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Rational Choice versus Cognitive Dissonance Essay -- Terrorism, Suici
Discerning Choice versus Cognitive Dissonance Presentation Discerning decision hypothesis can adequately clarify fear based oppression...
Thursday, October 31, 2019
Human Resource Essay Example | Topics and Well Written Essays - 2500 words - 1
Human Resource - Essay Example Essentially, it points directly to the contributions of the employees with regards to the underlying bottom line of the company by delineating employees as an invaluable resource. In order to fully understand this notion, it is necessary for us to operationally define human resource management. Simms (2002) offers one of the most clear and concise definition of human resource management when he indicated that human resources management was: the term increasingly used to refer to the philosophy, policies, procedures, and practices related to the management of an organizationââ¬â¢s employees. Human resources management is particularly concerned with all the activities that contribute to successfully attracting, developing, motivating, and maintaining a high-performing workforce that results in organizational success (Sims 2002). One of the primary functions of human resource management is to improve knowledge, skills and attitudes that enable employees to perform current and future jobs in order to help organizations achieve success. (Rothwell & Kazanas 1994). In fact Philip and Shaw (1998) stated that an integral part of human resource management needs to be that of training the employees and equipping them to deal with the rapid change in technology. This is tied into many other human resource functions such as recruitment, retention, creation of new positions, work systems and performance management systems. These systems would need to be aligned with the organizations missions and goals. Alignment would ensure that the training offered is what is required to achieve the mission and goals of the organization. Training is a very broad term that has many definitions and uses in the literature. Training is the process of getting the right knowledge, skills and abilities at the right time, in the correct way and in the correct priority order to an employee. The training process is aimed at preparing individuals to perform current and future jobs (DeSimone &
Tuesday, October 29, 2019
Quantitative Methods for Business Report Outline
Quantitative Methods for Business Report - Outline Example Therefore, it is the quality of the employees, rather than their quantity, that affects how the business will perform. To establish which factors is likely to affect business profitability more, between the number of employees and the employeesââ¬â¢ turnover in a business, a sample of 30 banking institutions was studied. The reason for selecting banking institutions is the fact that; banking institutions mainly deal with offering financial services to the customers (Gitman & McDaniel, 2009 p188). Additionally, banking institutions operates under a competitive industry, where poaching of employees by other banks, microfinance institutions or insurance companies is highly experienced. The banking sector also entails the offer of services, where the employees of the banks interact directly with the customers, a necessary factor in this study, since the level of customer satisfaction influences their confidence and loyalty to the business, and the consequent performance and profitability of the business (Aamodt, 2010 p395). Thus, the selection of banking institutions as the samples for this study pro vided the most plausible means of assessing how the employee turnover and the number of employees affect the profitability of the businesses. The analysis was undertaken by approaching the 30 different banking institutions, and requesting them for the data regarding the number of employees within the period 2005 to 2010. Additionally, the information regarding the number of employees who have been recruited by the institutions and the ones who have left the institutions, for other reasons other than retirement was collected. The information regarding the profitability of the businesses during this period was also collected. The study also entailed the collection of information regarding the training programs of the banking institutions, and the amount of resources they have been committing towards the training of any single employee. This
Sunday, October 27, 2019
Analysing Dasein According To Heidegger Philosophy Essay
Analysing Dasein According To Heidegger Philosophy Essay Martin Heidegger was a student of Husserl and even dedicated his book Being and Time to him. However, he ended up going against a lot of Husserls ideas. Where Husserls phenomenology is a phenomenology of description of objects and how they present themselves to us, Heideggers is a phenomenology of understanding and interpretation. As he says in Being and Time (1973: 25), Heideggers phenomenology is not pure, again going against his teacher, as Husserl strove for a pure phenomenological attitude he incorporates existential ontology into his phenomenology, which means being historically situated in the world. Husserl wilfully chose to leave history unexamined because of the implications it would have had on his science historical context would have made it impure. Heideggers phenomenology is almost hermeneutical (understanding and interpreting our historically lived situation through texts), so much so he applies this hermeneutical approach to human beings. Heidegger wants to move away from subject (that which remains unchanging) and consciousness and look at Being and his concept of Dasein. This essay will examine Heideggers concept of Dasein as a movement away from Husserls concept of consciousness of objects and subjectivity. It will begin by explaining what Dasein is and is not. Looking at it as ontologically situated in the world as having an understanding of the meaning of Being. It will then move on to looking at Dasein as the entity of all entities and seeking for the meaning of Being. This will lead onto the concept of the they-self and everydayness and how Dasein is situated in these which will inevitably move onto anxiety as a means of getting from the they to the my. This will link into the authentic and inauthentic self authentic being one-self and inauthentic being the they-self. Dasein literally means Being-there (Polt, 1999:29). It is not consciousness and it is not a person. It is not simply existence or a thing in the world. It is a verb to exist. Dasein is no-thing. It is the essential structure of a human being the way of Being of a human being. It is not static in the world, but active towards the world (towards the world coming back to Husserls idea of objects giving themselves towards the world). Dasein exists understandingly having the understanding of the meaning of Being ontologically always historically mediated. Dasein is ontological insofar as it understands the meaning of Being it only has an opaque and vague understanding of Being but it has some. (Heidegger, 1973: 31). Dasein is the condition of possibility of the world so it can be considered transcendental. However, at its simplest Dasein is just Being in the world. Heidegger refers to Beings as entities entities are anything that has existence (Polt, 1999: 2). He mentions that ). Entities are ontical they are out there in the world. Dasein is the entity that is distinct from all other entities in that it is out there and it exists towards the world. It is the entity of all entities. As Heidegger says in Being and Time (1973: 32), Entities present themselves towards the world simply as they are in their being. Heidegger is interested in the meaning of Being. Things are but Being is nowhere you cannot point to Being or Dasein like you can point to an object. Dasein is no-thing. We need to witness the no-thing of our Being we need to look for the meaning of our Being or at least have an understanding of it. Human existence Dasein is being interrogated. The Being of our being is been asked about. To get to the meaning of Being, we must first go through the human being and the Dasein. To do this, Heidegger talks about seeking (ibid: 24). When we look for something we must have an idea of what we are looking for we cannot look for something we have no experience of. Dasein is primordially temporal in three ways 1. Existence: Daseins potentiality for Being projects Being on various possibilities. 