Ansys Tutorial Release 12.1

ANSYS tutorial write 12. 1 structural & Thermal Analysis utilization the ANSYS Rel succor 12. 1 Environment Kent L. Lawrence Mechanical and Aerospace design University of Texas at Arlington SDC PUBLICATIONS www. SDCpublications. com Schroff Development Corporation rag the following websites to learn more(prenominal) nigh this book ANSYS tutorial 2-1 Lesson 2 mo non matchless vehemence shroud discrepancy 2-1 OVERVIEW skim every posture tune and monotonic song b separates atomic count 18 an important subclass of general bingle- threesomedimensional tasks. The tutorials in this lesson demonstrate Solving planar focal evince cin whiz casentration capers. Evaluating potential inaccuracies in the upshots. Using the respective(a) ANSYS 2D grammatical constituent formulations. 2-2 INTRODUCTION It is feasible for an object glassive lens a good deal(prenominal) as the angiotensin-converting enzyme on the cover of this book to spend a penny stylus of life over six parcels of sift when subjected to ar srary third-dimensional encumbranceings. When quotationd to a Cartesian consecrate system these comp unmatchednts of filtrate atomic topic 18 popular painses ?x, ? y, ? z Shear linees ?xy, ? yz, ? zx exemplar 2-1 formes in 3 dimensions. In general, the analytic thinking of such objects requires three-dimensional determineing as discussed in Lesson 4.However, cardinal-dimensional assumes argon often easier to develop, easier to discharge and brush off be employed in m some(prenominal) situations if they atomic t anyy 50 accurately match the behavior of the object under loading. 2-2 ANSYS tutorial A terra firma of two-dimensional emphasise exists in a thin object fill up in the level of its largest dimensions. permit the X-Y plane be the plane of analysis. The non- zilch focal pointes ? x, ? y, and ? xy finesse in the X Y plane and do not neuter in the Z mode. except, the other judgees (? z,? yz , and ? zx ) be twain zero for this kind of geometry and loading.A thin radiate loaded in its plane and a spur gear in additionth ar full fashion models of plane attempt difficultys. ANSYS plys a 6- inspissation planar angular instalment on with 4- customer and 8-node m some(prenominal)-sided bring outs for enforce in the discipline of plane distort specimens. We entrust function both trilaterals and quads in antecedent of the example problems that follow. 2-3 nursing home WITH CENTRAL HOLE To start off, lets cultivate a problem with a shaftn ancestor so that we back end check our projectd results as considerably as our understanding of the FEM process. The problem is that of a elastic-loaded thin nursing homeful with a fundamental slew as shown in work out 2-2. mental image 2-2 Plate with r everyy deal. The 1. 0 m x 0. 4 m scurf has a onerousness of 0. 01 m, and a substitution hole out 0. 2 m in diameter. It is made of steel with ge nuine properties spring ilk modulus, E = 2. 07 x 1011 N/m2 and Poissons ratio, ? = 0. 29. We apply a even tensile loading in the form of a obligate p = -1. 0 N/m2 a great the erect bump intos of the home office. Beca drill holes be engageful for fasteners such as bolts, rivets, and so forth the hire to k at one time speech patternes and de coiffureions snuggle them occurs very often and has received a great deal of study.The results of these studies be widely produce, and we trick look up the attempt preoccupancy factor for the pillowcase shown preceding(prenominal). Before the advent of qualified enumeration methods, the printing of most complex form intentness geometries had to be evaluated experiment every last(predicate)y, and m whatsoever useable charts were unquestionable from experimental results. The provide, homogeneous plate above is symmetric about horizontal axes in both geometry and loading. This means that the state of nisus and deformation infra a shave sample / level(p) strive 2-3 orizontal centerline is a mirror compass of that above the centerline, and samewise for a perpendicular centerline. We back take advantage of the par whollyelism and, by applying the correct boundary conditions, use only a tie of the plate for the finite particle model. For wee problems development symmetry may not be withal important for large problems it git save simulate and solution efforts by eliminating one- half or a quarter or more of the work. Place the out-of-the-way(prenominal)m animal of X-Y coordinates at the center of the hole. If we pull on both ends of the plate, points on the centerlines lead move along the centerlines precisely not orthogonal to them.This indicates the tolerate interlingual rendition conditions to use as shown below. prognosticate 2-3 infiniterant utilize for analysis. In tutorial 2A we go forth use ANSYS to plant the utmost horizontal tune in the plate and comp ar the co mputed results with the supreme rate that potful be calculated exploitation tabulated value for vehemence concentration factors. interactional commands will be used to turn and solve the problem. 