Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1216

# Search results for: bending rectangular plates

##### 1216 An Analytical Method for Bending Rectangular Plates with All Edges Clamped Supported

Authors: Yang Zhong, Heng Liu

Abstract:

The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last. Downloads 474

Authors: Mahmoudi Noureddine

Abstract:

In this study the use of two variable refined plate theories of laminated composite plates to static response of laminated plates. The plate theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The validity of the present theory is demonstrated by comparison with solutions available in the literature and finite element method. The result is presented for the static response of simply supported rectangular plates under uniform sinusoidal mechanical loadings.

Keywords: bending, composite, laminate, plates, fem

##### 1214 A Comparative Study of Force Prediction Models during Static Bending Stage for 3-Roller Cone Frustum Bending

Authors: Mahesh Chudasama, Harit Raval

Abstract:

Conical sections and shells of metal plates manufactured by 3-roller conical bending process are widely used in the industries. The process is completed by first bending the metal plates statically and then dynamic roller bending sequentially. It is required to have an analytical model to get maximum bending force, for optimum design of the machine, for static bending stage. Analytical models assuming various stress conditions are considered and these analytical models are compared considering various parameters and reported in this paper. It is concluded from the study that for higher bottom roller inclination, the shear stress affects greatly to the static bending force whereas for lower bottom roller inclination it can be neglected. Downloads 173
##### 1213 A Superposition Method in Analyses of Clamped Thick Plates

Authors: Alexander Matrosov, Guriy Shirunov

Abstract:

A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling. Downloads 432
##### 1212 Transverse Vibration of Non-Homogeneous Rectangular Plates of Variable Thickness Using GDQ

Authors: R. Saini, R. Lal

Abstract:

The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y. Numerical results have been computed for fully clamped and fully simply supported boundary conditions. The solution procedure by means of GDQ method has been implemented in a MATLAB code. The effect of various plate parameters has been investigated for the first three modes of vibration. A comparison of results with those available in literature has been presented. Downloads 306
##### 1211 Application of the Extended Kantorovich Method to Size-Dependent Vibrational Analysis of Fully Clamped Rectangular Micro-Plates

Authors: Amir R. Askari, Masoud Tahani

Abstract:

The objective of the present paper is to investigate the effect of size on the vibrational behavior of fully clamped rectangular micro-plates based on the modified couple stress theory (MCST). To this end, a size-dependent Kirchhoff plate model is considered and the equation of motion which accounts for the effect of residual and couple stress components is derived using the Hamilton's principle. The eigenvalue problem associated with the free vibrations of fully clamped micro-plates is extracted and solved analytically using the extended Kantorovich method (EKM). The present findings are compared and validated by available results in the literature and an excellent agreement between them is observed. A parametric study is also conducted to show the significant effects of couple stress components on natural frequencies of fully clamped micro-plates. It is found that the ratio of MCST natural frequencies to those obtained by the classical theory (CT) only depends on the Poisson's ratio of the plate and is totally independent of plate's aspect ratio for cases with no residual stresses. Downloads 308
##### 1210 Analysis of Plates with Varying Rigidities Using Finite Element Method

Abstract:

This paper presents Finite Element Method (FEM) for analyzing the internal responses generated in thin rectangular plates with various edge conditions and rigidity conditions. Comparison has been made between the FEM (ANSYS software) results for displacement, stresses and moments generated with and without the consideration of hole in plate and different aspect ratios. In the end comparison for responses in plain and composite square plates has been studied.