2. Thrownness: Represents Daseins structure phenomenon of the past that represents past as having been historically. It could be argued that we are forced to be who we are because of our past we 3. Falleness: Being alongside Daseins place among other Daseins made possible by those present and being in the world. It is the result of being thrown into the world from the past (ibid: 76). As Polt (1999:76) says, . The human needs to be taken away from this simple subjectivity and looked at in the broader sense I am as they. This is where the concept of Das-Man or the they-self comes into play. Dasein has an aspect to itself as a they-self. The opinions that are out there. What other people tell us about ourselves determines us. In the they-self, the Dasein is comfortable; it seeks refuge in the they-self. There is a tranquilising familiarity of the they -self. In the they-self we feel at home but philosophy is not about feeling at home. We are on the run from our meaning of Being we are on the run from ourselves. The they-self defines who we are so we can never really get out of it fully. The they-self is everydayness. Dasein has to retrieve itself from the Das-Man in order to truly be itself. To do this, Heidegger says we must undergo anxiety. Heidegger asks how do we get form the they to the my? Husserl suspends the empirical or natural attitude for the phenomenological. It is a wilful suspension. For Heidegger, suspension is affective and comes in the form of anxiety. He also wants to suspend the natural attitude for the phenomenological, but for him, he calls the natural attitude, the everyday. I am affected by anxiety. When I am anxious Im brought back to my proper Dasein. Anxiety is how we get from the they to the my. Heidegger says that we should let anxiety overcome us in order to get back to my-self or one-self. However, one-self is a task for Dasein, as Dasein is an entity concerned by its own being and is comforted by the they-self. We are anxious about our being in the world our Being is determined by the fact that sometime we will not be in the world. My Being towards death is an indeterminable determinacy there is something indeterminate about death, but it determines me. In this anxiousness we emancipate ou rselves from the they-self. Letting anxiety overwhelm us, is the only way to get to our authentic self. Heidegger says that we are merely actors in our daily lives and that we have to get back to who we really are. This is where authenticity and inauthenticity comes into practice. Dasein encompasses both the authentic and inauthentic. There is a Dasein of the they and a Dasein of the my. Authenticity is who I am it can be argued that we are trying to get back to our authentic selves. For the most part we are inauthentic and improper we live through the they-self in everydayness. In the they-self the authentic self is dormant. However, we can never fully leave one or get into the other. Heidegger (in Keane, N., 1927: 65) says, Silence, according to Heidegger is how we get back to our-self our authentic self. Not saying anything at all, says more than idle-talk. As he says in Being and Time (1973: 213), Being as Dasein is Being toward the world. Being toward the world means concern. ). Heidegger says in Being and Time (1973: 237), that at its most basic level, Being-in-the-world is care. As such, Dasein is fundamentally care. Dasein is always out ahead of itself it is born into a world that already has meaning. Caring implies things that matter to us so we do care about our Being (Polt, 1999: 79). Dasein is human existence. It is the way of Being for human beings. At its most basic it is Being-in-the-world humans existence in the world. It is the entity of all entities so it can be argued that it is the way of Being over all other ways of Being of human beings. Dasein lives through the world in the everyday sense of the they-self. We are what other people perceive us to be. We can only truly be our authentic self by undergoing anxiety and letting it overwhelm us. Dasein can be understood as the essence of human existence having lived through its historically lived situation. It is a part of a fundamental ontology. Dasein is active towards the world as having a history by living through the world. It has to try find (seeking) its authentic self or owness through anxiety. Dasein is basically Being-there Being-in-the-world.
Friday, October 25, 2019
The Waterfall :: Place Essay, Description Essaay
Visiting a waterfall, especially on a hot sultry day, can be a favorite way to spend a day. You get in your car, drive for miles, then get out and walk the remainder of the way to a waterfall. Civilization has cleared and marked a pathway for you and the many thousands like you who have come to enjoy these named landmarks. Rarely do you get to enjoy the natural beauty of one by just stepping out into your own backyard. Behind my house, barely noticeable, is a trail leading through the woods to a waterfall. The trail is narrow but well worn. Any shrubbery that would have grown has been trampled down and all that is left is a very narrow path, overhung with branches from the trees that mark its sides. As I start down the trail, I begin to feel the trees closing around me until the house can no longer be seen. I follow the trail to where it stops at the creek's edge, approaching quietly so as not to disturb any of the wild creatures that has come to enjoy the cool fresh water. I gently cross over the creek using the stones, which show the wear of several previous crossing, so that I can have full view of the creek and the beauty it possesses. I can hear the rush of the water long before I see the falls. As I sit down on the big gray slate rock that has been warmed by the early morning sun, I begin to gulp in the beauty as a starving man would gulp down food. I start my usual ritual of examining the banks of the creek by gazing down the right side of it first. I notice that the wild azaleas are in full bloom and that the trees have regained all their leaves. They stand tall and majestic as if they are soldiers standing guard. My gaze travels up one of the trees to find two squirrels chattering down at me as if to say "Go away and leave us in peace." Further down starts the gentle bend that takes the remainder of the creek from my view. My gaze shifts to the left side of the bank and there lies an old oak tree that has fallen long ago. It still lies partially upon its stump so that it looks like the shape of an "L".
