Computational Methods in Engineering

---

Trigonometric functions are among the most useful functions in the digital signal processing applications. The design introduced in this paper computes the trigonometric functions by means of the systolic arrays. The method for computing these functions for an arbitrary angle, , is the CORDIC algorithm. A simple standard cell is used for the systolic array. Due to the fixed inputs, in some cases, a number of the cells are optimized. The control unit and a read only memory are the essential parts of any CORDIC implementation. The introduced hardware does not use any of these two structures, which makes it a simple and expandable design

---

In order to carry out experimental investigations on radial inflow gas turbine, a special test laboratory was designed and constructed at Sharif University of Technology. This laboratory is introduced in the present paper and experimental procedures are elaborated on. Then, some test results are presented and discussed. The trends of performance characterisitics match our expectation and show good agreement with the published research results in this field. Keywords: Radial inflow gas turbine, Experimental, Laboratory, Performance characteristics

---

Application of gravity and magnetic separation methods to upgrade low grade Manganese ores from Venaj Mine has been reported elsewhere. This paper discusses the results of flotation tests, as well as combination of flotation and magnetic method to concentrate fine particles (less than 150 microns) of manganese ore. Results obtained from various direct and reverse flotation tests, using different types of reagents, indicated that manganese fines cannot easily be concentrated by flotation. In this investigation, combination of direct flotation and magnetic separation for fine particles (finer than 150 microns) with 8.36% Mn, 34.11% SiO2, 23.05% Fe2O3 yielded a manganese concentrate with 26.78% Mn, 11.64% SiO2, 20.37% Fe2O3 and 56% recovery. Desliming 10-15 micron particles prior to flotation tests improved product quality and the recovery. Keywords: Mineral Processing, Flotation, Manganese, Vanarj Mine

---

Overhead transmission lines are influenced by different factors which are mostly electrical and mechanical. These factors can cause problems for lines, distortions in network and outage of line. In designing transmission lines mechanical properties are evaluated after selecting a suitable conductor and clearance with regard to electrical properties. In lines designing, an important mechanical parameter for estimating of phase distance is oscillations. Strong wind or ice fall from conductor surfaces or simultaneous presence of ice and wind may cause different oscillations. These oscillations are classified to aeoliane, galloping, and swing. Aeoliane is of high frequency (5-100Hz) and low amplitude (about a few centimeters), galloping is of low frequency (0.1 to 0.3Hz) and high amplitude (about of span sagging), also swing is of horizontal oscillation. In this paper, the mechanism of conductor galloping oscillation and its different types are described. Also these oscillations are simulated on the typical span by personal computer. Keywords: Galloping, Overhead transmission lines, Single conductors, Modeling

---

Dense Silicon nitride was investigated to determine the effect of its microstructural parameters and densification on thermo-mechanical properties and thermal stress resistance to fracture initiation during a hot or cold mechanical and thermal shock testing. The different materials and microstructures were obtained by changing the parameters such as the type of the powder, additive, forming process and sintering condition. Maximum crack growth and thermal shock resistance of dense Si3N4 are achieved after complete conversion of the aàB transformation, and after the change in grain morphology towards elongated grain and the relative crystallization of the second phases have been obtained. The characteristics are obtained by a high a phase content of the starting powder, high Y2O3, and sintering condition of higher temperature (2000ْC), longer soaking times (1h) and load application at the beginning of the thermal cycle. Keywords: Silicon nitride, Thermo- mechanical properties, Thermal shock resistance, Crack propagation resistance

---

---

Hidden Markov Model is a popular statisical method that is used in continious and discrete speech recognition. The probability density function of observation vectors in each state is estimated with discrete density or continious density modeling. The performance (in correct word recognition rate) of continious density is higher than discrete density HMM, but its computation complexity is very high, especially in very large discrete utterance recognition problems. For real time implementation of very large discrete utterance recognition, we must use discrete density HMM (DDHMM). To increase the performance of DDHMM, one usual solution is fuzzy interpolation. In this study, we present a new method named Gaussian interpolation. We implemented and compared the performance of two types of interpolation methods for 1500 Persian speech command words. Results show that precision and flexibility of Gaussian interpolation is better thanthose of the fuzzy interpolation.

---

Zinc-Nickel electrodeposits have been widely adopted for surface treatment of automobile steel sheet for high corrosion resistance. In this work the effect of pulse parameters on the Zn-Ni alloy electrodeposits was investigated. The hardness, thickness, corrosion resistance and composition of deposits thus produced were investigated. The surface topography of the deposits was also observed in SEM and results are reported. It has been shown that the thickness of the pulse electrodeposits was almost even. The hardness in the pulse electrodeposits increased by increasing the on-time period and by decreasing the current density. It was also noticed that increasing the on-time period increases the nickel content of the deposit. Pulse electrodposits had fine structure and the structure become finer by reducung the on-time period and pulse frequency. The corrosion dehaviors of the deposits were then investigated. The results showed that the corrosion resistance of the DC electrodeposits improves in their nickel content increases. Pulse electodeposits show the same behavior, but deposits with about 13% nickel show maximum corrosion resistance.

