ADINA Publications

Page 37

The Theory used in ADINA is richly documented in the following books by K.J. Bathe and co-authors

Finite Element Procedures

Finite Element Procedures in Engineering Analysis

Numerical Methods in Finite Element Analysis

The Mechanics of Solids and Structures — Hierarchical ...

The Finite Element Analysis of Shells — Fundamentals

Inelastic Analysis of Solids and Structures

To Enrich Life
(Sample pages here)


Following are more than 700 publications — that we know of — with reference to the use of ADINA. The pages give the Abstracts of some papers published since 1986 referring to ADINA. The most recent papers are listed first. All these papers may be searched using the box:

(latest on Page 43)
Page 43 Page 42 Page 41 Page 40 Page 39 Page 38 Page 37 Page 36 Page 35 Page 34
Page 33 Page 32 Page 31 Page 30 Page 29 Page 28 Page 27 Page 26 Page 25 Page 24
Page 23 Page 22 Page 21 Page 20 Page 19 Page 18 Page 17 Page 16 Page 15 Page 14
Page 13 Page 12 Page 11 Page 10 Page 9  Page 8  Page 7  Page 6  Page 5  Page 4 
Page 3  Page 2  Page 1 

Computational modeling of cold-formed steel

B.W. Schafer1, Z. Li1, C.D. Moen2

1 Department of Civil Engineering, Johns Hopkins University, Baltimore, MD, United States
2 Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA, United States

Thin-Walled Structures, 48:752–762, 2010

The objective of this paper is to provide an overview of computational modeling, both elastic buckling and nonlinear collapse analysis, for cold-formed steel members. Recent research and experiences with computational modeling of cold-formed steel members conducted within the first author’s research group at Johns Hopkins University are the focus of the presented work. This admittedly biased view of computational modeling focuses primarily on the use of the semi-analytical finite strip method and collapse modeling using shell finite elements. Issues addressed include how to fully compare finite strip and finite element solutions, and the importance of imperfections, residual stresses, material modeling, boundary conditions, element choice, element discretization, and solution controls in collapse modeling of cold-formed steel. Examples are provided to demonstrate the expected range of sensitivity in cold-formed steel collapse modeling. The paper concludes with a discussion of areas worthy of future study that are within the domain of cold-formed steel modeling.

Keywords: Cold-formed steel - Finite strip method - Imperfection sensitivity -  Collapse modeling

Forming of the titanium elements by bending

J. Adamus, P. Lacki

Faculty of the Mechanical Engineering and Computer Sciences, Institute of Metal Working, Quality Engineering and Bioengineering, Czestochowa University of Technology, 21, Armii Krajowej Ave, 42-200 Czestochowa, Poland

Computational Materials Science, In press, 2010

Abstract: Titanium alloys are superior to nearly all metals in terms of a combination of high mechanical strength and low weight. Therefore, titanium is used whenever the construction weight and its strength are essential. Bending is one of the most frequently used methods for forming titanium elements. However, current knowledge of titanium and its alloys forming by cold working is insufficient. Many phenomena, such as spring-back, need to be investigated and explained. This study was undertaken in order to investigate the titanium bending process. A numerical simulation of the bending of a Ti6Al4V ELI titanium alloy bar was carried out with the ADINA System, based on the finite element method. The influence of bar diameter, bending radius and bending angle on the strain and stress distribution in the deformed element was analysed. The numerical calculations demonstrated that the spring-back was dependent on the size of the middle material zone, which remained in an elastic state during bending process. This in turn was dependent on the value of the bending radius, bending angle and diameter/thickness of the bent element. Knowledge of the spring-back is very important because it essentially decreases the forming accuracy of the bent elements. This is especially important when vital titanium elements, such as: body implants or aircraft elements, are bent. Therefore, the calculation results were validated experimentally.

