Search results for: symmetry solution

Authors: Tae Hyun Ahn, Gyo Woo Lee, Man Young Kim

Abstract:

Because of high thermal efficiency and low CO2 emission, diesel engines are being used widely in many industrial fields although it makes many PM and NOx which give both human health and environment a negative effect. NOx regulations for diesel engines, however, are being strengthened and it is impossible to meet the emission standard without NOx reduction devices such as SCR (Selective Catalytic Reduction), LNC (Lean NOx Catalyst), and LNT (Lean NOx Trap). Among the NOx reduction devices, urea-SCR system is known as the most stable and efficient method to solve the problem of NOx emission. But this device has some issues associated with the ammonia slip phenomenon which is occurred by shortage of evaporation and thermolysis time, and that makes it difficult to achieve uniform distribution of the injected urea in front of monolith. Therefore, this study has focused on the mixing enhancement between urea and exhaust gases to enhance the efficiency of the SCR catalyst equipped in catalytic muffler by changing inlet gas temperature and spray conditions to improve the spray uniformity of the urea water solution. Finally, it can be found that various parameters such as inlet gas temperature and injector and injection angles significantly affect the evaporation and mixing of the urea water solution with exhaust gases, and therefore, optimization of these parameters are required.

Keywords: Evaporation, Injection, Selective Catalytic Reduction (SCR), Thermolysis, UWS (Urea-Water-Solution).

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Authors: Giovanni Incerti

Abstract:

In this paper the vibration of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the model here proposed also takes into consideration the electromagnetic response of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations, without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the above-mentioned software.

Keywords: Belt drive, Vibrations, Startup, DC motor.

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Authors: Abdulrahman Abdulrahman

Abstract:

Critical depth meters, such as abroad crested weir, Venture Flume and combined control flume are standard devices for measuring flow in open channels. The discharge relation for these devices cannot be solved directly, but it needs iteration process to account for the approach velocity head. In this paper, analytical solution was developed to calculate the discharge in a combined critical depth-meter namely, a hump combined with lateral contraction in rectangular channel with subcritical approach flow including energy losses. Also analytical formulae were derived for approach velocity head coefficient for different types of critical depth meters. The solution was derived by solving a standard cubic equation considering energy loss on the base of trigonometric identity. The advantage of this technique is to avoid iteration process adopted in measuring flow by these devices. Numerical examples are chosen for demonstration of the proposed solution.

Keywords: Broad crested weir, combined control meter, control structures, critical flow, discharge measurement, flow control, hydraulic engineering, hydraulic structures, open channel flow.

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Authors: Ismail El Gayar, Ossama Ismail, Yousri El Gamal

Abstract:

This paper presented a technique to solve one of the transportation problems that faces us in real life which is the Bus Scheduling Problem. Most of the countries using buses in schools, companies and traveling offices as an example to transfer multiple passengers from many places to specific place and vice versa. This transferring process can cost time and money, so we build a decision support system that can solve this problem. In this paper, a genetic algorithm with the shortest path technique is used to generate a competitive solution to other well-known techniques. It also presents a comparison between our solution and other solutions for this problem.

Keywords: Bus scheduling problem, decision support system, genetic algorithm, operation planning, shortest path, transportation.

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Authors: Aurelian Octavian Ciucâ, Ioan Bitir-Istrate, Mircea Scripcariu

Abstract:

The rapidly increasing costs of power line extensions and fossil fuel, combined with the desire to reduce carbon dioxide emissions pushed the development of hybrid power system suited for remote locations, the purpose in mind being that of autonomous local power systems. The paper presents the suggested solution for a “high penetration" hybrid power system, it being determined by the location of the settlement and its “zero policy" on carbon dioxide emissions. The paper focuses on the technical solution and the power flow management algorithm of the system, taking into consideration local conditions of development.

Keywords: Renewable energy, hybrid power system, wind turbine, photovoltaic panels, bio-diesel cogeneration, bio-fuel.