Keywords: ANSYS, finite element method, plates, static analysis

##### 1209 Numerical Investigation of the Effect of Geometrical Shape of Plate Heat Exchangers on Heat Transfer Efficiency

Authors: Hamed Sanei, Mohammad Bagher Ayani

Abstract:

Optimizations of Plate Heat Exchangers (PHS) have received great attention in the past decade. In this study, heat transfer and pressure drop coefficients are compared for rectangular and circular PHS employing numerical simulations. Plates are designed to have equivalent areas. Simulations were implemented to investigate the efficiency of PHSs considering heat transfer, friction factor and pressure drop. Amount of heat transfer and pressure drop was obtained for different range of Reynolds numbers. These two parameters were compared with aim of F "weighting factor correlation". In this comparison, the minimum amount of F indicates higher efficiency. Results reveal that the F value for rectangular shape is less than circular plate, and hence using rectangular shape of PHS is more efficient than circular one. It was observed that, the amount of friction factor is correlated to the Reynolds numbers, such that friction factor decreased in both rectangular and circular plates with an increase in Reynolds number. Furthermore, such simulations revealed that the amount of heat transfer in rectangular plate is more than circular plate for different range of Reynolds numbers. The difference is more distinct for higher Reynolds number. However, amount of pressure drop in circular plate is less than rectangular plate for the same range of Reynolds numbers which is considered as a negative point for rectangular plate efficiency. It can be concluded that, while rectangular PHSs occupy more space than circular plate, the efficiency of rectangular plate is higher. Downloads 213
##### 1208 Existence and Construction of Maximal Rectangular Duals

Authors: Krishnendra Shekhawat

Abstract:

Given a graph G = (V, E), a rectangular dual of G represents the vertices of G by a set of interior-disjoint rectangles such that two rectangles touch if and only if there is an edge between the two corresponding vertices in G. Rectangular duals do not exist for every graph, so we can define maximal rectangular duals. A maximal rectangular dual is a rectangular dual of a graph G such that there exists no graph G ′ with a rectangular dual where G is a subgraph of G ′. In this paper, we enumerate all maximal rectangular duals (or, to be precise, the corresponding planar graphs) up to six nodes and presents a necessary condition for the existence of a rectangular dual. This work allegedly has applications in integrated circuit design and architectural floor plans. Downloads 141
##### 1207 Comparative Study of Static and Dynamic Bending Forces during 3-Roller Cone Frustum Bending Process

Authors: Mahesh K. Chudasama, Harit K. Raval

Abstract:

3-roller conical bending process is widely used in the industries for manufacturing of conical sections and shells. It involves static as well dynamic bending stages. Analytical models for prediction of bending force during static as well as dynamic bending stage are available in the literature. In this paper, bending forces required for static bending stage and dynamic bending stages have been compared using the analytical models. It is concluded that force required for dynamic bending is very less as compared to the bending force required during the static bending stage. Downloads 223
##### 1206 Steady State Natural Convection in Vertical Heated Rectangular Channel between Two Vertical Parallel MTR-Type Fuel Plates

Authors: Djalal Hamed

Abstract:

The aim of this paper is to perform an analytic solution of steady state natural convection in a narrow rectangular channel between two vertical parallel MTR-type fuel plates, imposed under a cosine shape heat flux to determine the margin of the nuclear core power at which the natural convection cooling mode can ensure a safe core cooling, where the cladding temperature should not be reach the specific safety limits (90 °C). For this purpose, a simple computer program is developed to determine the principal parameter related to the nuclear core safety such as the temperature distribution in the fuel plate and in the coolant (light water) as a function of the reactor power. Our results are validated throughout a comparison against the results of another published work, which is considered like a reference of this study. Downloads 248
##### 1205 Dynamic Relaxation and Isogeometric Analysis for Finite Deformation Elastic Sheets with Combined Bending and Stretching

Authors: Nikhil Padhye, Ellen Kintz, Dan Dorci

Abstract:

Recent years have seen a rising interest in study and applications of materially uniform thin-structures (plates/shells) subject to finite-bending and stretching deformations. We introduce a well-posed 2D-model involving finite-bending and stretching of thin-structures to approximate the three-dimensional equilibria. Key features of this approach include: Non-Uniform Rational B-Spline (NURBS)-based spatial discretization for finite elements, method of dynamic relaxation to predict stable equilibria, and no a priori kinematic assumption on the deformation fields. The approach is validated against the benchmark problems,and the use of NURBS for spatial discretization facilitates exact spatial representation and computation of curvatures (due to C1-continuity of interpolated displacements) for this higher-order accuracy 2D-model. Downloads 72
##### 1204 Buckling Behavior of FGM Plates Using a Simplified Shear Deformation Theory