---

A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient algorithm is developed to find surrogate multipliers in each stage of dynamic programming in order to transform the original problem to a single constraint problem called surrogate problem. The upper and lower bounds obtained by solving the surrogate problem can eliminate a large number of state variables in dynamic programming and extremely reduce the duality gap according to our computational results.

---

In this paper, the Radiation Transfer Equation(RTE) for a non-gray gas between two large parallel planes has been solved and the temperature distribution obtained. With the RTE, solution heat fluxes are also determined. Since and are two components of most combustion products, the problem has been solved for these two gases. The results were, whenever possible, compared with data reported elsewhere. Since the simulation of exact absorbing bands has been used, it can be claimed to be relatively close to exact solution. From the results otained, it can be maintained that treating, the above mentioned gases as a gray gas could cause considerable errors in the determination of temperature distribution and heat fluxes. The error would be more for water vapour than for carbon dioxide.

---

Artificial Neural Networks are information processing systems. Over the past several years, these algorithms have received much attention for their applications in pattern completing, pattern matching and classification and also for their use as a tool in various areas of problem solving. In this work, an Artificial Neural Network model is presented for predicting the tensile properties of cotton-covered nylon core yarns. Multilayer Feedforward network with Back Propagation learning algorithm was used to study the relationship and mapping among the process parameters, i.e. count of sheath part, count of core part, applying pretension to the core part, inserted twist to the core spun-yarn as well as tensile properties, i.e. breaking strength and breaking elongation. The results show that ANN is an effective method for the prediction of the tensile properties of these yarns. This is due to the fact that in each case, standard deviation of prediction error for test and train data was less than that obtained from the expreiments.

---

A physical model of gabion overflow dams was studied to determine the velocity profile and Reynolds shear stress. Physical tests were done under two different conditions of dam crest, overflow dams with impermeable and with permeable crests. Instantaneous velocity components over dam crest were measured by an ADV (Acoustic Doppler Velocimeter) instrument. This instrument is capable of measuring instantaneous velocity components with frequencies up to 25 Hz. Average velocity components and bed shear stress were extracted from ADV measurements. The results of this research show the effect of crest permeability on velocity and Reynolds shear stress. The magnitude of Reynolds shear stresses, horizontal velocity components, and absolute value of vertical velocity components under the permeable scenario are bigger than those of the impermeable scenario. Velocity distribution over the dam crest is different from the universal logarithmic profile.

---

A systolic serial multiplier for unsigned numbers is presented which operates without zero words inserted between successive data words, outputs the full product and has only one clock cycle latency. The multiplier is based on a modified serial/parallel scheme with two adjacent multiplier cells. Systolic concept is a well-known means of intensive computational task through replication of functional units and their repetitive use. Digital signal processing applications often involve high-speed sequential data. Bit-serial processing in particular can result in efficient communications, both within and between VLSI chips because of the reduced number of interconnections required. Serial input multipliers have received considerable attention, particularly for hardwired VLSI algorithms used in signal processing application, due to their minimal chip area required for interconnections. Bit-serial architectures are often used in parallel systems with high connectivity to reduce the wiring down to a reasonable level. The conventional add-shift technique for multiplication, which uses a minimum number of gates, is inexpensive to implement, but too slow to achieve the desired result. Iterative array multipliers are needed to satisfy the high speed requirement of systems. With the advantage of high scale integration, the hardware is not regarded as a major obstacle in implementation.

---

In this paper, two suboptimum detectors are proposed for coherent radar signal detection in K-distributed clutter. Assuming certain values for several initial moments of clutter amplitude, the characteristic function of the clutter amplitude is approximated by a limited series. Using the Pade approximation, it is then converted to a rational fraction. Thus, the pdf of the clutter amplitude is obtained as a sum of simple exponential functions. Using such a pdf, we develop the suboptimum detectors PGLR and PAALR, which are simplified forms of the GLR and AALR. Computer simulations show that the suggested detectors have appropriate performance compared to OLD, GLR and AALR detectors.

---

This paper presents a nonlinear mixed-integer programming model to minimize the stoppage cost of mixed-model assembly lines. Nowadays, most manufacturing firms employ this type of line due to the increasing varieties of products in their attempts to quickly respond to diversified customer demands. Advancement of new technologies, competitiveness, diversification of products, and large customer demand have encouraged practitioners to use different methods of improving production lines. Minimizing line stoppage is regarded as a main factor in determining the sequence of processing products. Line stoppage results in idleness of operators and machines, reduced throughput, increased overhead costs, and decreased overall productivity. Due to the complexity of the model proposed, which belongs to a class of NP-hard problems, a meta-heuristic method based on a genetic algorithm (GA) is proposed to obtain near-optimal solutions in reasonable time, especially for large-scale problems. To show the efficiency of the proposed GA, the computational results are compared with those obtained by the Lingo software.