Keywords: Titanium - Titanium alloys - Bending - Numerical simulation

Finite-element simulation of temperature-dependent three-point bending process of glass

M. Pernach1, M. Sroda2, M. Pietrzyk1

1 Faculty of Metals Engineering and Industrial Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland
2 Faculty of Material Science and Ceramics, al. Mickiewicza 30, 30-059 Krakow, Poland

J Therm Anal Calorim, DOI 10.1007/s10973-010-0884-8, 2010

Abstract : Simulation of strains and stresses distributions in the glass subjected to a bending load during heat treatment is presented in the paper. The main objective of the work is to combine the temperature-dependent experimental test of three-point bending with simulation of this test and to apply inverse analysis to determine the properties of glass. The thermo-mechanical analysis (TMA) was used to test a temperature-dependent glass deformation. The ADINA finite element software was used for simulations of the viscous flow. Two parameters in the Williams–Landell–Ferry (WLF) equation were identified by optimization of the square root error between measured and predicted deflection of the sample. Performed experiments and simulations yielded the values of these coefficients: C1 = 26.3 and C2 = 62.7. The proposed model with the optimized coefficients confirmed good agreement with the experimental data.

Keywords:  Finite-element simulation – Glass - Viscous flow - Three-point bending – Williams-Landell-Ferry equation

An In Vitro Device for Evaluation of Cellular Response to Flows Found at the Apex of Arterial Bifurcations

Z. Zeng, B.J. Chung, M. Durka, and A.M. Robertson

Department of Mechanical Engineering and Materials Science, McGowan Institute for Regenerative Medicine, Center for Vascular Remodeling and Regeneration (CVRR); University of Pittsburgh, Pittsburgh, PA 15261, USA

R. Rannacher, A. Sequeira (eds.), Advances in Mathematical Fluid Mechanics, 631-657, 2010

Abstract: Intracranial aneurysms (ICA) are abnormal dilations of the cerebral arteries, most commonly located at the apices of bifurcations. The ability of the arterial wall, particularly the endothelial cells forming the inner lining of the wall, to respond appropriately to hemodynamic stresses is critical to arterial health. ICA initiation is believed to be caused by a breakdown in this homeostatic mechanism leading to wall degradation. Due to the complex nature of this process, there is a need for both controlled in vitro and in vivo studies. Chung et al. developed an in vitro chamber for analyzing the response of biological cells to the hemodynamic wall shear stress fields generated by the impinging flows found at arterial bifurcations. Here, we build on this work and design an in vitro flow chamber that can be used to reproduce specific magnitudes of wall shear stress (WSS) and gradients of wall shear stress. Particular attention is given to reproducing spatial distributions of these functions that have been shown to induce pre-aneurysmal changes in vivo. We introduce a measure of the gradient of the wall shear stress vector (WSSVG) which is appropriate for complex 3D flows and reduces to expected measures in simple 2D flows. The WSSVG is a scalar invariant and is therefore appropriate for use in constitutive equations for vessel remodeling in response to hemodynamic loads.

Keywords Intracranial aneurysm - Wall shear stress gradient - Flow chamber - Bifurcation

On the analysis of Catalan thin vaults

S. Benfratello, L. Palizzolo, F. Giambanco & M. D’Avenia

High Performance Structures and Materials V, Ed.: P. de Wilde, C.A. Brebbi, and U. Mander, 2010

Abstract: This paper is concerned with the identification, modelling and analysis of thin layered vaults, typical in the Catalan constructions of the XIX century. These special structures, also known as bòvedas tabicadas, are characterized by very low thickness with respect to the medium surface dimensions and by the presence of different superimposed layers of bricks tied with mortar, are studied in order to individuate a coherent mechanical model for describing the material behaviour, to recognize the structural response utilizing as comparison adequate experimental results, and to extend the obtained results for the analysis of new vaults or for the restoration design of existing vaults. Firstly, the constitutive material is studied by effecting a compression and bending test on samples taken from a real structure. The characterization is made by considering alternatively the material as homogeneous or stratified. Once the constitutive behaviour of the materials and of the structural elements has been experimentally characterized, a semi inverse method for the identification of the optimum mechanical parameters of an equivalent homogeneous ideal material and of a stratified one, is adopted on the grounds of finite element analysis, reproducing the executed experimental tests. The comparison between the results obtained experimentally and the ones based on numerical tests allows us to make evaluations on the mechanical characteristics of the identified materials and proves that the stratified model better describes the behaviour of the real material. Further experimental tests have been made on a real vault and the related numerical analysis has developed making reference to the two material mechanical models. The obtained results are encouraging in the utilization of the stratified model.

Keywords: thin vaults - material mechanical modelling - experimental and numerical analysis - restoration design.