Authors: Mokhtar Bouazza

Abstract:

In this paper, the simplified theory will be used to predict the thermoelastic buckling behavior of rectangular functionally graded plates. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The simplified theory is used to obtain the buckling of the plate under different types of thermal loads. The thermal loads are assumed to be uniform, linear, and non-linear distribution through the thickness. Additional numerical results are presented for FGM plates that show the effects of various parameters on thermal buckling response. Downloads 265
##### 1203 Analytical Study of Flexural Strength of Concrete-Filled Steel Tube Beams

Authors: Maru R., Singh V. P.

Abstract:

In this research, analytical study of the flexural strength of Concrete Filled Steel Tube (CFST) beams is carried out based on wide-range finite element models to obtain the better perspective for flexural strength achievement with the use of ABAQUS finite element program. This work adopts concrete damaged plasticity model to get the actual simulation of CFST under bending. To get the decent interaction between concrete and steel, normal and tangential surface interaction provided by ABAQUS is used with hard contact for normal surface interaction and for 0.65 friction coefficient for tangential surface interactions. In this study, rectangular and square CFST beam model cross-sections are adopted with its limits pertained to Eurocode specifications. To get the visualization for flexural strength of CFST beams, total of 74 rectangular CFST beams and 86 square CFST beams are used with four-point bending test setup and the length of the beam model as 1000mm. The grades of concrete and grades of steel are used as 30 MPa & 35MPa and 235 MPa and 275MPa respectively for both sections to get the confinement factor 0.583 to 2.833, steel ratio of 0.069 to 0.236 and length to depth ratio of 4.167 to 16.667. It was found based on this study that flexural strength of CFST beams falls around strain of 0.012. Eurocode provides the results harmonically with finite elemental results. It was also noted for square sections that reduction of steel ratio is not useful as compared to rectangular section although it increases moment capacity up to certain limits because for square sectional area similar to that of rectangular, it possesses lesser depth than rectangular sections. Also It can be said that effect of increment of grade of concrete can be achieved when thicker steel tube is present. It is observed that there is less increment in moment capacity initially but after D/b ratio 1.2, moment capacity of CFST beam rapidly. Downloads 68
##### 1202 Durability Study of Pultruded CFRP Plates under Sustained Bending in Distilled Water and Seawater Immersions: Effects on the Visco-Elastic Properties

Authors: Innocent Kafodya, Guijun Xian

Abstract:

This paper presents effects of distilled water, seawater and sustained bending strains of 30% and 50% ultimate strain at room temperature, on the durability of unidirectional pultruded carbon fiber reinforced polymer (CFRP) plates. In this study, dynamic mechanical analyzer (DMA) was used to investigate the synergic effects of the immersions and bending strains on the visco-elastic properties of (CFRP) such as storage modulus, tan delta and glass transition temperature. The study reveals that the storage modulus and glass transition temperature increase while tan delta peak decreases in the initial stage of both immersions due to the progression of curing. The storage modulus and Tg subsequently decrease and tan delta increases due to the matrix plasticization. The blister induced damages in the unstrained seawater samples enhance water uptake and cause more serious degradation of Tg and storage modulus than in water immersion. Increasing sustained bending decreases Tg and storage modulus in a long run for both immersions due to resin matrix cracking and debonding. The combined effects of immersions and strains are not clearly reflected due to the statistical effects of DMA sample sizes and competing processes of molecular reorientation and postcuring. Downloads 195
##### 1201 Free Vibration and Buckling of Rectangular Plates under Nonuniform In-Plane Edge Shear Loads