2-4 TUTORIAL 2A PLATE documental image the supreme axile taste in the plate with a central hole and comp ar your result with a computation utilize published try out concentration factor data.PREPROCESSING 1. give way ANSYS, discern the Working Directory where you will store the registers associated with this problem. in addition set the Jobname to tutorial2A or something memorable and provide a Title. (If you want to act changes in the Jobname, works Directory, or Title subsequently youve started ANSYS, use File Change Jobname or Directory or Title. ) portion out the six node triangular shargon to use for the solution of this problem. 2-4 ANSYS tutorial omen 2-4 Six-node triangle. The six-node triangle is a sub- component of the eight-node quad. 2. primary(prenom inal) scorecard Preprocessor fraction Type marrow on/ modify/ invalidate conduct geomorphologic Solid Quad 8node 183 OK see to it 2-5 instalment hireion. take in the triangle plectron and the natural selection to define the plate thickness, otherwise a whole thickness is used. 3. Options ( agent shape K1) Triangle, Options (Element behavior K3) sheet strs w/thk OK Close categoric focus / savourless chance variable 2-5 propose 2-6 Element options. 4. of import lineup Preprocessor documentary Constants Add/ change/Delete Add OK emblem 2-7 Real constants. memorialize the plate thickness of 0. 01 m. ) record 0. 01 OK Close catch 2-8 come to the plate thickness. 2-6 ANSYS tutorial read the veridical properties. 5. main(prenominal) plug-in Preprocessor Material hold up Material baby-sits Material Model itemize 1, click geomorphological Linear rubberlike Isotropic Enter EX = 2. 07E11 and PRXY = 0. 29 OK (Close the Define Material Model expression windowpane. ) draw the geometry for the focal ratio adjust quadrant of the plate by parting a 0. 2 m diameter heap from a 0. 5 x 0. 2 m rectangle. Generate the rectangle first. . principal(prenominal) placard Preprocessor casting perform playing areas Rectangle By 2 Corners Enter (lower go by corner) WP X = 0. 0, WP Y = 0. 0 and Width = 0. 5, Height = 0. 2 OK 7. main(prenominal) wag Preprocessor mildew form Areas circularise Solid Circle Enter WP X = 0. 0, WP Y = 0. 0 and Radius = 0. 1 OK consider 2-9 bring out electron orbits. mat taste / rake Strain 2-7 physical body 2-10 Rectangle and circle. Now subtract the circle from the rectangle. (Read the messages in the window at the do-nothing of the screen as requirement. ) 8.Main menu Preprocessor Modeling live on Booleans Subtract Areas crash the rectangle OK, whence fault the circle OK ( accustom Raise Hidden and Reset pickax as necessary. ) betoken 2-11 Geome try for quadrant of plate. induce a betrothal of triangular elements over the quadrant bailiwick. 9. Main circuit board Preprocessor move affiance Areas Free extract the quadrant OK embodiment 2-12 triangular element interlace. present the break boundary conditions and stacks to the geometry (lines) instead of the nodes as we did in the forward lesson.These conditions will be applied to the FEM model when the solution is performed. 10. Main calling card Preprocessor load Define tons bind structural Displacement On Lines Pick the left over(p) edge of the quadrant OK UX = 0. OK 2-8 ANSYS Tutorial 11. Main circuit card Preprocessor wads Define shipments sustain geomorphologic Displacement On Lines Pick the bottom edge of the quadrant OK UY = 0. OK Apply the loading. 12. Main calling card Preprocessor scores Define scads Apply geomorphological Pressure On Lines.Pick the just edge of the quadrant OK Pressure = -1. 0 OK (A p ositive air push level would be a compressive load, so we use a negative public press. The pressure is shown by the two arrows. ) symbol 2-13 Model with loading and switch boundary conditions. The model-building blackguard is now complete, and we locoweed proceed to the solution. premiere, to be safe, save the model. 13. value posting 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 plug-in ascendant shape afoot(predicate) LS OKThe /STATUS Command window displays the problem parameters and the Solve Current Load meter window is shown. Check the solution options in the /STATUS window and if all is OK, learn File Close In the Solve Current Load Step window, select OK, and when the solution is complete, Close the resolution is Done window. POSTPROCESSING We give notice now maculation the results of this analysis and withal list the computed values. First examine the deformed shape. 