Thursday, October 24, 2019
Ansys Tutorial Release 12.1
à ® ANSYS Tutorial Release 12. 1 Structural & Thermal Analysis Using the ANSYS Release 12. 1 Environment Kent L. Lawrence Mechanical and Aerospace Engineering University of Texas at Arlington SDC PUBLICATIONS www. SDCpublications. com Schroff Development Corporation Visit the following websites to learn more about this book: ANSYS Tutorial 2-1 Lesson 2 Plane Stress Plane Strain 2-1 OVERVIEW Plane stress and plane strain problems are an important subclass of general threedimensional problems. The tutorials in this lesson demonstrate: à ¦Solving planar stress concentration problems. Evaluating potential inaccuracies in the solutions. à ¦Using the various ANSYS 2D element formulations. 2-2 INTRODUCTION It is possible for an object such as the one on the cover of this book to have six components of stress when subjected to arbitrary three-dimensional loadings. When referenced to a Cartesian coordinate system these components of stress are: Normal Stresses ?x, ? y, ? z Shear Stresses ? xy, ? yz, ? zx Figure 2-1 Stresses in 3 dimensions. In general, the analysis of such objects requires three-dimensional modeling as discussed in Lesson 4.However, two-dimensional models are often easier to develop, easier to solve and can be employed in many situations if they can accurately represent the behavior of the object under loading. 2-2 ANSYS Tutorial A state of Plane Stress exists in a thin object loaded in the plane of its largest dimensions. Let the X-Y plane be the plane of analysis. The non-zero stresses ? x, ? y, and ? xy lie in the X ââ¬â Y plane and do not vary in the Z direction. Further, the other stresses (? z,? yz , and ? zx ) are all zero for this kind of geometry and loading.A thin beam loaded in its plane and a spur gear tooth are good examples of plane stress problems. ANSYS provides a 6-node planar triangular element along with 4-node and 8-node quadrilateral elements for use in the development of plane stress models. We will use both triangles and qua ds in solution of the example problems that follow. 2-3 PLATE WITH CENTRAL HOLE To start off, letââ¬â¢s solve a problem with a known solution so that we can check our computed results as well as our understanding of the FEM process. The problem is that of a tensile-loaded thin plate with a central hole as shown in Figure 2-2.Figure 2-2 Plate with central hole. The 1. 0 m x 0. 4 m plate has a thickness of 0. 01 m, and a central hole 0. 2 m in diameter. It is made of steel with material properties; elastic modulus, E = 2. 07 x 1011 N/m2 and Poissonââ¬â¢s ratio, ? = 0. 29. We apply a horizontal tensile loading in the form of a pressure p = -1. 0 N/m2 along the vertical edges of the plate. Because holes are necessary for fasteners such as bolts, rivets, etc, the need to know stresses and deformations near them occurs very often and has received a great deal of study.The results of these studies are widely published, and we can look up the stress concentration factor for the case s hown above. Before the advent of suitable computation methods, the effect of most complex stress concentration geometries had to be evaluated experimentally, and many available charts were developed from experimental results. The uniform, homogeneous plate above is symmetric about horizontal axes in both geometry and loading. This means that the state of stress and deformation below a Plane Stress / Plane Strain 2-3 orizontal centerline is a mirror image of that above the centerline, and likewise for a vertical centerline. We can take advantage of the symmetry and, by applying the correct boundary conditions, use only a quarter of the plate for the finite element model. For small problems using symmetry may not be too important; for large problems it can save modeling and solution efforts by eliminating one-half or a quarter or more of the work. Place the origin of X-Y coordinates at the center of the hole. If we pull on both ends of the plate, points on the centerlines will move al ong the centerlines but not perpendicular to them.This indicates the appropriate displacement conditions to use as shown below. Figure 2-3 Quadrant used for analysis. In Tutorial 2A we will use ANSYS to determine the maximum horizontal stress in the plate and compare the computed results with the maximum value that can be calculated using tabulated values for stress concentration factors. Interactive commands will be used to formulate and solve the problem. 2-4 TUTORIAL 2A ââ¬â PLATE Objective: Find the maximum axial stress in the plate with a central hole and compare your result with a computation using published stress concentration factor data.PREPROCESSING 1. Start ANSYS, select the Working Directory where you will store the files associated with this problem. Also set the Jobname to Tutorial2A or something memorable and provide a Title. (If you want to make changes in the Jobname, working Directory, or Title after youââ¬â¢ve started ANSYS, use File > Change Jobname or Di rectory or Title. ) Select the six node triangular element to use for the solution of this problem. 2-4 ANSYS Tutorial Figure 2-4 Six-node triangle. The six-node triangle is a sub-element of the eight-node quadrilateral. 2.Main Menu > Preprocessor > Element Type > Add/Edit/Delete > Add > Structural Solid > Quad 8node 183 > OK Figure 2-5 Element selection. Select the triangle option and the option to define the plate thickness, otherwise a unit thickness is used. 3. Options (Element shape K1) > Triangle, Options (Element behavior K3) > Plane strs w/thk > OK > Close Plane Stress / Plane Strain 2-5 Figure 2-6 Element options. 4. Main Menu > Preprocessor > Real Constants > Add/Edit/Delete > Add > OK Figure 2-7 Real constants. Enter the plate thickness of 0. 01 m. ) >Enter 0. 01 > OK > Close Figure 2-8 Enter the plate thickness. 2-6 ANSYS Tutorial Enter the material properties. 5. Main Menu > Preprocessor > Material Props > Material Models Material Model Number 1, click Structural > Line ar > Elastic > Isotropic Enter EX = 2. 07E11 and PRXY = 0. 29 > OK (Close the Define Material Model Behavior window. ) Create the geometry for the upper right quadrant of the plate by subtracting a 0. 2 m diameter circle from a 0. 5 x 0. 2 m rectangle. Generate the rectangle first. . Main Menu > Preprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners Enter (lower left corner) WP X = 0. 0, WP Y = 0. 0 and Width = 0. 5, Height = 0. 2 > OK 7. Main Menu > Preprocessor > Modeling > Create > Areas > Circle > Solid Circle Enter WP X = 0. 0, WP Y = 0. 0 and Radius = 0. 1 > OK Figure 2-9 Create areas. Plane Stress / Plane Strain 2-7 Figure 2-10 Rectangle and circle. Now subtract the circle from the rectangle. (Read the messages in the window at the bottom of the screen as necessary. ) 8.Main Menu > Preprocessor > Modeling > Operate > Booleans > Subtract > Areas > Pick the rectangle > OK, then pick the circle > OK (Use Raise Hidden and Reset Picking as necessary. ) Figure 2-11 Geo metry for quadrant of plate. Create a mesh of triangular elements over the quadrant area. 9. Main Menu > Preprocessor > Meshing > Mesh > Areas > Free Pick the quadrant > OK Figure 2-12 Triangular element mesh. Apply the displacement boundary conditions and loads to the geometry (lines) instead of the nodes as we did in the previous lesson.These conditions will be applied to the FEM model when the solution is performed. 10. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the left edge of the quadrant > OK > UX = 0. > OK 2-8 ANSYS Tutorial 11. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the bottom edge of the quadrant > OK > UY = 0. > OK Apply the loading. 12. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Pressure > On Lines.Pick the right edge of the quadrant > OK > Pressure = -1. 0 > OK (A positive pressure would be a compressive load, so we use a nega tive pressure. The pressure is shown by the two arrows. ) Figure 2-13 Model with loading and displacement boundary conditions. The model-building step is now complete, and we can proceed to the solution. First, to be safe, save the model. 13. Utility Menu > File > Save as Jobname. db (Or Save as â⬠¦. ; use a new name) SOLUTION The interactive solution proceeds as illustrated in the tutorials of Lesson 1. 14. Main Menu > Solution > Solve > Current LS > OKThe /STATUS Command window displays the problem parameters and the Solve Current Load Step window is shown. Check the solution options in the /STATUS window and if all is OK, select File > Close In the Solve Current Load Step window, select OK, and when the solution is complete, Close the ââ¬ËSolution is Done! ââ¬â¢ window. POSTPROCESSING We can now plot the results of this analysis and also list the computed values. First examine the deformed shape. 15. Main Menu > General Postproc > Plot Results > Deformed Shape > Def. + Undef. > OK Plane Stress / Plane Strain 2-9 Figure 2-14 Plot of Deformed shape.The deformed shape looks correct. (The undeformed shape is indicated by the dashed lines. ) The right end moves to the right in response to the tensile load in the X direction, the circular hole ovals out, and the top moves down because of Poissonââ¬â¢s effect. Note that the element edges on the circular arc are represented by straight lines. This is an artifact of the plotting routine not the analysis. The six-node triangle has curved sides, and if you pick on a mid-side of one these elements, you will see that a node is placed on the curved edge. The maximum displacement is shown on the graph legend as 0. 2e-11 which seems reasonable. The units of displacement are meters because we employed meters and N/m2 in the problem formulation. Now plot the stress in the X direction. 16. Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Stress > X-Component of stress > OK Use PlotCtrls > Symbols [/PSF] Surface Load Symbols (set to Pressures) and Show pre and convect as (set to Arrows) to display the pressure loads. Figure 2-15 Surface load symbols. Also select Display All Applied BCs 2-10 ANSYS Tutorial Figure 2-16 Element SX stresses.The minimum, SMN, and maximum, SMX, stresses as well as the color bar legend give an overall evaluation of the ? x (SX) stress state. We are interested in the maximum stress at the hole. Use the Zoom to focus on the area with highest stress. (Your meshes and results may differ a bit from those shown here. ) Figure 2-17 SX stress detail. Plane Stress / Plane Strain 2-11 Stress variations in the actual isotropic, homogeneous plate should be smooth and continuous across elements. The discontinuities in the SX stress contours above indicate that the number of elements used in this model is oo few to calculate with complete accuracy the stress values near the hole because of the stress gradients there. We will not accept this stress solu tion. More six-node elements are needed in the region near the hole to find accurate values of the stress. On the other hand, in the right half of the model, away from the stress riser, the calculated stress contours are smooth, and SX would seem to be accurately determined there. It is important to note that in the plotting we selected Element Solu (Element Solution) in order to look for stress contour discontinuities.If you pick Nodal Solu to plot instead, for problems like the one in this tutorial, the stress values will be averaged before plotting, and any contour discontinuities (and thus errors) will be hidden. If you plot nodal solution stresses you will always see smooth contours. A word about element accuracy: The FEM implementation of the truss element is taken directly from solid mechanics studies, and there is no approximation in the solutions for node-loaded truss structures formulated and solved in the ways discussed in Lesson 1.The continuum elements such as the ones for plane stress and plane strain, on the other hand, are normally developed using displacement functions of a polynomial type to represent the displacements within the element, and the higher the polynomial, the greater the accuracy. The ANSYS six-node triangle uses a quadratic polynomial and is capable of representing linear stress and strain variations within an element. Near stress concentrations the stress gradients vary quite sharply. To capture this variation, the number of elements near the stress concentrations must be increased proportionately.To obtain more elements in the model, return to the Preprocessor and refine the mesh, first remove the pressure. All elements are subdivided and the mesh below is created 17. Main Menu > Preprocessor > Loads > Define Loads > Delete > Structural > Pressure > On Lines. Pick the right edge of the quadrant. Main Menu > Preprocessor > Meshing > Modify Mesh > Refine At > All (Select Level of refinement 1. ) Figure 2-18 Global mesh refineme nt. 2-12 ANSYS Tutorial We will also refine the mesh selectively near the hole. 18.Main Menu > Preprocessor > Meshing > Modify Mesh > Refine At > Nodes. (Select the three nodes shown. ) > OK (Select the Level of refinement = 1) > OK Figure 2-19 Selective refinement at nodes. (Note: Alternatively you can use Preprocessor > Meshing > Clear > Areas to remove all elements and build a completely new mesh. Plot > Areas afterwards to view the area again. Note also that too much local refinement can create a mesh with too rapid a transition between fine and coarse mesh regions. ) Reapply the pressure loading, repeat the solution, and replot the stress SX. 9. Main Menu > Solution > Solve > Current LS > OK Save your work. 20. File > Save as Jobname. db Plot the stresses in the X direction. 21. Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Stress > X-Component of stress > OK Plane Stress / Plane Strain 2-13 Figure 2-20 SX stress contour after mesh refinement. Figu re 2-21 SX stress detail contour after mesh refinement. The element solution stress contours are now smooth across element boundaries, and the stress legend shows a maximum value of 4. 386 Pa, a 4. percent change in the SX stress computed using the previous mesh. To check this result, find the stress concentration factor for this problem in a text or reference book or from a suitable web site. For the geometry of this example we find Kt = 2. 17. We can compute the maximum stress using (Kt)(load)/(net cross sectional area). Using the pressure p = 1. 0 Pa we obtain. ? x MAX = 2. 17 * p * (0. 4)(0. 01) /[(0. 4 ? 0. 2) * 0. 01] = 4. 34 Pa 2-14 ANSYS Tutorial The computed maximum value is 4. 