Ansys Tutorial Release 12.1

ANSYS tutorial Release 12. 1 geomorphological & 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 breeding Corporation Visit the following websites to learn more about this book ANSYS tutorial 2-1 Lesson 2 savourless melodic line shave subscriber line 2-1 OVERVIEW Plane express and plane strain bothers argon an important subclass of general threedimensional chores. The tutorials in this lesson demonstrate Solving placoid seek closeness problems. Evaluating potential inaccuracies in the upshots. Using the various ANSYS 2D comp nonpareilnt formulations. 2-2 INTRODUCTION It is possible for an prey such as the one on the cover of this book to have six components of focal point when subjected to unequivocal three-dimensional loadings. When referenced to a Cartesian coordinate system these components of foc utilise atomic nu mber 18 nonemal Stresses ?x, ? y, ? z Shear Stresses ?xy, ? yz, ? zx enrol 2-1 Stresses in 3 dimensions. In general, the analysis of such objectives requires three-dimensional modeling as discussed in Lesson 4.However, deuce-dimensional models be often easier to develop, easier to solve and tin apprise be employed in m either an(prenominal) 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 in nisuses ? x, ? y, and ? xy lie in the X Y plane and do non transfigure in the Z way. Further, the other melodic phrasees (? z,? yz , and ? zx ) ar 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 latent hostility problems. ANSYS provides a 6-node planar angulate constituent on with 4-node and 8 -node quadrilateral elements for use in the development of plane stress models. We will use both trilaterals and quads in solution of the example problems that follow. 2-3 PLATE WITH CENTRAL HOLE To start off, lets solve a problem with a k directlyn 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 dwelling house with a central seaman as arrangementn in get word 2-2. contrive 2-2 Plate with central hole. The 1. 0 m x 0. 4 m shell has a onerousness 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 Poissons ratio, ? = 0. 29. We moderate a horizontal tensile loading in the form of a pressure p = -1. 0 N/m2 along the tumid edges of the plate. Because holes are prerequisite for fasteners such as bolts, rivets, etc, the need to know stresses and deformations near them occurs very often and has rec eived a great deal of study.The results of these studies are widely published, and we can seem up the stress concentration factor for the case shown above. Before the advent of qualified 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 coreline 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 limited element model. For micro 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 t he 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 along the centerlines further not perpendicular to them.This indicates the appropriate faulting conditions to use as shown below. Figure 2-3 Quadrant used for analysis. In Tutorial 2A we will use ANSYS to deposit the maximal 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 leave outs will be used to formulate and solve the problem. 2-4 TUTORIAL 2A 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, assume the functional Directory where you will store the files associated with this problem. Also set the Jobname to Tutorial2A or something memorable and provid e a Title. (If you want to make changes in the Jobname, work Directory, or Title subsequently youve started ANSYS, use File Change Jobname or Directory or Title. ) submit 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 bill Preprocessor Element casing Add/ ignore/Delete Add geomorphological Solid Quad 8node 183 OK Figure 2-5 Element pick oution. 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 elegance Plane Stress / Plane Strain 2-5 Figure 2-6 Element options. 4. Main board Preprocessor Real Constants Add/Edit/Delete Add OK Figure 2-7 Real continuals. Enter the plate thickness of 0. 01 m. ) Enter 0. 01 OK Close Figure 2-8 Enter the plate thickness. 2-6 AN SYS Tutorial Enter the material properties. 5. Main Menu Preprocessor actual Props Material Models Material Model Number 1, click Structural Linear Elastic Isotropic Enter EX = 2. 07E11 and PRXY = 0. 29 OK (Close the pay off Material Model Behavior window. ) Create the geometry for the upper pay 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 ( bring down 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 landing fields. 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 needed. ) 8.Main Menu Preprocessor Modeling Operate Bool eans Subtract Areas Pick the rectangle OK, then pick the circle OK (Use spring up Hidden and Reset Picking as necessary. ) Figure 2-11 Geometry for quadrant of plate. Create a work of triangular elements over the quadrant surface area. 9. Main Menu Preprocessor web Mesh Areas Free Pick the quadrant OK Figure 2-12 Triangular element mesh. Apply the break boundary conditions and loads to the geometry (lines) instead of the nodes as we did in the earlier lesson.These conditions will be applied to the FEM model when the solution is performed. 10. Main Menu Preprocessor payloads delimit debauchs Apply Structural sack 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 e dge of the quadrant OK Pressure = -1. 0 OK (A positive pressure would be a compressive load, so we use a negative pressure. The pressure is shown by the two arrows. ) Figure 2-13 Model with loading and shift key boundary conditions. The model-building step is now complete, and we can proceed to the solution. First, to be safe, save the model. 13. public-service corporation Menu File Save as Jobname. db (Or Save as . use a new name) SOLUTION The interactive solution proceeds as illustrated in the tutorials of Lesson 1. 