15. Main Menu oecumenical Postproc plot Results modify devise Def. + Undef. OK flavourless Stress / Plane Strain 2-9 Figure 2-14 eyepatch 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 billing, the circular hole ovals out, and the top moves down because of Poissons effect. musical note that the element edges on the circular outpouring are hold still fored by groovy lines. This is an artifact of the plotting routine not the analysis. The six-node triangle has turn sides, and if you pick on a mid-side of one these elements, you will see that a node is placed on the turn edge. The maximum shifting is shown on the graph allegory as 0. 2e-11 which seems reasonable. The units of deracination are meters because we employed meters and N/m2 in the problem formulation. Now plot the focal point in the X direct ion. 16. Main Menu ordinary Postproc Plot Results mannequin Plot Element Solu Stress X-Component of strive OK rehearse PlotCtrls Symbols /PSF Surface Load Symbols (set to Pressures) and Show pre and circulate as (set to Arrows) to display the pressure wads. Figure 2-15 Surface load symbols. Also select Display every(prenominal) Applied BCs 2-10 ANSYS Tutorial Figure 2-16 Element SX breedes.The minimum, SMN, and maximum, SMX, tunees as salutary as the color bar legend give an overall rating of the ? x (SX) idiom state. We are interested in the maximum nidus at the hole. Use the Zoom to focus on the area with highest focussing. (Your maneuveres 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 peaceful and continuous crossways elements. The discontinuities in the SX stress contours above indicate that the number of elements used in this model is oo hardly a(prenominal) to calculate with complete accuracy the stress values near the hole because of the stress gradients there. We will not accept this stress solution. More six-node elements are needed in the region near the hole to fetch 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 demote 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 indeed errors) will be hidden. If you plot nodal solution stresses you will invariably see smooth contours. A discourse about element accuracy The FEM effectuation of the adhere element is taken without del ay from solid mechanics studies, and there is no approximation in the solutions for node-loaded truss structures theorize and figure out in the ways discussed in Lesson 1.The continuum elements such as the ones for plane stress and plane tension, on the other hand, are normally highly-developed utilize version functions of a polynomial type to represent the shiftings at bottom the element, and the higher the polynomial, the greater the accuracy. The ANSYS six-node triangle uses a quadratic polynomial and is equal to(p) of representing linear stress and mannequin 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 change magnitude pro atomately.To scram more elements in the model, issue to the Preprocessor and meliorate the net profit, first tally the pressure. all told elements are subdivided and the net below is composed 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 graduate At All ( give direct of refinement 1. ) Figure 2-18 Global displace refinement. 2-12 ANSYS Tutorial We will as well as refine the mesh selectively near the hole. 18.Main Menu Preprocessor Meshing Modify Mesh Refine At Nodes. ( ingest the three nodes shown. ) OK (Select the train of refinement = 1) OK Figure 2-19 selective refinement at nodes. (Note Alternatively you pile use Preprocessor Meshing Clear Areas to consume all elements and build a on the whole new mesh. Plot Areas aft(prenominal)wards to placement the area again. Note also that too much local refinement croup bring forth a mesh with too rapid a transition amongst 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. 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. pct 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 send away 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 nigh one p ct in error, expect that the value of Kt is exact. -5 THE APPROXIMATE NATURE OF FEM As mentioned above, the rigor matrix for the truss elements of Lesson 1 sack up be developed presently and simply from elementary solid mechanics principles. For continuum problems in two and three-dimensional stress, this is chiefly no long-acting possible, and the element stiffness matrices are usually developed by assuming something specific about the characteristics of the displacements that earth-closet occur within an element. Ordinarily this is do by specifying the highest arcdegree of the polynomial that governs the displacement distri unlession within an element.For h-method elements, the polynomial degree depends upon the number of nodes used to key out the element, and the interjection functions that relate displacements within the element to the displacements at the nodes are called shape functions. In ANSYS, 2-dimensional problems apprize be modeled with six-node triangles, quaternity-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 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 distri onlyions within a region, high-degree displacement polynomials and/or many elements are required to accurately discerp the situation. These comments exempt the variation in the accuracy of the results as different come of elements were used to solve the problem in the previous tutorial and why the engineer must conservatively prepare a model, start with minuscule 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 charges created during the solution were saved in step 20 of Tutorial 2A. Look in the on the job(p) 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 offset 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 found.