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Authors: Sukhveer Singh, Sandeep Singh

Abstract:

A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: Transportation problem, efficient solution, ranking function, fuzzy transportation problem.

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Authors: F. Elashhab, L. Sheha, R. Fawzi Elsupikhe, A. E. A. Youssef, R. M. Sheltami, T. Alfazani

Abstract:

Chitosans, CSs, in solution are increasingly used in a range of geometric properties in various academic and industrial sectors, especially in the domain of pharmaceutical and biomedical engineering. In order to provide a tailoring guide of CSs to the applicants, gamma (γ)-irradiation technology and simple viscosity measurements have been used in this study. Accordingly, CS solid discs (0.5 cm thickness and 2.5 cm diameter) were exposed in air to Cobalt-60 (γ)-radiation, at room temperature and constant 50 kGy dose for different periods of exposer time (tγ). Diluted solutions of native and different irradiated CS were then prepared by dissolving 1.25 mg cm-3 of each polymer in 0.1 M NaCl/0.2 M CH3COOH. The single-concentration relative viscosity (ƞr) measurements were employed to obtain their intrinsic viscosity ([ƞ]) values and interrelated parameters, like: the molar mass (Mƞ), hydrodynamic radiuses (RH,ƞ), radius of gyration (RG,ƞ), and second virial coefficient (A2,ƞ) of CSs in the solution. The results show an exponential decrease of ƞr, [ƞ], Mƞ, RH,ƞ and RG,ƞ with increasing tγ. This suggests the influence of random chain-scission of CSs glycosidic bonds, with rate constant kr and kr-1 (lifetime τr ~ 0.017 min-1 and 57.14 min, respectively). The results also show an exponential decrease of A2ƞ with increasing tγ, which can be attributed to the growth of excluded volume effect in CS segments by tγ and, hence, better solution quality. The results are represented in following scaling laws as a tailoring guide to the applicants: RH,ƞ = 6.98 x 10-3 Mr0.65; RG,ƞ = 7.09 x 10-4 Mr0.83; A2,ƞ = 121.03 Mƞ,r-0.19.

Keywords: Gamma irradiation, geometric properties, kinetic model, scaling laws, viscosity measurement.

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Authors: C. A. Corzo, N. Zhang, F. Corzo

Abstract:

Insider abuse has recently been reported as one of the more frequently occurring security incidents, suggesting that more security is required for detecting and preventing unauthorised financial transactions entered by authorised users. To address the problem, and based on the observation that all authorised interbanking financial transactions trigger or are triggered by other transactions in a workflow, we have developed a security solution based on a redefined understanding of an audit workflow. One audit workflow where there is a log file containing the complete workflow activity of financial transactions directly related to one financial transaction (an electronic deal recorded at an e-trading system). The new security solution contemplates any two parties interacting on the basis of financial transactions recorded by their users in related but distinct automated financial systems. In the new definition interorganizational and intra-organization interactions can be described in one unique audit trail. This concept expands the current ideas of audit trails by adapting them to actual e-trading workflow activity, i.e. intra-organizational and inter-organizational activity. With the above, a security auditing service is designed to detect integrity drifts with and between organizations in order to detect unauthorised financial transactions entered by authorised users.

Keywords: Intrusion Detection and Prevention, Authentica-transtionand Identification.

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Authors: N. Ebrahimi, J. Rashidinia

Abstract:

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

Keywords: Convergence analysis, Cubic B-spline, Newton- Cotes formula, System of Fredholm and Volterra integral equations.

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

Abstract:

In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: Difference Equations, Jost Functions, Asymptotics, Eigenvalues, Continuous Spectrum, Spectral Singularities.

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Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan

Abstract:

The analytical bright two soliton solution of the 3- coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two-soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.

Keywords: Optical soliton, soliton interaction, soliton switching, WDM.

