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This paper presents a new finite element formulation of the upper bound theorem. The formulation uses a six‐noded linear strain triangular element. Each node has two unknown velocities and each corner of a triangle is associated with a specified number of unknown plastic multiplier rates. The major advantage of using a linear strain element, rather than a constant strain element, is that the velocity field can be modelled more accurately. In addition, the incompressibility condition can be easily satisfied without resorting to special arrangements of elements in the mesh. The formulation permits kinematically admissible velocity discontinuities at specified locations within the finite element mesh. To ensure that finite element formulation of the upper bound theorem leads to a linear programming problem, the yield criterion is expressed as a linear function of the stresses. The linearized yield surface is defined to circumscribe the parent yield surface so that the solution obtained is a rigorous upper bound. During the solution phase, an active set algorithm is used to solve the resulting linear programming problem. Several numerical examples are given to illustrate the capability of the new procedure for computing rigorous upper bounds. The efficiency and accuracy of the quadratic formulation is compared with that of the 3‐noded constant strain formulation in detail.

Revealed preference axioms provide a simple way of testing data from consumers or firms for consistency with optimizing behavior. The resulting non-parametric tests are very attractive, since they do not require any ad hoc functional form assumptions. A weakness of such tests, however, is that they are non-stochastic. In this paper, we provide a detailed analysis of two non-parametric approaches that can be used to derive statistical tests for utility maximization, which account for random measurement errors in the observed data. These same approaches can also be used to derive tests for separability of the utility function.

For the considered system, an enumeration method is applicable to evaluate the exact system reliability only for very small‐sized systems, because, when the size of system is large, it takes huge execution time. Therefore, the paper provides approximate values for the system reliability as useful for calculating the reliability of large systems in a reasonable execution time.

The paper provides upper and lower bounds of the system reliability, and limit theorem for the reliability of our considered system in i.i.d. case.

The paper experimentally finds that the proposed upper and lower bounds are effective when component reliabilities close to one or the value of k becomes larger. Next, it concludes approximate values for approximate equation derived from the limit theorem are always smaller than lower bound through numerical experiments.

The upper and lower bounds for the reliability of a system can be calculated by using the reliability of a small system by the same idea as previous study for two‐dimensional system.

Up to now some researchers studied multi‐dimensional consecutive‐k‐out‐of‐n:F systems, and showed promising applications of such multi‐dimensional models, e.g. diagnosis of a disease diagnosed by reading an X‐ray. As another examples, three‐dimensional system can be applied for the mathematical model of a three‐dimensional flash memory cell failure model, and so on.

The paper considers a kind of three‐dimensional k‐within‐consecutive‐r‐out‐of‐n:F system. It proposes upper and lower bounds of the system reliability and limit theorem.

The increasing popularity of ERP solutions has provided dietary supplement manufacturing companies with modules to manage pricing and inventory. However, the decisions made by these modules are often independent and rely on deterministic forecasts. This paper studies a multi-product dietary supplement manufacturing system under stochastic demands. The purpose is to maximize the long-run expected profit by jointly considering pricing and inventory strategies.

The authors investigate both the general cases and three special cases including stable demand, negligible backlog and instantaneous replenishment. A two-stage algorithm named PAS is proposed. In the strategy construction stage, the constructed objective bounds are combined to provide estimates which then help to derive the optimal product prices. In the system operation stage, replenishment decisions are further made based on the prices generated from the previous stage.

It is proved that base-stock policy is optimal for the studied system, and the optimal based-stock level is provided. The global optimal strategies are obtained for three important special cases. For the general case, theoretical objective bounds are established. These bounds provide quick and reliable performance estimates for practical applications.

Very few studies have jointly considered pricing and inventory strategies with uncertainty demands in the dietary supplement industry. The PAS algorithm developed integrates these decisions and consistently generates high-quality solutions even under highly varying demands. Such algorithm could be a valuable add-on to the pricing and inventory management modules in ERP systems.

The purpose of this paper is to develop a mathematical solution to estimate the deformation pattern and required power in cold plate rolling using coupled stream function method and upper bound theorem.

In the first place, an admissible velocity field and the geometry of deformation zone are derived from a new stream function. Then, the optimum velocity field is obtained by minimizing the corresponding power function. Also, to calculate the adiabatic heating during high speed rolling operations, a two-dimensional conduction-convection problem is sequentially coupled with the mechanical model. To verify the predictions, rolling experiments on aluminum plates are conducted and also, a finite element analysis is performed by Abaqus/Explicit. The predicted deformation zone is then compared with the experimentally measured region as well as with the results of the finite element analysis.