Authors: T. H. Young, Y. J. Tsai

Abstract:

A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed. Downloads 70
##### 1200 Relative Study of the Effect of the Temperature Gradient on Free Vibrations of Clamped Visco-Elastic Rectangular Plates with Linearly and Exponentially Thickness Variations Respectively in Two Directions

Authors: Harvinder Kaur

Abstract:

Rayleigh–Ritz method is a broadly used classical method for the calculation of the natural vibration frequency of a structure in the second or higher order. Here it is used to construct a mathematical model of relative study of the thermal effect on free transverse vibrations of clamped (c-c-c-c type) visco-elastic rectangular plate with linearly and exponentially thickness variations respectively in two directions. Researchers in the field of Engineering always make an effort for better designs of mechanical structures. In-depth study of the vibration behavior of tapered plates with diverse thickness variation under high temperature would ultimately help to finalize the accurate design of a structure. The perfect tapered structure saves weight and as well as expenses. In the present paper, the comparison has been done for deflection and time period corresponding to the first two modes of vibrations of clamped plate for various values of aspect ratio, thermal constants, and taper constants of both the cases. Downloads 148
##### 1199 The Numerical and Experimental Analysis of Compressed Composite Plate in Asymmetrical Arrangement of Layers

Authors: Katarzyna Falkowicz

Abstract:

The work focused on the original concept of a thin-walled plate element with a cut-out, for use as a spring or load-bearing element. The subject of the study were rectangular plates with a cut-out with variable geometrical parameters and with a variable angle of fiber arrangement, made of a carbon-epoxy composite with high strength properties in an asymmetrical arrangement, subjected to uniform compression. The influence of geometrical parameters of the cut-out and the angle of fiber arrangement on the value of critical load of the structure and buckling form was investigated. Uniform thin plates are relatively cheap to manufacture, however due to their low bending stiffness; they can carry relatively small loads. The lowest form of loss of plate stability, which is the bending form, leads to its rapid destruction due to high deflection increases, with a slight increase in compressive load - low rigidity of the structure. However, the stiffness characteristics of the structure change significantly when the work of plate is forcing according to the higher flexural-torsional form of buckling. The plate is able to carry a much higher compressive load while maintaining much stiffer work characteristics in the post-critical range. The calculations carried out earlier show that plates with forced higher form of buckling are characterized by stable, progressive paths of post-critical equilibrium, enabling their use as elastic elements. The characteristics of such elements can be designed in a wide range by changing the geometrical parameters of the cut-out, i.e. height and width as well as by changing the angle of fiber arrangement The commercial ABAQUS program using the finite element method was used to develop the discrete model and perform numerical calculations. The obtained results are of significant practical importance in the design of structures with elastic elements, allowing to achieve the required maintenance characteristics of the device. Downloads 41
##### 1198 Numerical Analysis of the Flexural Behaviour of Concrete-Filled Rectangular Flange Girders

Authors: R. Al-Dujele, K. A. Cashell

Abstract:

A tubular flange girder is an I-shaped steel girder with either one of both of the usual flat flange plates replaced with a hollow section. Typically, these hollow sections are either rectangular or circular in shape. Concrete filled tubular flange girders (CFTFGs) are unconventional I-shaped beams that use a hollow structural section as the top flange which is filled with concrete. The resulting section offers very high lateral torsional buckling strength and stiffness compared with conventional steel I-beams of similar depth, width and weight, typically leading to a reduction in lateral bracing requirements. This paper is focussed on investigating the ultimate capacity of concrete filled rectangular tubular flange girders (CFRTFGs). These are complex members and their behaviour is governed by a number of inter-related parameters. The FE model is developed using ABAQUS software, 3-D finite element (FE) model for simply supported CFRTFGs subjected to two point loads applied at the third-span points is built. An initial geometrical imperfection of (L/1000), as well as geometrical and material nonlinearities, are introduced into the model, where L denotes the span of the girder. In this numerical model, the concrete and steel materials are modelled using eight-node solid and four-node shell elements, respectively. In addition to the FE model, simplified analytical expressions for the flexural capacity are also proposed, and the results are compared to those from the FE analyses. The analytical expressions, which are suitable for design, are also shown to be capable of providing an accurate depiction of the bending moment capacity. Downloads 78
##### 1197 Multifunctional Bending and Straightening Machines for Shipbuilding

