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

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.

Slipping of a Viscoplastic Fluid Flowing on a Circular Cylinder

The slipping effect during creeping flow of viscoplastic fluids around a circular cylinder has been investigated via numerical simulations. For the bulk behavior of the fluid, a Herschel–Bulkley law is considered. For the parietal behavior, an original and recent slip law based on an elastohydrodynamic lubrication model defined with a physical approach has been implemented. In particular, this law represents the behavior of Carbopol gels, which are commonly used during experimental studies on yield stress fluid mechanics and in industry. This law has two parameters that control the kinematic conditions at the fluid–structure interface. Variations in the plastic drag coefficient are given as a function of these parameters. It has been shown in particular the decreasing of the drag coefficient when there is slipping at the fluid–structure interface. The kinematic field has been analyzed and the evolution of rigid zones is illustrated. Results are provided for different slipping conditions ranging from the no-slip to the perfect-slip (PS) case. The sheared zone becomes smaller so the flow is more and more confined due to the slip, which induces modifications on the rigid zones. Some of the results are compared with existing asymptotic plastic drag coefficients and experimental data.

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

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

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

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.

Thermal-Structural Analysis of the Super-Heater Tubes of a Unit of 158 MW

The thermal-structural analysis of the super-heater tubes for a 158 MW unit, applying FLUENT® (CFD) and ANSYS® (FEA), is presented. The analysis includes the spacers (union piece between tubes), welding and tubes. The failures of these elements are related with the operation of the unit and the selection of the weld and materials involved in the affected zone. The distribution of temperature in each metal depends of the thermal conductivity and coefficient of thermal expansion, provoking stress concentration in the rigid zones. The CFD study considers a three-dimensional model where the conjugate heat transfer, including internal flow (steam) and external flow (gases), was analyzed to full load of the unit in steady state. In the FEA study, the thermal-structural stresses were analyzed considering the temperature distribution obtained from the CFD study. The results obtained show that the spacer is of greater temperature than the tubes, provoking gradients of temperature through tube walls, spacers and welds. The highest stress located on the interior tube wall (on the direction of plane where the spacer is welded) is attributed to the different thermal dilatation and pressure expansion of the tube, spacer and weld. The study includes the analysis of some geometries of the union piece (spacer) to release the thermal-structural stresses.

Modeling and simulation of planar flexible link manipulators with rigid tip connections to revolute joints

This paper presents the basis of a mathematical model for simulation of planar flexible-link manipulators, taking into consideration the effect of higher stiffness zones at the link tips. The proposed formulation is a variation of the finite segment multi-body dynamics approach. The formulation employs a consistent mass matrix in order to provide better approximation than the traditional lumped masses often encountered in the finite segment approach. The formulation is implemented into a computational code and tested through three examples; cantilever beam, rotating beam and three-link manipulator. In these examples, the length of the rigid tips at both sides of each link ranges from 0% to 6.25% of the whole link length. The zones of higher stiffness at the link tips are treated as short rigid zones. The effect of the rigid zones is averaged along with some portions of the flexible links, thereby allowing further simplification of the dynamic equations of motion. The simulation results demonstrate the effectiveness of the proposed modeling technique and show the importance of not ignoring the effect of the rigid tips.

Geometric nonlinear vibration analysis of steel frames with semi-rigid connections and rigid-zones

To obtain an accurate insight into the behavior of the most realistic steel frames, joint flexibility should be allowed for in the analysis. So far, most research work is concentrated on the linear and geometric nonlinear static analysis of steel frames with flexible connections. Very few papers were contributed to the dynamic and vibration analysis of these types of frames. This paper proposes a numerical method for geometric nonlinear vibration analysis of frames with semi-rigid connections and rigid-zones. The effect of initial stress due to the applied load is accounted for in the suggested method, which is believed to be more general than the existing methods and does not involve complex calculations.