Stress Analysis of the Superconducting Magnet of LPT

X. Wu1, P. Yuan2, L.Z. Ma2, X.Q. Zhang2, Y. He2, Q.G. Yao1, W. Wu1, B.L. Guo1, S.F. Han2, B. Zhang2, S.L. Zhang2, and W.X. Huang2

1 Graduate School of Chinese Academy of Sciences, Beijing 100039, China
2 Institute of Modern Physics of Chinese Academy of Sciences, Lanzhou 730000, China

IEEE Transactions On Applied Superconductivity, 20(3):1904-1907, 2010

Abstract: The superconducting magnet of the LPT (Lanzhou Penning trap) consists of nine coaxial coils. The maximum magnetic field is 7 T and thus results in a large magnetic force. In order to assure the mechanical stability, it is necessary to do the stress analysis of the magnet system. The 3D Finite Element Analysis of thermal and mechanical behavior was presented in this paper. For the numerical simulation and analysis of the phenomena inside the structure, the ADINA and TOSCA code were chosen right from start. The ADINA code is commonly used for numerical simulations of the structure analysis and the TOSCA code is professional software to calculate the magnetic field and Lorentz Forces. The results of the analysis were evaluated in terms of the stress and deformation.

Keywords: ADINA - finite element method - Lorentz forces – superconducting coils – TOSCA

Stress Concentration Factors For Pressurized Elliptic Crossbores In Blocks—Part II—Effect Of Block Geometry

E.A. Badr

School of Engineering and Architecture, Lebanese American University, Byblos, Lebanon.

Experimental Techniques, doi: 10.1111/j.1747-1567.2009.00531.x, 2010

The stress concentration point at the intersection of elliptical crossbores in rectangular blocks is investigated. Again, the results show that elliptical crossbores intersection produce stress concentration factors lower than those found at circular crossbores intersections. These findings corroborate with Faupel’s results concerning stress concentration factors for elliptic side holes in cylinders and infinite plates. Furthermore, this study shows that stress concentration factors of elliptical crossbores in rectangular blocks are lower than those found in cubical blocks.

Stress field evolution law of mining environment reconstructing structure with change of filling height

Q. Chen1,2, K. Zhou1, L. Wang1

1 School of Resources and Safety Engineering, Central South University, Changsha 410083, China
2 College of Resources and Metallurgy, Guangxi University, Nanning 530004, China

J. Cent. South Univ. Technol., 17: 738-743, 2010

Abstract: For improving global stability of mining environment reconstructing structure, the stress field evolution law of the structure with the filling height change of low-grade backfill was studied by ADINA finite element analysis code. Three kinds of filling schemes were designed and calculated, in which the filling heights were 2, 4, and 7 m, separately. The results show that there are some rules in the stress field with the increase of the filling height as follows: (1) the maximum value of tension stress of the roof decreases gradually, and stress conditions are improved gradually; (2) the tension stress status in the vertical pillar is transformed into the compressive stress status, and the carrying capacity is improved gradually; however, when the filling height is beyond 2.8 m, the carrying capacity of the vertical pillar grows very slowly, so, there is little significance to continue to fill the low-grade backfill; (3) the bottom pillar suffers the squeezing action from the vertical pillars at first and then the gravity action of the low-grade backfill, and the maximum value of tension stress of the bottom pillar firstly increases and then decreases. Considering the economic factor, security and other factors, the low-grade backfill has the most reasonable height (2.8 m) in the scope of all filling height.

Keywords: mining environment reconstructing structure - stress field - filling height - evolution law

Modeling the EPRI-Wisconsin Power and Light Broken Wire Tests

A.B. Peabody1 and G. McClure2

1 Construction Management Program, University of Alaska Anchorage, Anchorage, AK 99508 USA
2 Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, QC H3A 2K6, Canada

IEEE Transactions On Power Delivery, 25(3):1826-1833, 2010

Abstract: In the late 1970s, the Electric Power Research Institute and Wisconsin Power and Light performed a series of tests to measure the forces on a power transmission tower due to broken conductors. Three of those tests have been modeled using ADINA, a finite-element structural analysis program with the ability to perform nonlinear time history analyses of dynamic events. When a wire breaks, the time history of the force on the tower typically has two peaks. The first peaks were modeled accurately in time and magnitude. The second peaks were modeled accurately in time; however, the magnitudes were larger than those measured during the tests. The simulated time histories contained high frequencies due to the discretization of the real structure into the finite elements. Numerical filtering was used to remove these modeling artifacts.