Authors: V. Yu. Shungin, A. V. Popov

Abstract:

At present, one of the main tasks of Russian shipbuilding yards is implementation of new technologies and replacement of main process equipment. In particular, conventional bending technologies with dies are being replaced with resource-saving methods of rotation (roller) banding. Such rolling bending is performed by multiple rolling of a plat in special bending rollers. Studies, conducted in JSC SSTC, allowed developing a theory of rotation bending, methods for calculation of process parameters, requirements to roller presses and bending accessories. This technology allows replacing old and expensive presses with new cheaper roller ones, having less power consumption and bending force. At first, roller presses were implemented in ship repair, however now they are widely employed at major shipbuilding yards. JSC SSTC develops bending technology and carries out design, manufacturing and delivery of roller presses. Downloads 499
##### 1196 Structural Performance of Concrete Beams Reinforced with Steel Plates: Experimental Study

Authors: Mazin Mohammed S. Sarhan

Abstract:

This study presents the performance of concrete beams reinforced with steel plates as a technique of reinforcement. Three reinforced concrete beams with the dimensions of 200 mm x 300 mm x 4000 mm (width x height x length, respectively) were experimentally investigated under flexural loading. The deformed steel bars were used as the main reinforcement for the first beam. A steel plate placed horizontally was used as the main reinforcement for the second beam. The bond between the steel plate and the surrounding concrete was enhanced by using steel bolts (with a diameter of 20 mm and length of 100 mm) welded to the steel plate at a regular distance of 200 mm. A pair of steel plates placed vertically was used as the main reinforcement for the third beam. The bond between the pair steel plates and the surrounding concrete was enhanced by using 4 equal steel angles (with the dimensions of 75 mm x 75 mm and the thickness of 8 mm) for each vertical steel plate. Two steel angles were welded at each end of the steel plate. The outcomes revealed that the bending stiffness of the beams reinforced with steel plates was higher than that reinforced with deformed steel bars. Also, the flexural ductile behavior of the second beam was much higher than the rest beams.

Keywords: concrete beam, deflection, ductility, plate

##### 1195 Deformation of Metallic Foams with Closed Cell at High Temperatures

Authors: Emrah Ersoy, Yusuf Ozcatalbas

Abstract:

The aim of this study is to investigate formability of Al based closed cell metallic foams at high temperature. The foam specimens with rectangular section were produced from AlMg1Si0.6TiH20.8 alloy preform material. Bending and free bending tests based on gravity effect were applied to foam specimens at high temperatures. During the tests, the time-angular deformation relationships with various temperatures were determined. Deformation types formed in cell walls were investigated by means of Scanning Electron Microscopy (SEM) and optical microscopy. Bending deformation about 90° was achieved without any defect at high temperatures. The importance of a critical temperature and deformation rate was emphasized in maintaining the deformation. Significant slip lines on surface of cell walls at tensile zones of bending specimen were observed. At high strain rates, the microcrack formation in boundaries of elongated grains was determined.