The results show that the predicted deformation zone and the temperature distribution fit reasonably with the experimental data while much lower computational cost needs comparing to the fully finite element analysis.

A new stream function is proposed to properly describe the velocity field and deformation pattern during plate rolling considering the neutral point. Furthermore, the employed algorithm can be simply coupled with the thermal finite element analysis.

The safety assessment of engineering structures under repeated variable dynamic loads such as seismic and wind loads can be considered as a dynamic shakedown problem. This paper aims to extend the stress compensation method (SCM) to perform lower bound dynamic shakedown analysis of engineering structures and a double-closed-loop iterative algorithm is proposed to solve the shakedown load.

The construction of the dynamic load vertexes is carried out to represent the loading domain of a structure under both dynamic and quasi-static load. The SCM is extended to perform lower bound dynamic shakedown analysis of engineering structures, which constructs the self-equilibrium stress field by a series of direct iteration computations. The self-equilibrium stress field is not only related to the amplitude of the repeated variable load but also related to its frequency. A novel double-closed-loop iterative algorithm is presented to calculate the dynamic shakedown load multiplier. The inner-loop iteration is to construct the self-equilibrated residual stress field based on the certain shakedown load multiplier. The outer-loop iteration is to update the dynamic shakedown load multiplier. With different combinations of dynamic load vertexes, a dynamic shakedown load domain could be obtained.

Three-dimensional examples are presented to verify the applicability and accuracy of the SCM in dynamic shakedown analysis. The example of cantilever beam under harmonic dynamic load with different frequency shows the validity of the dynamic load vertex construction method. The shakedown domain of the elbow structure varies with the frequency under the dynamic approach. When the frequency is around the resonance frequency of the structure, the area of shakedown domain would be significantly reduced.

In this study, the dynamical response of structure is treated as perfect elastoplastic. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.

This study provides a direct method for the dynamical shakedown analysis of engineering structures under repeated variable dynamic load.

Approaches the shakedown optimal design of reinforced concrete (RC) structures, subjected to variable and repeated external quasi‐static actions which may generate the well‐known shakedown or adaptation phenomenon, when constraints are imposed on deflection and/or deformation parameters, in order to simulate the limited flexural ductility of the material, in the presence of combined axial stress and bending. Within this context, the classical shakedown optimal design problem is revisited, using a weak upper bound theorem on the effective plastic deformations. For this problem a new computational algorithm, termed evolution strategy, is herein presented. This algorithm, derived from analogy with the biological evolution, is based on random operators which allow one to treat the areas of steel reinforcements at each RC cross‐section of the structure as design variables of discrete type, and to use refined non‐linear approximations of the effective bending moment – axial force M‐N interaction diagrams of each RC cross‐section. The results obtained from case studies available in the literature show the advantages of the method and its effectiveness.

The purpose of this paper is to propose a mathematical model to estimate required energy and temperature distribution during cold extrusion process.

An admissible velocity field is generated based on stream function technique. Then, the required energy and the temperature distributions in the metal and the extrusion die are determined by a coupled upper bound‐finite element analysis.

To examine the proposed model, cold extrusion of AA6061‐10%SiC_p is considered and the predicted extrusion force‐displacement diagrams in different reductions are compared with the experimental ones and reasonable agreement is observed. Furthermore, it is found that there is a linear relationship between maximum temperature and logarithm of ram velocity for the examined composite.

This approach requires shorter run‐time as compared with fully finite element analyses while the model is particularly appropriate for high speed extrusion processes where the adiabatic heating is of importance.

The purpose of this paper is to investigate the thermomechanical behavior of stainless steel AISI 304L during rolling at elevated temperatures.

Two-dimensional finite element analysis together with the upper-bound solution were used for predicting temperature field and required power in warm and hot rolling operations. The required power and heat of deformation were estimated employing an upper-bound solution based on cylindrical velocity field and at the same time, temperature distributions within the rolling steel and the work rolls were determined by means of a thermal finite element analysis. To consider the effect of flow stress and its dependence on temperature, strain and strain rate, a neural network model was used and combined with the thermal and mechanical models. Finally, the microstructure of rolled steel was studied and the effect of rolling conditions was justified employing the predictions.

The results have shown that the predicted temperature variations were in good agreement with the experiments. Moreover, the model was shown to be capable of determining the effects of various rolling parameters such as reduction and rolling speed with low-computational cost as well as reasonable accuracy.

A combined upper-bound finite element analysis was developed to predict the required power and temperature field during plate rolling while the model can be employed under both hot and warm rolling conditions.