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Authors: C. E. Nugraheni, L. Abednego

Abstract:

This paper introduces a framework based on the collaboration of multi agent and hyper-heuristics to find a solution of the real single machine production problem. There are many techniques used to solve this problem. Each of it has its own advantages and disadvantages. By the collaboration of multi agent system and hyper-heuristics, we can get more optimal solution. The hyper-heuristics approach operates on a search space of heuristics rather than directly on a search space of solutions. The proposed framework consists of some agents, i.e. problem agent, trainer agent, algorithm agent (GPHH, GAHH, and SAHH), optimizer agent, and solver agent. Some low level heuristics used in this paper are MRT, SPT, LPT, EDD, LDD, and MON

Keywords: Hyper-heuristics, multi-agent systems, scheduling problem.

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Authors: Chouvalit Khancome, Veera Boonjing

Abstract:

This paper proposes a new solution to string matching problem. This solution constructs an inverted list representing a  string pattern to be searched for. It then uses a new algorithm to process an input string in a single pass. The preprocessing phase  takes 1) time complexity O(m) 2) space complexity O(1) where m is  the length of pattern. The searching phase time complexity takes 1)  O(m+α ) in average case 2) O(n/m) in the best case and 3) O(n) in  the worst case, where α is the number of comparing leading to  mismatch and n is the length of input text.

Keywords: String matching, inverted list, inverted index, pattern, algorithm.

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Authors: Abdel-Reza Hatamlou, Mohammad Reza Meybodi

Abstract:

In this paper we present a hybrid search algorithm for solving constraint satisfaction and optimization problems. This algorithm combines ideas of two basic approaches: complete and incomplete algorithms which also known as systematic search and local search algorithms. Different characteristics of systematic search and local search methods are complementary. Therefore we have tried to get the advantages of both approaches in the presented algorithm. The major advantage of presented algorithm is finding partial sound solution for complicated problems which their complete solution could not be found in a reasonable time. This algorithm results are compared with other algorithms using the well known n-queens problem.

Keywords: Constraint Satisfaction Problem, Hybrid SearchAlgorithm.

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Authors: M. R. Haboğlu, A. Kurşun, Ş. Aksoy, H. Aykul, N. B. Bektaş

Abstract:

Athermal elastic stress analysis of steel fiber reinforced aluminum laminated composite plate is investigated. Four sides of the composite plate are clamped and subjected to a uniform temperature load. The analysis is performed both analytically and numerically. Laminated composite is manufactured via hot pressing method. The investigation of the effects of the orientation angle is provided. Different orientation angles are used such as [0°/90°]s, [30°/-30°]s, [45°/-45°]s, and [60/-60]s. The analytical solution is obtained via classical laminated composite theory and the numerical solution is obtained by applying finite element method via ANSYS.

Keywords: Laminated Composites, Thermo Elastic Stress, Finite Element Method.

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Authors: K. N. Dinesh Babu, R. Ramaprabha, V. Rajini, V. Nagarajan

Abstract:

In this paper, various methods of providing restricted earth fault protection are discussed. The proper operation of high and low impedance Restricted Earth Fault (REF) protection for various applications has been discussed. The maloperation of a relay due to improper placement of CTs has been identified and a simple/unique solution has been proposed in this work with a case study. Moreover, it is found that the proper placement of CT in high impedance method will provide the same result with reduced CT. This methodology has been successfully implemented in Al Takreer refinery for a 2000 KVA transformer. The outcome of the paper may be included in IEEEC37.91 standard to give the proper guidance for protection engineers to sort out the issues related to mal functioning of REF relays.

Keywords: Relay maloperation, transformer, low impedance REF, MatLab, 64R, IEEE C37.91.

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Authors: Saeed Sarabadan, Kamal Rashedi

Abstract:

This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. The instability of the problem is resolved by taking advantage of the Landweber’s iterations as an admissible regularization strategy. In computations, we find the stable and low-cost results which demonstrate the efficiency of the technique.

Keywords: Inverse problem, parabolic equations, heat equation, Ritz-Galerkin method, Landweber iterations.