39 Pa which is around one percent in error, assuming that the value of Kt is exact. -5 THE APPROXIMATE NATURE OF FEM As mentioned above, the stiffness matrix for the truss elements of Lesson 1 can be developed directly and simply from elementary solid mechanics principles. For continuum problems in t wo and three-dimensional stress, this is generally no longer possible, and the element stiffness matrices are usually developed by assuming something specific about the characteristics of the displacements that can occur within an element. Ordinarily this is done by specifying the highest degree of the polynomial that governs the displacement distribution within an element.For h-method elements, the polynomial degree depends upon the number of nodes used to describe the element, and the interpolation functions that relate displacements within the element to the displacements at the nodes are called shape functions. In ANSYS, 2-dimensional problems can be modeled with six-node triangles, four-node quadrilaterals or eight-node quadrilaterals. Figure 2-22 Triangular and quadrilateral elements. The greater the number of nodes, the higher the order of the polynomial and the greater the accuracy in describing displacements, stresses and strains within the element. If the stress is constan t throughout a region, a very imple model is sufficient to describe the stress state, perhaps only one or two elements. If there are gradients in the stress distributions within a region, high-degree displacement polynomials and/or many elements are required to accurately analyze the situation. These comments explain the variation in the accuracy of the results as different numbers of elements were used to solve the problem in the previous tutorial and why the engineer must carefully prepare a model, start with small models, grow the models as understanding of the problem develops and carefully interpret the calculated results.The ease with which models can be prepared and solved sometimes leads to careless evaluation of the computed results. Plane Stress / Plane Strain 2-15 2-6 ANSYS FILES The files created during the solution were saved in step 20 of Tutorial 2A. Look in the working directory and you see Tutorial2A files with extensions BCS, db, dbb, esav, full, mntr, rst, and sta t. However, the Tutorial 2A problem can be reloaded using only Tutorial2A. db, so if you want to save disk space, you can delete the others. 2-7 ANSYS GEOMETRY The finite element model consists of elements and nodes and is separate from the geometry on which it may be based.It is possible to build the finite element model without consideration of any underlying geometry as was done in the truss examples of Lesson 1, but in many cases, development of the geometry is the first task. Two-dimensional geometry in ANSYS is built from keypoints, lines (straight, arcs, splines), and areas. These geometric items are assigned numbers and can be listed, numbered, manipulated, and plotted. The keypoints (2,3,4,5,6), lines (2,3,5,9,10), and area (3) for Tutorial 2A are shown below. (Your numbering may differ. ) Figure 2-23 Keypoints, lines and areas.The finite element model developed previously for this part used the area A3 for development of the node/element FEM mesh. The loads, displacement b oundary conditions and pressures were applied to the geometry lines. When the solution step was executed, the loads were transferred from the lines to the FEM model nodes. Applying boundary conditions and loads to the geometry facilitates remeshing the problem. The geometry does not change, only the number and location of nodes and elements, and at solution time, the loads are transferred to the new mesh.Geometry can be created in ANSYS interactively (as was done in the previous tutorial) or it can be created by reading a text file. For example, the geometry of Tutorial 2A can be generated with the following text file using the File > Read Input from command sequence. (The keypoint, line, etc. numbers will be different from those shown above. ) 2-16 ANSYS Tutorial /FILNAM,Geom /title, Stress Concentration Geometry ! Example of creating geometry using keypoints, lines, arcs /prep7 ! Create geometry k, 1, 0. 0, 0. 0 ! Keypoint 1 is at 0. 0, 0. 0 k, 2, 0. 1, 0. 0 , 3, 0. 5, 0. 0 k, 4, 0. 5, 0. 2 k, 5, 0. 0, 0. 2 k, 6, 0. 0, 0. 1 L, L, L, L, 2, 3, 4, 5, 3 4 5 6 ! Line from keypoints 2 to 3 ! arc from keypoint 2 to 6, center kp 1, radius 0. 1 LARC, 2, 6, 1, 0. 1 AL, 1, 2, 3, 4, 5 ! Area defined by lines 1,2,3,4,5 Geometry for FEM analysis also can be created with solid modeling CAD or other software and imported into ANSYS. The IGES (Initial Graphics Exchange Specification) neutral file is a common format used to exchange geometry between computer programs. Tutorial 2B demonstrates this option for ANSYS geometry development. -8 TUTORIAL 2B ââ¬â SEATBELT COMPONENT Objective: Determine the stresses and deformation of the prototype seatbelt component shown in the figure below if it is subjected to tensile load of 1000 lbf. Figure 2-24 Seatbelt component. The seatbelt component is made of steel, has an over all length of about 2. 5 inches and is 3/32 = 0. 09375 inches thick. A solid model of the part was developed in a CAD system and exported as an IGES file. The f ile is imported into ANSYS for analysis. For simplicity we will analyze only the right, or ââ¬Ëtongueââ¬â¢ portion of the part in this tutorial.Plane Stress / Plane Strain 2-17 Figure 2-25 Seatbelt ââ¬Ëtongueââ¬â¢. PREPROCESSING 1. Start ANSYS, Run Interactive, set jobname, and working directory. Create the top half of the geometry above. The latch retention slot is 0. 375 x 0. 8125 inches and is located 0. 375 inch from the right edge. If you are not using an IGES file to define the geometry for this exercise, you can create the geometry directly in ANSYS with key points, lines, and arcs by selecting File > Read Input from to read in the text file given below and by skipping the IGES import steps 2, 3, 4, and 10 below. FILNAM,Seatbelt /title, Seatbelt Geometry ! Example of creating geometry using keypoints, lines, arcs /prep7 ! Create geometry k, 1, 0. 0, 0. 0 ! Keypoint 1 is at 0. 0, 0. 0 k, 2, 0. 75, 0. 0 k, 3, 1. 125, 0. 0 k, 4, 1. 5, 0. 0 k, 5, 1. 5, 0. 5 k, 6, 1. 2 5, 0. 75 k, 7, 0. 0, 0. 75 k, 8, 1. 125, 0. 375 k, 9, 1. 09375, 0. 40625 k, 10, 0. 8125, 0. 40625 k, 11, 0. 75, 0. 34375 k, 12, 1. 25, 0. 5 k, 13, 1. 09375, 0. 375 k, 14, 0. 8125, 0. 34375 2-18 L, L, L, L, L, L, L, L, ANSYS Tutorial 1, 2 3, 4 4, 5 6, 7 7, 1 3, 8 9, 10 11, 2 ! arc LARC, LARC, LARC, Line from keypoints 1 to 2 from keypoint 5 to 6, center kp 12, radius 0. 25, etc. 5,6, 12, 0. 25 8, 9, 13, 0. 03125 10, 11, 14, 0. 0625 AL,all ! Use all lines to create the area. 2. Alternatively, use a solid modeler to create the top half of the component shown above in the X-Y plane and export an IGES file of the part. To import the IGES file 3. Utility Menu > File > Import > IGES Select the IGES file you created earlier. Accept the ANSYS import default settings. If you have trouble with the import, select the alternate options and try again.Defeaturing is an automatic process to remove inconsistencies that may exist in the IGES file, for example lines that, because of the modeling or th e file translation process, do not quite join to digital precision accuracy. Figure 2-26 IGES import. Turn the IGES solid model around if necessary so you can easily select the X-Y plane. Plane Stress / Plane Strain 2-19 4. Utility Menu > PlotCtrls > Pan, Zoom, Rotate > Back, or use the side-bar icon. Figure 2-27 Seatbelt solid, front and back. 5.Main Menu > Preprocessor > Element Type > Add/Edit/Delete > Add > Solid > Quad 8node 183 > OK (Use the 8-node quadrilateral element for this problem. ) 6. Options > Plane strs w/thk > OK > Close Enter the thickness 7. Main Menu > Preprocessor > Real Constants > Add/Edit/Delete > Add > (Type 1 Plane 183) > OK > Enter 0. 