Keywords: Conductors -  finite-element methods – modeling - power transmission lines -  power transmission mechanical factors - power transmission testing.

Performance based design of reinforced concrete beams under impact

S. Tachibana1, H. Masuya2, and S. Nakamura3

1 Hokukon Co., Ltd., Fukui, Japan
2 Faculty of Environmental Design, Institute of Science and Engineering, Kanazawa University, Kanazawa, Japan
3 Nihon Samicon Co., Ltd., Niigata, Japan

Nat. Hazards Earth Syst. Sci., 10, 1069–1078, 2010

Abstract: The purpose of this research is to collect fundamental data and to establish a performance-based design method for reinforced concrete beams under perpendicular
impact load. Series of low speed impact experiments using reinforced concrete beams were performed varying span length, cross section and main reinforcement. The experimental results are evaluated focusing on the impact load characteristics and the impact behaviours of reinforced concrete beams. Various characteristic values and their relationships are investigated such as the collision energy, the impact force duration, the energy absorbed by the beams and the beam response values. Also the bending performance of the reinforced concrete beams against perpendicular impact is evaluated. An equation is proposed to estimate the maximum displacement of the beam based on the collision energy and the static ultimate bending strength. The validity of the proposed equation is confirmed by comparison with experimental results
obtained by other researchers as well as numerical results obtained by FEM simulations. The proposed equation allows for a performance based design of the structure accounting for the actual deformation due to the expected impact action.

Design and FEM Modelling of Steel Truss Girder Joints

I. Radiæ, D. Markulak and M. Mikolin

Faculty of Civil Engineering, J.J. Strossmayer University of Osijek, Crkvena 21, HR - 31000 Osijek, Republic of Croatia

Strojarstvo, 52(2):125-135, 2010

Abstract: This paper critically presents the codified design of joints in steel truss girders, according to the latest european norms, as contemporary norms in which this issue is included and processed in detail for the first time. Rules in EN 1993-1-8, Eurocode 3: Design of steel structures – Part 1-8 are based on simplified analytical models in combination with experimental research, so the regulations consist of semi-empirical calculation formulae which are valid in limited conditions. Thus, in engineering practice it is required to take care of parameters which affect the global or local behaviour of truss girder such as secondary bending moments, bending moments resulting from eccentric member joints, and joint deformability, so this paper gives distinct attention to these effects. Typical truss girder behaviour modelling modes using finite element method (FEM) are illustrated so to predict their values, and take them in the final estimate if needed. The steel truss girder made of hollow rectangular sections with welded joints is reviewed in detail and numerically exemplified. The accuracies are compared and  recommendations are given for the application of each model.

Keywords: Finite element method - Joints - Rectangular hollow sections - Truss girder

Association between Biomechanical Structural Stresses of Atherosclerotic Carotid Plaques and Subsequent Ischaemic Cerebrovascular Events — A Longitudinal in Vivo Magnetic Resonance Imaging-based Finite element Study

U. Sadat1,2, Z. Teng1, V.E. Young1, S.R. Walsh2, Z.Y. Li1, M.J. Graves1, K. Varty2, J.H. Gillard1

1 University Department of Radiology, University of Cambridge, Cambridge, UK
2 Cambridge Vascular Unit, Cambridge University Hospitals NHS Foundation Trust, Cambridge, UK

Eur J Vasc Endovasc Surg, In press, 2010

Background: High-resolution magnetic resonance (MR) imaging has been used for MR imaging-based structural stress analysis of atherosclerotic plaques. The biomechanical stress profile of stable plaques has been observed to differ from that of unstable plaques; however, the role that structural stresses play in determining plaque vulnerability remains speculative.
Methods: A total of 61 patients with previous history of symptomatic carotid artery disease underwent carotid plaque MR imaging. Plaque components of the index artery such as fibrous tissue, lipid content and plaque haemorrhage (PH) were delineated and used for finite element analysis-based maximum structural stress (M-C Stress) quantification. These patients were followed up for 2 years. The clinical end point was occurrence of an ischaemic cerebrovascular event. The association of the time to the clinical end point with plaque morphology and M-C Stress was analysed.
Results: During a median follow-up duration of 514 days, 20% of patients (nZ12) experienced an ischaemic event in the territory of the index carotid artery. Cox regression analysis indicated that M-C Stress (hazard ratio (HR): 12.98 (95% confidence interval (CI): 1.32e26.67, pZ0.02), fibrous cap (FC) disruption (HR: 7.39 (95% CI: 1.61e33.82), p Z 0.009) and PH (HR: 5.85 (95% CI: 1.27e26.77), p Z 0.02) are associated with the development of subsequent cerebrovascular events. Plaques associated with future events had higher M-C Stress than those which had remained asymptomatic (median (interquartile range, IQR): 330 kPa (229e494) vs. 254 kPa (166e290), p Z0.04).
Conclusions: High biomechanical structural stresses, in addition to FC rupture and PH, are associated with subsequent cerebrovascular events.