Keywords: Al alloy, Closed cell, Hot deformation, Metallic foam

##### 1194 Efficiency of the Strain Based Approach Formulation for Plate Bending Analysis

Abstract:

In recent years many finite elements have been developed for plate bending analysis. The formulated elements are based on the strain based approach. This approach leads to the representation of the displacements by higher order polynomial terms without the need for the introduction of additional internal and unnecessary degrees of freedom. Good convergence can also be obtained when the results are compared with those obtained from the corresponding displacement based elements, having the same total number of degrees of freedom. Furthermore, the plate bending elements are free from any shear locking since they converge to the Kirchhoff solution for thin plates contrarily for the corresponding displacement based elements. In this paper the efficiency of the strain based approach compared to well known displacement formulation is presented. The results obtained by a new formulated plate bending element based on the strain approach and Kirchhoff theory are compared with some others elements. The good convergence of the new formulated element is confirmed. Downloads 213
##### 1193 Vibration Response of Soundboards of Classical Guitars

Abstract:

Research is focused on the response of soundboards of Classical guitars at frequencies up to 5 kHz as the soundboard is a major contributor to acoustic radiation at high frequencies when compared to the bridge and sound hole. A thin rectangular plate of variable thickness that is simply-supported on all sides is used as an analytical model of the research. This model is used to study the response of the guitar soundboard as the latter can be considered as a modified form of a rectangular plate. Homotopy Perturbation Method (HPM) is selected as a mathematical method to obtain an analytical solution of the 4th-order parabolic partial differential equation of motion of the rectangular plate of constant thickness viewed as a linear problem. This procedure is generalized to the nonlinear problem of the rectangular plate with variable thickness and an analytical solution can also be obtained. Sound power is used as a parameter to investigate the acoustic radiation of soundboards made from spruce using various bracing patterns. The sound power of soundboards made from Malaysian softwood such as damar minyak, sempilor or podo are investigated to determine the viability of replacing spruce as future materials for soundboards of Classical guitars. Downloads 122
##### 1192 Nonlinear Finite Element Analysis of Concrete Filled Steel I-Girder Bridge

Authors: Waheed Ahmad Safi, Shunichi Nakamura

Abstract:

Concrete filled steel I-girder (CFIG) bridge was proposed and the bending and shear strength was confirmed by experiments. The area surrounded by the upper and lower flanges and the web is filled with concrete in CFIG, which is used to the intermediate support of a continuous girder. Three-dimensional finite element models were established to simulate the bending and shear behaviors of CFIG and to clarify the load transfer mechanism. Steel plates and filled concrete were modeled as a three-dimensional 8-node solid element and steel reinforcement bars as a three-dimensional 2-node truss element. The elements were mostly divided into the 50 x 50 mm mesh size. The non-linear stress-strain relation is assumed for concrete in compression including the softening effect after the peak, and the stress increases linearly for concrete in tension until concrete cracking but then decreases due to tension stiffening effect. The stress-strain relation for steel plates was tri-linear and that for reinforcements was bi-linear. The concrete and the steel plates were rigidly connected. The developed FEM model was applied to simulate and analysis the bending behaviors of the CFIG specimens. The vertical displacements and the strains of steel plates and the filled concrete obtained by FEM agreed very well with the test results until the yield load. The specimens collapsed when the upper flange buckled or the concrete spalled off. These phenomena cannot be properly analyzed by FEM, which produces a small discrepancy at the ultimate states. The FEM model was also applied to simulate and analysis the shear tests of the CFIG specimens. The vertical displacements and strains of steel and concrete calculated by FEM model agreed well with the test results. A truss action was confirmed by the FEM and the experiment, clarifying that shear forces were mainly resisted by the tension strut of the steel plate and the compression strut of the filled concrete acting in the diagonal direction. A trail design with the CFIG was carried out for a four-span continuous highway bridge and the design method was established. Construction cost was estimated about 12% lower than that of a conventional steel I-section girder. Downloads 150
##### 1191 Strengthening of Reinforced Concrete Beams Using Steel Plates

Abstract:

In this paper, external reinforcement to enhance a reinforced concrete structure performance has been done using externally bonded steel plate. This technique has been reported effective in enhancing the strength of reinforced concrete beam, a study to determine the effectiveness of steel plate as an external reinforcement was carried out. A total of two groups of beams and one group content five beams, each 750 mm long, 150 mm wide, and 150 mm deep were cast, strengthened and tested till failure under two point loads. One beam was act as a control beam without strengthening and other four beams were strengthened with steel plate at a different arrangement. Other group beams were strengthened with steel plate in shear zone and also strengthened at bottom as first group. The behaviours of the strengthened beams were studied through their load-deflection characteristic upon bending, cracking and mode of failure. The results confirmed that all steel plate arrangements enhanced the strength of the reinforced concrete beam, the positioning of the steel plate affect the moment carrying capacity of the beam.