09375 > OK > Close Enter the material properties 8. Main Menu > Preprocessor > Material Props > Material Models Material Model Number 1, click Structural > Linear > Elastic > Isotropic Enter EX = 3. 0E7 and PRXY = 0. > OK (Close Define Material Model Behavior window. ) Now mesh the X-Y plane area. (Turn on area numbers if it helps. ) 9. Main Menu > Preprocessor > Meshing > Mesh > Areas > Free. Pick the X-Y planar area > OK IMPORTANT NOTE: The mesh below was developed from an IGES geometry file. Using the text file geometry definition, may produce a much different mesh. If so, use the Modify Mesh refinement tools to obtain a mesh density that produces results with accuracies comparable to those given below. Computed stress values can be surprisingly sensitive to mesh differences. -20 ANSYS Tutorial Figure 2-28 Quad 8 mesh. The IGES solid model is no longer needed, and since its lines and areas may interfere with subsequent modeling operations, we can delete it from the session. 10. Main Menu > Preprocessor > Modeling > Delete > Volume and Below (Donââ¬â¢t be surprised if everything disappears. Just Plot > Elements to see the mesh again. ) 11. Utility Menu > PlotCtrls > Pan, Zoom, Rotate > Front front side of mesh. ) (If necessary to see the Figure 2-29 . Mesh, front view. Now apply displacement and pr essure boundary conditions.Zero displacement UX along left edge and zero UY along bottom edge. 12. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the left edge > UX = 0. > OK 13. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the lower edge > UY = 0. > OK The 1000 lbf load corresponds to a uniform pressure of about 14,000 psi along the ? inch vertical inside edge of the latch retention slot. [1000 lbf/(0. 09375 in. x 0. 75 in. )]. 14.Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Pressure > On Lines Plane Stress / Plane Strain 2-21 Select the inside line and set pressure = 14000 > OK Figure 2-30 Applied displacement and pressure conditions. Solve the equations. SOLUTION 15. Main Menu > Solution > Solve > Current LS > OK POSTPROCESSING Comparing the von Mises stress with the material yield stress is an accepted way of evaluating static load yielding for du ctile metals in a combined stress state, so we enter the postprocessor and plot the element solution of von Mises stress, SEQV. 16.Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Stress > (scroll down) von Mises > OK Zoom in on the small fillet where the maximum stresses occur. The element solution stress contours are reasonably smooth, and the maximum von Mises stress is around 118,000 psi. Further mesh refinement gives a stress value of approximately 140,000 psi. The small fillet radius of this geometry illustrates the challenges that can arise in creating accurate solutions, however you can easily come within a few percent of the most likely true result using the methods discussed thus far.Figure 2-31 Von Mises stresses. 2-22 ANSYS Tutorial Redesign to reduce the maximum stress requires an increase in the thickness or fillet radius. Look at charts of stress concentration factors, and you notice that the maximum stress increases as the radius of the str ess raiser decreases, approaching infinite values at zero radii. If your model has a zero radius notch, your finite-size elements will show a very high stress but not infinite stress. If you refine the mesh, the stress will increase but not reach infinity.The finite element technique necessarily describes finite quantities and cannot directly treat an infinite stress at a singular point, so donââ¬â¢t ââ¬Ëchase a singularityââ¬â¢. If you do not care what happens at the notch (static load, ductile material, etc. ) do not worry about this location but examine the stresses and strains in other regions. If you really are concerned about the maximum stress in a particular location (fatigue loads or brittle material), then use the actual part notch radius however small (1/32 for this tutorial); do not use a zero radius.Also examine the stress gradient in the vicinity of the notch to make sure the mesh is sufficiently refined near the notch. If a crack tip is the object of the anal ysis, you should look at fracture mechanics approaches to the problem. (See ANSYS help topics on fracture mechanics. ) The engineerââ¬â¢s responsibility is not only to build useful models, but also to interpret the results of such models in intelligent and meaningful ways. This can often get overlooked in the rush to get answers. Continue with the evaluation and check the strains and deflections for this model as well. 7. Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Strain-total > 1st prin > OK The maximum principal normal strain value is found to be approximately 0. 004 in/in. 18. Main Menu > General Postproc > Plot Results > Contour Plot > Nodal Solu > DOF Solution > X-Component of displacement > OK Figure 2-32 UX displacements. Plane Stress / Plane Strain 2-23 The maximum deflection in the X direction is about 0. 00145 inches and occurs as expected at the center of the right-hand edge of the latch retention slot. -9 MAPPED MESHING Quadrilateral m eshes can also be created by mapping a square with a regular array of cells onto a general quadrilateral or triangular region. To illustrate this, delete the last line, AL,all, from the text file above so that the area is not created (just the lines) and read it into ANSYS. Use PlotCtrls to turn Keypoint Numbering On. Then use 1. Main Menu > Preprocessor > Modeling > Create > Lines > Lines > Straight Line. Successively pick pairs of keypoints until the four interior lines shown below are created. Figure 2-33 Lines added to geometry. 2.Main Menu > Preprocessor > Modeling > Create > Areas > Arbitrary > By Lines Pick the three lines defining the lower left triangular area. > Apply > Repeat for the quadrilateral areas. > Apply > OK Figure 2-34 Quadrilateral/Triangular regions. 3. Main Menu > Preprocessor > Modeling > Operate > Booleans > Glue > Areas > Pick All 2-24 ANSYS Tutorial The glue operation preserves the boundaries between areas that we will need for mapped meshing. 4. Main Men u > Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines Enter 4 for NDIV, No. lement divisions > OK All lines will be divided into four segments for mesh creation. Figure 2-35 Element size on picked lines. 5. Main Menu > Preprocessor > Element Type > Add/Edit/Delete > Add > Solid > Quad 8node 183 > OK (Use the 8-node quadrilateral element for the mesh. ) 6. Main Menu > Preprocessor > Meshing > Mesh > Areas > Mapped > 3 or 4 sided > Pick All The mesh below is created. Applying boundary and load conditions and solving gives the von Mises stress distribution shown.The stress contours are discontinuous because of the poor mesh quality. Notice the long and narrow quads near the point of maximum stress. We need more elements and they need to be better shaped with smaller aspect ratios to obtain satisfactory results. Plane Stress / Plane Strain 2-25 Figure 2-36 Mapped mesh and von Mises results. One can tailor the mapped mesh by specifying how many elements are to be plac ed along which lines. This allows much better control over the quality of the mesh, and an example of using this approach is described in Lesson 4. 