Keywords: Biomechanical stress - Structural stress - Plaque - Atherosclerosis - Finite element analysis – Stroke

Research on visco-elastic-plastic creep model of artificially frozen soil under high confining pressures

D.-W. Li1,2,3, J.-H. Fan3, R.-H. Wang1,2,3

1 Engineering Research Center of Mining Underground Engineering, Ministry of Education, Huainan 232001, China
2 Key Laboratory of Mine Building in Universities of Anhui, Huainan 232001, China
3 College of Civil Engineering and Architecture; Anhui University of Science and Technology, Huainan 232001, China

Cold Regions Science and Technology, doi: 10.1016/j.coldregions.2010.08.006, 2010

Abstract: The triaxial creep experiment of artificially frozen soil in deep alluvium was performed by a self-developed machine of triaxial creep frozen soil. After analyzing the experiment results, applying parabolic yield criterion for improved viscoplasticity in the Nishihara model, a new creep constitutive model was established for describing frozen-soil's creep characteristics under high confining pressures. The secondary development tools and data interface had been used to add the visco-elastic-plastic creep constitutive model to standard ADINA FEM. Numerical simulation of the shaft well excavation process and field measurement displacements of frozen wall were performed in the mine; and the results showed that the visco-elastic-plastic creep constitutive model was suitable and reasonable. This constitutive model could be significance for the frozen soil structure long-term stability analysis and the displacement forecasting.

Key words: high confining pressures -  ADINA FEM -  parabolic yield criterion - visco-elasticplastic model - artificially frozen soil -  secondary development

An analytical study on the water penetration and diffusion into concrete under water pressure

J.-H. Yoo1, H.-S. Lee1, M.A. Ismail2

1 School of Architecture & Architectural Engineering, Hanyang University, Ansan 425-791, Republic of Korea
2 Faculty of Civil Engineering, Universiti Teknologi Malaysia, Skudai 81310, Malaysia

Construction and Building Materials, In press, 2010

Abstract: Because concrete is a type of porous material, water or air can permeate freely into the concrete and that decreases the durability of concrete. Therefore, it is possible to permeate some corrosion inhibitors from the surface of concrete to inside the concrete due to its porosity even the steel-frame location by applying water pressure. The objective of this study is to investigate the depth of the water penetration in concrete forced under pressure. For achieving this purpose, the experiments for the depth of penetration were executed through selecting related factors and levels, such as water pressure and water pressurizing time. The water flow in concrete was examined theoretically and experimentally. As a result, in the case of the low water pressure approximately at 0.15 MPa or less, it was found that the flow showed a Darcy seepage flow and the same flow as an ordinary sand stratum. However, in the case of the high water pressure, the flow was diffused as a seepage flow that is accompanied by an internal deformation of concrete. This study attempts to develop a method that penetrates corrosion inhibitors to the location of steel bars and investigate the penetration depth of corrosion inhibitors by verifying water penetration in concrete under applied pressure.

Keywords: Darcy’s law -  Coefficient of diffusion - Water penetration of concrete - FEM analysis

Vibration Response of Elastic Disks in Surrounding Fluid: Viscous Versus Acoustic Effects

A. Jana, A. Raman

School of Mechanical Engineering, and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907-2088