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

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The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler Plate Equation, Numerical Simulations, Stability, Energy Decay, Finite Difference Method.

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Authors: Bandula-Heva, T., Dhanasekar, M.

Abstract:

True stress-strain curve of railhead steel is required to investigate the behaviour of railhead under wheel loading through elasto-plastic Finite Element (FE) analysis. To reduce the rate of wear, the railhead material is hardened through annealing and quenching. The Australian standard rail sections are not fully hardened and hence suffer from non-uniform distribution of the material property; usage of average properties in the FE modelling can potentially induce error in the predicted plastic strains. Coupons obtained at varying depths of the railhead were, therefore, tested under axial tension and the strains were measured using strain gauges as well as an image analysis technique, known as the Particle Image Velocimetry (PIV). The head hardened steel exhibit existence of three distinct zones of yield strength; the yield strength as the ratio of the average yield strength provided in the standard (σyr=780MPa) and the corresponding depth as the ratio of the head hardened zone along the axis of symmetry are as follows: (1.17 σyr, 20%), (1.06 σyr, 20%-80%) and (0.71 σyr, > 80%). The stress-strain curves exhibit limited plastic zone with fracture occurring at strain less than 0.1.

Keywords: Stress-Strain Curve, Tensile Test, Particle Image Velocimetry, Railhead Metal Properties

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Authors: Hazem M. El-Bakry, Qiangfu Zhao

Abstract:

In recent years, fast neural networks for object/face detection have been introduced based on cross correlation in the frequency domain between the input matrix and the hidden weights of neural networks. In our previous papers [3,4], fast neural networks for certain code detection was introduced. It was proved in [10] that for fast neural networks to give the same correct results as conventional neural networks, both the weights of neural networks and the input matrix must be symmetric. This condition made those fast neural networks slower than conventional neural networks. Another symmetric form for the input matrix was introduced in [1-9] to speed up the operation of these fast neural networks. Here, corrections for the cross correlation equations (given in [13,15,16]) to compensate for the symmetry condition are presented. After these corrections, it is proved mathematically that the number of computation steps required for fast neural networks is less than that needed by classical neural networks. Furthermore, there is no need for converting the input data into symmetric form. Moreover, such new idea is applied to increase the speed of neural networks in case of processing complex values. Simulation results after these corrections using MATLAB confirm the theoretical computations.

Keywords: Fast Code/Data Detection, Neural Networks, Cross Correlation, real/complex values.

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Authors: A. M. Sagir

Abstract:

In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: Yi-Pin Hsu, Shin-Yu Lin

Abstract:

An efficient parallel form in digital signal processor can improve the algorithm performance. The butterfly structure is an important role in fast Fourier transform (FFT), because its symmetry form is suitable for hardware implementation. Although it can perform a symmetric structure, the performance will be reduced under the data-dependent flow characteristic. Even though recent research which call as novel memory reference reduction methods (NMRRM) for FFT focus on reduce memory reference in twiddle factor, the data-dependent property still exists. In this paper, we propose a parallel-computing approach for FFT implementation on digital signal processor (DSP) which is based on data-independent property and still hold the property of low-memory reference. The proposed method combines final two steps in NMRRM FFT to perform a novel data-independent structure, besides it is very suitable for multi-operation-unit digital signal processor and dual-core system. We have applied the proposed method of radix-2 FFT algorithm in low memory reference on TI TMSC320C64x DSP. Experimental results show the method can reduce 33.8% clock cycles comparing with the NMRRM FFT implementation and keep the low-memory reference property.

Keywords: Parallel-computing, FFT, low-memory reference, TIDSP.

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Authors: Akbar Banitalebi, Mohd Ismail Abd Aziz, Rohanin Ahmad

Abstract:

A new stochastic algorithm called Probabilistic Global Search Johor (PGSJ) has recently been established for global optimization of nonconvex real valued problems on finite dimensional Euclidean space. In this paper we present convergence guarantee for this algorithm in probabilistic sense without imposing any more condition. Then, we jointly utilize this algorithm along with control parameterization technique for the solution of constrained optimal control problem. The numerical simulations are also included to illustrate the efficiency and effectiveness of the PGSJ algorithm in the solution of control problems.