2-10 CONVERGENCEThe goal of finite element analysis as discussed in this lesson is to arrive at computed estimates of deflection, strain and stress that converge to definite values as the number of elements in the mesh increases, just as a convergent series arrives at a definite value once enough terms are summed. For elements based on assumed displacement functions that produce continuum models, the computed displacements are smaller in theory than the true displacements because the assumed displacement functions place an artificial constraint on the deformations that can occur.These constraints are relaxed as the element polynomial is increased or as more elements are used. Thus your computed displacements usually converge smoothly from below to fixed values. Strains are the x and/or y derivatives of the displacements and thus depend o n the distribution of the displacements for any given mesh. The strains and stresses may change in an erratic way as the mesh is refined, first smaller than the final computed values, then larger, etc. Not all elements are developed using the ideas discussed above, and some will give displacements that converge from above. (See Lesson 6. In any case you should be alert to computed displacement and stress variations as you perform mesh refinement during the solution of a problem. 2-11 TWO-DIMENSIONAL ELEMENT OPTIONS The analysis options for two-dimensional elements are: Plane Stress, Axisymmetric, Plane Strain, Plane Stress with Thickness and Generalized Plane Strain. The two examples thus far in this lesson were of the third type, namely problems of plane stress in which we provided the thickness of the part. 2-26 ANSYS Tutorial The first analysis option, Plane Stress, is the ANSYS default and provides an analysis for a part with unit thickness.If you are working on a design problem in which the thickness is not yet known, you may wish to use this option and then select the thickness based upon the stress, strain, and deflection distributions found for a unit thickness. The second option, Axisymmetric analysis is covered in detail in Lesson 3. Plane Strain occurs in a problem such as a cylindrical roller bearing caged against axial motion and uniformly loaded in a direction normal to the cylindrical surface. Because there is no axial motion, there is no axial strain.Each slice through the cylinder behaves like every other and the problem can be conveniently analyzed with a planar model. Another plane strain example is that of a long retaining wall, restrained at each end and loaded uniformly by soil pressure on one or both faces. The Generalized Plane Strain feature assumes a finite deformation domain length in the Z direction, as opposed to the infinite value assumed for standard plane strain. 2-12 SUMMARY Problems of stress concentration in plates subject to in-plane loadings were used to illustrate ANSYS analysis of plane stress problems.Free triangular and quadrilateral element meshes were developed and analyzed. Mapped meshing with quads was also presented. Similar methods are used for solving problems involving plane strain; one only has to choose the appropriate option during element selection. The approach is also applicable to axisymmetric geometries as discussed in the next lesson. 2-13 PROBLEMS In the problems below, use triangular and/or quadrilateral elements as desired. Triangles may produce more regular shaped element meshes with free meshing.The six-node triangles and eight-node quads can approximate curved surface geometries and, when stress gradients are present, give much better results than the four-node quad elements. 2-1 Find the maximum stress in the aluminum plate shown below. Use tabulated stress concentration factors to independently calculate the maximum stress. Compare the two results by determining the percen t difference in the two answers. Convert the 12 kN concentrated force into an equivalent pressure applied to the edge. Plane Stress / Plane Strain 2-27 Figure P2-1 -2 Find the maximum stress for the plate from 2-1 if the hole is located halfway between the centerline and top edge as shown. You will now need to model half of the plate instead of just one quarter and properly restrain vertical rigid body motion. One way to do this is to fix one keypoint along the centerline from UY displacement. Figure P2-2 2-28 ANSYS Tutorial 2-3 An aluminum square 10 inches on a side has a 5-inch diameter hole at the center. The object is in a state of plane strain with an internal pressure of 1500 psi. Determine the magnitude and location of the maximum principal stress, the maximum rincipal strain, and the maximum von Mises stress. Note that no thickness need be supplied for plane strain analysis. Figure P2-3 2-4 Repeat 2-3 for a steel plate one inch thick in a state of plane stress. 2-5 See if yo u can reduce the maximum stress for the plate of problem 2-1 by adding holes as shown below. Select a hole size and location that you think will smooth out the ââ¬Ëstress flowââ¬â¢ caused by the load transmission through the plate. Figure P2-5 2-6 Repeat 2-1 but the object is now a plate with notches or with a step in the geometry. (See the next figure. ) Select your own dimensions, materials, and loads.Use published stress concentration factor data to compare to your results. The published results are for plates that are relatively long so that there is a uniform state of axial stress at either end relatively far from notch or hole. Create your geometry accordingly. Plane Stress / Plane Strain 2-29 Figure P2-6 2-7 Solve the seatbelt component problem of Tutorial 2B again using six node triangular elements instead of the quadrilaterals. Experiment with mesh refinement. Turn on Smart Sizing using size controls to examine the effect on the solution. See if you can compute a maxi mum von Mises stress of around 140 kpsi. -8 Determine the stresses and deflections in an object ââ¬Ëat handââ¬â¢ (such as a seatbelt tongue or retaining wall) whose geometry and loading make it suitable for plane stress or plane strain analysis. Do all the necessary modeling of geometry (use a CAD system if you wish), materials and loadings. 2-9 A cantilever beam with a unit width rectangular cross section is loaded with a uniform pressure along its upper surface. Model the beam as a problem in plane stress. Compute the end deflection and the maximum stress at the cantilever support. Compare your results to those you would find using elementary beam theory.Figure P2-8 Restrain UX along the cantilever support line, but restrain UY at only one keypoint along this line. Otherwise, the strain in the Y direction due to the Poisson effect is prevented here, and the root stresses are different from elementary beam theory because of the singularity created. (Try fixing all node points in UX and UY and see what happens. ) Select your own dimensions, materials, and pressure. Try a beam thatââ¬â¢s long and slender and one thatââ¬â¢s short and thick. The effect of shear loading becomes more important in the deflection analysis as the slenderness decreases.