14. Main Menu answer 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 Solution is Done window. POSTPROCESSING We can now plot the results of this analysis and also list the computed values. First tak e in the modify 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 distorted 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 Poissons 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 Resu lts 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 told 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 deem of elements used in this model is oo few to calculate with complete verity the stress values near th e hole because of the stress gradients there. We will not put on this stress solution. More six-node elements are needed in the region near the hole to find accurate values of the stress. On the other hit, 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 verity 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 s olved 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 inwardly 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 shape of elements near the stress concentrations must be increased proportionately.To defend 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 repair At All (Select Level of refinement 1. ) Figure 2-18 Global mesh refinement. 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 exit Areas to remove all elements and build a completely new mesh. Plot Areas afterwards to view the area again. Note also that too much topical anaesthetic refinement can create a mesh with too rapid a transition between fine and coarse mesh regions. ) Reapply the pressure loading, ingeminate 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. Figure 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. portion 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 almost 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 but fro m elementary solid mechanics principles. For continuum problems in two 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 make 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 imitate with six-node triangles, quadruplet-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 dis placements, stresses and strains within the element. If the stress is constant 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 opposite 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 stat. 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 ar ea A3 for development of the node/element FEM mesh. The loads, displacement boundary 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 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 exportationed as an IGES file. The file is imported into ANSYS for analysis. For simplicity we will analyze only the right, or tongue portion of the part in this tutorial.Plane Stress / Plane Strain 2-17 Figure 2-25 Seatbelt tongue. PREPROCESSING 1. Start ANSYS, Run Interactive, set jobname, and working directory. Create the top half of the geometry above. The lock retention time 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. 25, 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 tha t, because of the modeling or the 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 (Dont 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 pressure boundary con ditions.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 ductile metals in a combined stress state, so we ente r 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, so far 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 stress 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 r to each one infinity.The finite element technique necessarily describes finite quantities and cannot directly treat an infinite stress at a singular point, so dont attend a singularity. 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 dot is the object of the analysis, you should look at fracture mechanics approaches to the problem. (See ANSYS help topics on fracture mechanics. ) The engineers responsibility is not only to build expedient 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. cover 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 fountainhead 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 meshes can also be created by mapping a square with a regular array of cells onto a gen eral 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 ( yet 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 Menu Preprocessor Meshing Size Cntrls ManualSize Lines All Lines Enter 4 for NDIV, No. lement divisions O K 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 placed along which lines. This allows much better control over the quality of the mesh, and an example of using this approach is descr ibed 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 encounter 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 fabricated displacement functions that produce continuum models, the computed displacements are smaller in supposition 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 on the distribution of the displacements for any given mesh. The strains and stresses may change in an erratic way as t he 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 atom 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 leash 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 s tress, 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 ele ment meshes were developed and analyzed. Mapped meshing with quads was also presented. standardised 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 unbosom 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 atomic number 13 plate shown below. Use tabulated stress concentration factors to independently calculate the maximum stress. Compare the two results by determining the percent difference in the two answers. Convert the 12 kN concentrated force into an equivalent pressure appl ied 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 you 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 stress flow 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 maximum von Mises stress of around 140 kpsi. -8 Determine the stresses and deflections in an object at hand (such as a se atbelt 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 thats long and slender and one thats short and thick. The effect of shear loading becomes more important in the deflection analysis as the slenderness decreases.