Keywords: Optimal Control Problem, Constraints, Direct Methods, Stochastic Algorithm

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Authors: Waraporn Apiwatanapiwat, Pilanee Vaithanomsat, Phanu Somkliang, Taweesiri Malapant

Abstract:

This was the first document revealing the investigation of protein hydrolysate production optimization from J. curcas cake. Proximate analysis of raw material showed 18.98% protein, 5.31% ash, 8.52% moisture and 12.18% lipid. The appropriate protein hydrolysate production process began with grinding the J. curcas cake into small pieces. Then it was suspended in 2.5% sodium hydroxide solution with ratio between solution/ J. curcas cake at 80:1 (v/w). The hydrolysis reaction was controlled at temperature 50 °C in water bath for 45 minutes. After that, the supernatant (protein hydrolysate) was separated using centrifuge at 8000g for 30 minutes. The maximum yield of resulting protein hydrolysate was 73.27 % with 7.34% moisture, 71.69% total protein, 7.12% lipid, 2.49% ash. The product was also capable of well dissolving in water.

Keywords: Production, protein hydrolysate, Jatropha curcas cake, optimization.

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Authors: Yanmin Zhao, Siu Ming Yiu

Abstract:

To claim the ownership for an executable program is a non-trivial task. An emerging direction is to add a watermark to the program such that the watermarked program preserves the original program’s functionality and removing the watermark would heavily destroy the functionality of the watermarked program. In this paper, the first watermarking signature scheme with the watermark and the constraint function hidden in the symmetric key setting is constructed. The scheme uses well-known techniques of lattice trapdoors and a lattice evaluation. The watermarking signature scheme is unforgeable under the Short Integer Solution (SIS) assumption and satisfies other security requirements such as the unremovability security property.

Keywords: Short integer solution problem, signatures, the symmetric-key setting, watermarking schemes.

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Authors: Khaja Kamaluddin, Muhammed Yousoof

Abstract:

Bandwidth allocation in wired network is less complex and to allocate bandwidth in wireless networks is complex and challenging, due to the mobility of source end system.This paper proposes a new approach to bandwidth allocation to higher and lower priority mobile nodes.In our proposal bandwidth allocation to new mobile node is based on bandwidth utilization of existing mobile nodes.The first section of the paper focuses on introduction to bandwidth allocation in wireless networks and presents the existing solutions available for allocation of bandwidth. The second section proposes the new solution for the bandwidth allocation to higher and lower priority nodes. Finally this paper ends with the analytical evaluation of the proposed solution.

Keywords: Layered Approach, Bandwidth allocation, CBR, ABR, QOS.

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Authors: Khairil Iskandar Othman, Zarina Bibi Ibrahim, Mohamed Suleiman

Abstract:

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.

Keywords: Backward Differentiation Formula, block, ordinarydifferential equations.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: Weihua Ruan, Kuan-Chou Chen

Abstract:

This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Differential games, Hamilton-Jacobi-Bellman equations, infinite horizon, political-economy models.

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Authors: M. Jahanandish, M. B. Zeydabadinejad

Abstract:

In this paper, von Mises and Drucker-Prager yield criteria, as typical ones that consider the effect of intermediate principal stress σ2, have been selected and employed for investigating the influence of σ2 on the solution of a typical stability problem. The bearing capacity factors have been calculated under plane strain condition (strip footing) and axisymmetric condition (circular footing) using the method of stress characteristics together with the criteria mentioned. Different levels of σ2 relative to the other two principal stresses have been considered. While a higher σ2 entry in yield criterion gives a higher bearing capacity; its entry in equilibrium equations (axisymmetric) causes substantial reduction.

Keywords: Intermediate principal stress, plane strain, axisymmetric, yield criteria.

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