Wednesday, October 23, 2019
Mark Twain Case Essay
Mark Twain was an extremely productive author in his lifetime.à He wrote many famous books, articles and stories.à He was also a world traveler.à He visited five continents and crossed the Atlantic Ocean 29 times.à In general, he is notarized for his fiction works.à However, he also composed many successful non-fiction manuscripts as well. Many of Twainââ¬â¢s non-fiction works were written on his travels.à In his travels to the Old City, Twain took photographs to correspond with his written work.à He described the Old City, highlighting the methods and manners in which the Jewish people of the city worshipped and interacted with one another.à While doing this, he provided names to many of the places that he visited.à Many of these names have stuck, and have become the common names of landmarks (Journey to the Holy City, 2). à à à à à à à à à à à Most readers are already familiar with the broad brushstrokes of Mark Twainââ¬â¢s life.à Many interviews, however, were conducted in order to present a totally new facet of the Twain story, unfictionalized and in fascinating detail. These interviews appeared in a great diversity of American and international newspapers during the long course of his creative adult life (Nash).à The interviews provide information to the volumes and volumes of Twainââ¬â¢s imaginative and satirical capabilities.à Most famous of the non-fiction works written by Twain is his adult biography.à The biography tells the compelling story, from his own perspective, of life and the inspirations behind his works. Countless books have been written about Twainââ¬â¢s life.à One book, written by Ron Powers, has been hailed by critics as serving as a ââ¬Å"biography but much moreâ⬠¦Powers uses Twainââ¬â¢s life to tell us what America was like then and, tangentially, why weââ¬â¢re what we are todayâ⬠(Spiegel, 2). à à à à à à à à à à à Twainââ¬â¢s world travels began in 1867, when a California newspaper sent him on a five-month trip to Europe and the Middle East.à There, he wrote many letters that were later put together to form the book The Innocents Abroad (Twainââ¬â¢s Travels, 1). à à à à à à à à à à à Mark Twain is considered to be one of the worldââ¬â¢s greatest humorists.à His witty phrases and observations filled the pages of his non fiction works (WordPlay, 1).à Twain was also one of the first persons in his town in Hartford, Connecticut to have a telephone.à An example of his humorous use of satire to describe a situation occurred in 1880.à à Twain was amused by his new device, as it enabled persons who enjoyed eavesdropping to hear only one side of a conversation.à As a result, he wrote an amusing description of listening to his wife talk on the telephone (Twain, 1). à à à à à à à à à à à Twain composed many of his non-fiction works under his pen name.à His legal name was Samuel Clemens.à While often engaged in travel, Twain spent over 17 years at his beloved Hartford home.à While living there, he published six books.à These include: The Adventures of Tom Sawyer, A Tramp Abroad, The Prince and the Pauper, Life on the Mississippi, Adventures of Huckleberry Finn, and A Connecticut Yankee in King Arthurââ¬â¢s Court (Allen). à à à à à à à à à à à Literature critics have paid significant attention to Twainââ¬â¢s twang in his nonfiction writings, stating that ââ¬Å"he pours forth a flood of most graphic word painting. He talks slowly and extracts each of his vowels with a corkscrew twist that would make even the announcement of a funeral sound like a jokeâ⬠(Markââ¬â¢s Twang, 1). Critics have also spent significant amounts of time dissecting Twainââ¬â¢s life as well as books written about his life.à In an article by Middlekauff, the author describes Twain as an inspiration to biographers, historians and literary critics alike.à Middlekauff elaborates on this by concluding, ââ¬Å"Mark Twain, in all of his fascination, will never exhaust the interest of his readersâ⬠(1).à It seems as though Middlekauff hit it right on. In the past decade, in particular, Twainââ¬â¢s name has been used publicly to highlight achievement.à Schools have been named after him.à Additionally, many literary awards have been named after the famous author.à For example, in 2006, playwright Neil Simon was presented with the Ninth Annual Mark Twain Prize for American Humor (Awards and Prizes, 1). Works Cited Allen, Daniel.à Mark Twain.à Yankee.à November 2006.à Vol 70(9).à 1 pg. Awards and Prizes.à American Theatre.à September 2006.à Vol 23(7).à 1 pg. Journey to the Holy City in the Footsteps of Mark Twain.à PSA Journal.à October 2006. Volume 72(10).à 2 pg. Markââ¬â¢s Twang.à Harperââ¬â¢s Magazine.à September 2006.à Vol 313(1876).à 1 pg. Middlekauff, Robert.à Mark Twain: A Life.à Journal of American History.à September Vol 93(2). 1 pg. Nash, Charles.à Mark Twain: The Complete Interviews.à Library Journal.à October 1, Vol. 131(16). 2 pg. Spiegel, Pamela.à Leaders as Readers.à American Libraries.à May 2006.à Vol 37(5), 4 pg. Twain, Mark.à A Telephonic Conversation.à Atlantic.à September 2006.à Vol 298(2).à 1 pg. Twainââ¬â¢s Travels: Letters from home; from France, Morocco, Egypt and Russia.à Read. November 3, 2006.à Vol 56(6).à 2 pg. Wordplay.à Read.à November 3, 2006.à Vol 56(6).à 1 pg.
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