. For the analysis the analytical model is used which was obtained by upper-bound approach technique. Calibration measurement of accuracy of a model was carried out by numerical method in Deform 3D.

Abstract: Friction at die/billet interface is a complex phenomenon affected by various operating and process parameters in metal forming industries. In presence of lubricating layer at the interfacial contact friction effect is reduced and enhances tool life and surface quality of product. The lubricant viscosity is strongly dependent on pressure and temperature during deformation of hard material and an accurate prediction of lubricants viscosity leads to realistic results in the work zone. Therefore, the paper incorporates numerical simulation of friction at the die/billet interface in hydrostatic extrusion of tungsten alloy 93W for three different lubricants whose rheology is represented by a Non-Newtonian friction model. The billet heating effect is incorporated in the investigation and results show that the co-efficient of friction varies in a range (0.058 to 0.062) along the work zone for various lubricating conditions in hydrostatic extrusion process.

Abstract: The forging processes have usually been studied by analytical methods under simplifying assumptions such as the consideration of plane strain. Present work this study is approached from Upper Bound Theorem using the Triangular Rigid Zones model from a new approach, that is, through the analysis of Ring Compression Test, axisymmetric element under its canonical geometry ensures a similar aforementioned plane strain behavior. A new perspective of calculating the so-called neutral plane (defined by the radius at which the material flows in opposite directions), which is the basis element in solving the problem is proposed.

Abstract: 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

Abstract: Although a structural analysis of plates based on the linear elastic theory yields good results for deformations and stresses produced by working loads, it fails to assess the real load-carrying capacities of plates on the verge of yielding. In the case of a limit analysis of plates, the yield line theory is widely used on the basis of the upper bound theorem and theoretically it overestimates the strength of plates. That is why the p-version of the finite element method has been proposed for determining the accurate limit load of plates causing collapse. In this method, the hierarchical C^o -plate element for bending of elastic-plastic plates accounting for transverse shear effects has been formulated, and is based on the incremental theory of plasticity and the Reissner-Mindlin plate theory. The numerical results are presented for a variety of rectangular plate problems and are compared to the results obtained by the h-version software ADINA, as well as with the available analytical solutions in literature.

Abstract: Based on a curved failure mechanism, an upper bound solution of ultimate pullout capacity of strip plate anchor subjected to pore pressure is derived using the upper bound theorem of limit analysis in conjunction with Hoek-Brown failure criterion. The effect of water pressure which is assumed to be a work rate of external force is included in the upper bound analysis. By employing variational calculation to minimize the objective function, the upper solution of ultimate pullout capacity is obtained. In order to evaluate the validity of the method, the solutions in this paper are compared with the results using linear multiple blocks failure mechanism. The good agreement shows that the curved failure mechanism is an effective method for evaluating the upper solution of ultimate pullout capacity of strip plate anchor.

Abstract: The effect of seepage force on tunnel face stability with pipe roof reinforcement was studied based on the kinematic method of limit analysis. This method can be employed to define the safety factor and its corresponding critical failure mechanism for a given tunnel. The studies revealed that the existence of groundwater may seriously affect the face stability. Under the steady-state groundwater flow condition, most part of the total support pressure is owing to the seepage pressure acting on the tunnel face. There was a relatively large reduction in the seepage pressure by adopting the pipe roof reinforcement technique.

Abstract: The paper concerns with an effect of plastic anisotropy on the load required to deform hollow cylinders between two parallel, rough dies. It is assumed that the material obeys Hill’s quadratic yield criterion and its associated flow rule. The friction stress is supposed to be proportional to the corresponding shear yield stress, including the maximum friction law as a special case. The kinematically admissible velocity field is chosen such that the stress field following from the associated flow rule satisfies the boundary condition at the plane of symmetry. Moreover, this velocity field is singular in the vicinity of the friction surface. Therefore, in the case of the maximum friction law the friction law is satisfied, again if the associated flow rule is combined with the velocity field. A significant effect of plastic anisotropy on the limit load is illustrated.