Deformation of the material during cyclic expansion extrusion (CEE) is investigated using UPPER-BOUND theorem. The analytical approximation of forming loads agrees very well with the FEM results for different amounts of chamber diameter, friction factor and also for lower die angles. However, the difference between analytical and numerical solution increases at higher die angles, which is explained by the formation of dead-metal zones at these angles. The results show that the forming load increases at higher friction coefficients, higher chamber diameters, and lower amounts of corner fillet radius, but for the die angle there is a maximum value of load at about 60o. Forming load is enhanced by the increase of the die chamber diameter and friction factor. Increasing the die chamber diameter causes higher strains and, therefore, higher rate of homogenous work. The load slightly decreased by an increase of the die corner radius because of the lower and more homogeneous strain distribution in the material.

An analytical solution for forging processes using an elemental UPPER BOUND method was given in this paper. The ANALYSIS was carried out by dividing the cross section into some standard pre-defined elements. For each of these elements the velocity field was defined. When the cross section was divided into the elements, using the cinematically admissible velocity field of each element the BOUNDary conditions the general cinematically admissible velocity field for the deforming region was completely defined. Using the general cinematically admissible velocity field UPPER BOUND solutions were arrived at for both plane strain and ax symmetric forging processes. For the case of plane strain forging processes rectangular and trapezoidal elements were employed. Ring type elements of triangular and square cross sections were used for the ANALYSIS of ax symmetric forging problems. In this work the velocity fields were improved by modifying the previous work equations. Based on the above theory a computer program was written with the use of which simulation of both plane strain and ax symmetric forgings were presented. The influence of different process parameters such as friction factor, flash and geometrical dimensions were considered. The results obtained from this work were compared with previous work and improvements were observed.

The kinematic method of limit ANALYSIS approach is applied to study stability of reinforced slopes. The amount and length of reinforcement required to prevent the slope to collapse are determined based on different mechanisms. A new method consisting of horizontal blocks is used in translational mechanism. The failure wedge is divided into a number of horizontal slices involving reinforcements. The reinforcements do not intersect the slices. Thus, they have no direct influence on the inter-slice forces. The presented method can reduce difficulties of stability ANALYSIS for reinforced slopes. In this paper, the seismic stability of slopes reinforced with geosynthetics is investigated. The seismic ANALYSIS procedure is substituted with pseudo-static horizontal forces. While such an approach ignores the acceleration history of a structure, it is routinely used in practice. It has been assumed that the geosynthetics are uniformly distributed in the height of slope. Based on these assumptions, different possible failure mechanisms are considered and necessary analytical expressions for determining the design parameters are derived for each mechanism. The results of these analyses are presented to illustrate the influence of different parameters such as geometrical parameters of slopes, soil characteristics, and seismic forces on the stability of reinforced earth structures.

Presented is a rigorous solution for the three-dimensional stability ANALYSIS of convex slopes with corners in plan view. The method is based on the UPPER-BOUND theorem of limit ANALYSIS approach. A rigid-block translational collapse mechanism is considered, with energy dissipation taking place along planar velocity discontinuities. This mechanism is optimized to obtain the minimum factor of safety for stability of the corners. The algorithm can also be used to determine the ultimate limit load of a foundation located on a corner. Based on comparisons with known solutions, the method was generally found to be accurate in predicting the stability of such slopes. The numerical results indicate that the unloaded corners are more stable than the straight slopes. Dimensionless diagrams for various corner angles are also presented.

In this research, flat rolling process of bonded sandwich sheets is investigated by the method of UPPER BOUND. A kinematically admissible velocity field is developed for a single layer sheet and is extended into the rolling of the symmetrical sandwich sheets. The internal, shear and frictional power terms are derived and they are used in the UPPER BOUND model. Through the ANALYSIS, the rolling torque, the roll separating force and the thickness of each layer at the exit of deformation are determined. The validity of the proposed analytical method is discussed by comparing the theoretical predictions with the experimental data found in the literature and by the finite element method. It is shown that the accuracy of the newly developed analytical model is good.

A three dimensional slope stability ANALYSIS based on the UPPER-BOUND technique of limit ANALYSIS is presented. A transitional rigid block collapse mechanism and an admissible velocity field are considered, and energy dissipation taking place along planar velocity discontinuities together with the work done by external forces are calculated. The minimum UPPER-BOUND solution is determined by optimizing the shape of the blocks. The software prepared on this basis can be used to calculate the safety factor in slope stability problems as well as the bearing capacity of shallow foundations near slopes in three dimensional situations.

In this paper, a limit ANALYSIS of cylindrical shells with rectangular attachments well removed from the ends and subjected to local bending moments is performed. In the ANALYSIS, the UPPER BOUND technique is employed to give the minimum UPPER BOUND to the plastic limit load for a shell when it is subjected to local longitudinal and circumferential bending moments over a rectangular area of the cylindrical shell surface. In the ANALYSIS, a two-moment limited interaction yield surface is used. The results are presented for a range of practical geometrical parameters. An alternative collapse mechanism for longitudinal bending moment is examined.

Considering a kinematical velocity admissible field, the UPPER BOUND method has been used for predicting the amount of pressure in hydroforming of sheet metals. The effects of work hardening, friction and blank size have been considered in pressure prediction. Also the effect of sheet thickness variation has been considered in the present work formulations. The relation between pressure and punch stroke has been obtained and optimized by changing the selective parameters in the velocity components. The results for cylindrical and hemispheric parts have been obtained and compared with the published experimental results. The effects of work hardening, friction and blank size on hydroforming pressure have been examined on an elliptical part. Good agreement was found between the experimental and numerical results.

In this paper an analytical method of solution is presented for the three dimensional problem of rolling in order to investigate the deformation and material flow and calculate the torque and pressure. This theory was used to simulate the rolling of shaped sections and the influence of different process parameters on the UPPER BOUND on energy was investigated. The formulation was based on the UPPER BOUND method in which kinematically admissible velocity fields were derived using the deformation geometry. By optimizing different parameters given in the formulation the lowest UPPER BOUND was obtained. These parameters were defined in the formulation of the stream lines and stream surfaces which comprised the deformation zone. Rolling of different shapes such as circle, square, rectangle and ellipse were considered and the theory was applied to these processes. The flow of material under the actions of the rolls and the final shape of the rolled section was predicted by the simulation presented in here. The theoretical results obtained from this theory were compared with other workers experimental and theoretical results and good agreements were observed. The results indicated that the predictions made by the simulation based on this theory were very close to the experimental results and better than FEM and other theoretical results.