Journal of Vibration and Acoustics, Vol. 132 / 061001-1:8, 2010

Abstract: The vibrations of thin, elastic, circular disks such as musical cymbals, hard disk drives, and microscale resonators are significantly influenced by the presence of a surrounding fluid. The energy of disk vibrations is known to dissipate into viscous losses and to radiate away as sound. However, the relative importance of these mechanisms is not well understood. In this paper, we present three-dimensional computations of the fluidic impedance of thin, elastic disks vibrating with small amplitudes under ambient conditions. These computations encompass both macroscale and microscale disks, a wide range of operating frequencies, and different fluidic environments. Viscous fluidic impedances are computed using a finite element model, whereas acoustic fluidic impedances are computed using a boundary element method. For a disk with a given clamping ratio vibrating in a specific mode, the nondimensional viscous impedance depends on the unsteady Reynolds number, while the nondimensional acoustic impedance depends on the ratio of structural to acoustic wavelengths. It is shown that viscous losses dominate the fluid damping of disks in data storage and circular saw applications and of conventional disk microresonators. However, for ultrahigh frequency resonators, acoustic radiation must be taken into account to correctly estimate the overall fluid damping. The computed fluidic impedances are expected to be an important aid in the design of a wide range of disk resonators up to the megahertz regime.

Sensitivity of CFD Based Hemodynamic Results in Rabbit Aneurysm Models to Idealizations in Surrounding Vasculature

Z. Zeng1, D.F. Kallmes2, M.J. Durka3, Y. Ding4, D. Lewis4, R. Kadirvel4, A.M. Robertson5

1 Department of Mechanical Engineering and Materials Science, University of Pittsburgh, 3700 O’Hara Street, Pittsburgh, PA 15261
2 Department of Radiology, Mayo Clinic College of Medicine, 200 First Street Southwest, Rochester, MN 55905
3 Department of Mechanical Engineering and Materials Science, University of Pittsburgh, 3700 O’Hara Street, Pittsburgh, PA 15261
4 Department of Radiology, Mayo Clinic College of Medicine, 200 First Street Southwest, Rochester, MN 55905
5 Department of Mechanical Engineering and Materials Science and Center for Vascular Remodeling and Regeneration (CVRR), University of Pittsburgh, Pittsburgh, PA 15261

Journal of Biomechanical Engineering, 132:091009-1, 2010

Abstract: Computational fluid dynamics (CFD) studies provide a valuable tool for evaluating the role of hemodynamics in vascular diseases such as cerebral aneurysms and atherosclerosis. However, such models necessarily only include isolated segments of the vasculature. In this work, we evaluate the influence of geometric approximations in vascular anatomy on hemodynamics in elastase induced saccular aneurysms in rabbits. One representative high aspect ratio (AR — height/neck width) aneurysm and one low AR aneurysm were created at the origin of the right common carotid artery in two New Zealand white rabbits. Three-dimensional (3D) reconstructions of the aneurysm and surrounding arteries were created using 3D rotational angiographic data. Five models with varying extents of neighboring vasculature were created for both the high and low AR cases. A reference model included the aneurysm sac, left common carotid artery (LCCA), aortic arch, and downstream trifurcation/quadrification. Three-dimensional, pulsatile CFD studies were performed and streamlines, wall shear stress (WSS), oscillatory shear index, and cross sectional velocity were compared between the models. The influence of the vascular domain on intra-aneurysmal hemodynamics varied between the low and high AR cases. For the high AR case, even a simple model including only the aneurysm, a small section of neighboring vasculature, and simple extensions captured the main features of the steamline and WSS distribution predicted by the reference model. However, the WSS distribution in the low AR case was more strongly influenced by the extent of vasculature. In particular, it was necessary to include the downstream quadrification and upstream LCCA to obtain good predictions of WSS. The findings in this work demonstrate the accuracy of CFD results can be compromised if insufficient neighboring vessels are included in studies of hemodynamics in elastase induced rabbit aneurysms. Consideration of aspect ratio, hemodynamic parameters of interest, and acceptable magnitude of error when selecting the vascular domain will increase reliability of the results while decreasing computational time.

Keywords: aneurysms - animal models - parent vasculature – hemodynamics – CFD - wall shear stress


(latest on Page 43)
Page 43 Page 42 Page 41 Page 40 Page 39 Page 38 Page 37 Page 36 Page 35 Page 34
Page 33 Page 32 Page 31 Page 30 Page 29 Page 28 Page 27 Page 26 Page 25 Page 24
Page 23 Page 22 Page 21 Page 20 Page 19 Page 18 Page 17 Page 16 Page 15 Page 14
Page 13 Page 12 Page 11 Page 10 Page 9  Page 8  Page 7  Page 6  Page 5  Page 4 
Page 3  Page 2  Page 1 

Page 37

ADINA logo