---

In recent years, many different plans have been considered to use the nuclear energy gained from inertial confinement fusion (ICF) as attempts to obtain high energy efficiencies. In conventional ICF methods, a small amount (about mg) of the deuterium–tritium compound is confined in a small spherical chamber of a few millimeters in radius and compressed by laser or heavy ion beams with powers in the order of W. The consequent plasma froming at the center of the chamber is an essential issue for fusion. The hydrodynamical instabilities during the fuel compression process arising in the conventional ICF technique leads to a decline in energy efficiency. The new plans for reducing instabilities involve compression of the fuel chamber in two stages using laser or ion beams. In the first stage, fuel is preheated by laser or ion and in the second phase, relativistic electrons are constructed by -W laser phases in the fuel. This heating method has come to be known as a fast “ignition method”. More recently, cylindrical rather than spherical fuel chambers with magnetic control in the plasma domain have been also considered. In this work, fast ignition method in cylindrical fuel chambers will be investigated and transportation of the relativistic electrons will be calculated using MCNP code and the Fokker–Planck program. Furthermore, the transfer rate of relativistic electron energy to the fuel will be calculated. Our calculations show that the fast ignition method and cylindrical chambers guarantee a higher energy efficiency than the one-step ignition and that it can be considered an appropriate substitute for the current ICF techniques.

---

In this paper,  a numerical model  was first verified against dynamic centrifuge tests results performed on an
underground subway tunnel and then, the effect of underground structure on peak ground acceleration (PGA) at the ground
surface investigated considering linear and nonlinear behavior for the soil. The results show that in the range of natural
frequency of the system, nonlinear model shows deamplification of PGA with respected to the freefield. Whereas, linear model
shows opposite trend. Out of the range of natural frequency of the system, linear and nonlinear models predict same results and for both model, underground tunnel resulted in amplification of  low frequencies and deamplification of high frequencies with
respected to the freefield.

---

Utilizing one of the mesh free methods, the present paper concerns static analysis of thin plates with various geometric shapes based on the mindlin classical plate theories. In this numerical method, the domain of issue is solely expressed through a set of nods and no gridding or element is required. To express the domain of issues with various geometric shapes, first a set of nodes are defined in a standard rectangular domain , then via a three-order map with, these nodes are transferred to the main domain of the original issue; therefore plates of various geometric shapes can be analyzed. Among meshfree numerical methods, Element Free Galerkin method (EFG) is utilized here. The method is one of the weak form integral methods that uses MLS shape functions for approximation. Regarding the absence of Delta feature in MLS functions, boundary conditions cannot be imposed directly; hence the Lagrangian method is utilized to impose boundary conditions. At the end, our outputs are compared with those of analytic and finite element methods for plates, in order to validate the exactness of our solution method, and then after reliability is established, a few new examples will be solved.

---

This study shows how to create different types of crack and discontinuities by using isogeometric analysis approach (IGA) and extended finite element method (XFEM). In this contribution, two unique features of isogeometric analysis approach are utilized to create discontinuous zones. Discontinuities consist of crack and cohesive zone. In isogeometric analysis method NURBS is used to approximate both geometry and primary variable. NURBS can create quadratic shapes exactly. Also, stress intensity factors are calculated in the vicinity of the crack tips for two dimensional problems and are compared with corresponding analytical and numerical counterparts. Extended finite element method is the other numerical method which is used in this work. The enrichment procedure is utilized in extended finite element method to create discontinuities. The well-known path independent J-integral approach is used in order to calculate the stress intensity factors. Also, in mixed mode situation, the interaction integral (M-integral) is considered to calculate the stress intensity factors. Results show that isogeometric analysis method has desirable accuracy as it uses lower degree of freedoms and consequently lower computational efforts than extended finite element method. In addition, creating the internal cohesive zone as one of the most important issues in computational fracture mechanics is feasible due to the special features of isogeometric analysis. The present study demonstrates the capability of isogeometric analysis parametric space to control the inter-element continuity and create the cohesive zone.

---

In this paper, wave propagation method was applied to detect damage of structures. Spectral Finite Element Method
(SFEM) was used to analyze wave propagation in structures. Two types of structures i.e. rod and Euler-Bernoulli beam were
modelled using spectral elements. The advantage of spectral finite element over conventional Finite Element Method (FEM), in
wave propagation problems, is its accuracy and lower computational time. Two examples of rod and Euler-Bernoulli beam with
embeded concentrated mass were presented to illustrate the superiority of SFEM to FEM. Finally, a cracked beam was modeled
and analyzed using spectral finite elements and the location of the crack was determined using time history response of beam
structure.