Keywords: beams, bending, beflection, steel plates

##### 1190 An Inverse Approach for Determining Creep Properties from a Miniature Thin Plate Specimen under Bending

Authors: Yang Zheng, Wei Sun

Abstract:

This paper describes a new approach which can be used to interpret the experimental creep deformation data obtained from miniaturized thin plate bending specimen test to the corresponding uniaxial data based on an inversed application of the reference stress method. The geometry of the thin plate is fully defined by the span of the support, l, the width, b, and the thickness, d. Firstly, analytical solutions for the steady-state, load-line creep deformation rate of the thin plates for a Norton’s power law under plane stress (b → 0) and plane strain (b → ∞) conditions were obtained, from which it can be seen that the load-line deformation rate of the thin plate under plane-stress conditions is much higher than that under the plane-strain conditions. Since analytical solution is not available for the plates with random b-values, finite element (FE) analyses are used to obtain the solutions. Based on the FE results obtained for various b/l ratios and creep exponent, n, as well as the analytical solutions under plane stress and plane strain conditions, an approximate, numerical solutions for the deformation rate are obtained by curve fitting. Using these solutions, a reference stress method is utilised to establish the conversion relationships between the applied load and the equivalent uniaxial stress and between the creep deformations of thin plate and the equivalent uniaxial creep strains. Finally, the accuracy of the empirical solution was assessed by using a set of “theoretical” experimental data.

Keywords: bending, creep, thin plate, materials engineering

##### 1189 The Dynamics of Unsteady Squeezing Flow between Parallel Plates (Two-Dimensional)

Authors: Jiya Mohammed, Ibrahim Ismail Giwa

Abstract:

Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables. Downloads 384
##### 1188 Numerical Analysis of the Melting of Nano-Enhanced Phase Change Material in a Rectangular Latent Heat Storage Unit

Authors: Radouane Elbahjaoui, Hamid El Qarnia

Abstract:

Melting of Paraffin Wax (P116) dispersed with Al2O3 nanoparticles in a rectangular latent heat storage unit (LHSU) is numerically investigated. The storage unit consists of a number of vertical and identical plates of nano-enhanced phase change material (NEPCM) separated by rectangular channels in which heat transfer fluid flows (HTF: Water). A two dimensional mathematical model is considered to investigate numerically the heat and flow characteristics of the LHSU. The melting problem was formulated using the enthalpy porosity method. The finite volume approach was used for solving equations. The effects of nanoparticles’ volumetric fraction and the Reynolds number on the thermal performance of the storage unit were investigated. Downloads 269
##### 1187 Numerical Solution of Transient Natural Convection in Vertical Heated Rectangular Channel between Two Vertical Parallel MTR-Type Fuel Plates

Authors: Djalal Hamed

Abstract:

The aim of this paper is to perform, by mean of the finite volume method, a numerical solution of the transient natural convection in a narrow rectangular channel between two vertical parallel Material Testing Reactor (MTR)-type fuel plates, imposed under a heat flux with a cosine shape to determine the margin of the nuclear core power at which the natural convection cooling mode can ensure a safe core cooling, where the cladding temperature should not reach a specific safety limits (90 °C). For this purpose, a computer program is developed to determine the principal parameters related to the nuclear core safety, such as the temperature distribution in the fuel plate and in the coolant (light water) as a function of the reactor core power. Throughout the obtained results, we noticed that the core power should not reach 400 kW, to ensure a safe passive residual heat removing from the nuclear core by the upward natural convection cooling mode. Downloads 124