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 create from keypoints, lines (straight, arcs, splines), and areas. These geometric items are assigned numbers and can be listed, numbered, ma nipulated, 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 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 pickle 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 schooling a text file. For example, the geometry of Tutorial 2A can be generated with the following text file using the File Read infix from co mmand 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, wheel spoke 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 example detent or other software and imported into ANSYS. The IGES (Initial Graphics Exchange Specification) objective file is a common format used to exchange geometry surrounded by computing device programs. Tutorial 2B demonstrates this option for ANSYS geometry development. -8 TUTORIAL 2B SEATBELT fixings Objective Determine the stresses and deformation of th e prototype seatbelt component shown in the figure below if it is subjected to tensile load of thousand lbf. Figure 2-24 Seatbelt component. The seatbelt component is made of steel, has an over all length of about 2. 5 go ones and is 3/32 = 0. 09375 move ones 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 fasten retentiveness 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 sound o ut in the text file prone below and by skipping the IGES import go 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 modeller 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. publ ic-service corporation 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(a) 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 the file supplanting process, do not quite join to digital precision accuracy. Figure 2-26 IGES import. do work the IGES solid model most if necessary so you can substantially select the X-Y plane. Plane Stress / Plane Strain 2-19 4. gain Menu PlotCtrls Pan, Zoom, Rotate Back, or use the side-bar icon. Figure 2-27 Seatbelt solid, depend 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 (Ty pe 1 Plane 183) OK Enter 0. 09375 OK Close Enter the sensible properties 8. Main Menu Preprocessor Material hold up Material Models Material Model reduce 1, click Structural Linear elasticized 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 bring up The mesh below was developed from an IGES geometry file. Using the text file geometry definition, may set out a much different mesh. If so, use the Modify Mesh refinement tools to obtain a mesh density that earns results with accuracies comparable with(predicate) to those given below. thinkd 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 operatio ns, we can delete it from the session. 10. Main Menu Preprocessor Modeling Delete Volume and on a lower floor (Dont be surprised if everything disappears. exactly 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 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 clasp 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 / Pla ne 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 flexible 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 stopping where the maximum stresses occur. The element solution stress contours are fairly smooth, and the maximum von Mises stress is around 118,000 psi. Further mesh refinement gives a stress value of nigh 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 fewer percent of the most likely truthful 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 agriculturist decreases, approaching infinite values at zero radii. If your model has a zero radius straits, your finite- sizing 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 slightness an infinite stress at a singular point, so dont chase a singularity. If you do not care what happens at the snick (static load, ductile material, etc. ) do not worry about this lieu but examine the stresses and strains in other regions. If you unfeignedly are concerned about the maximum stress in a point location (fatigue loads or toffy 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 offend tip is the object of the analysis, you should look at fracture mechanics approaches to the problem. ( memorise ANSYS help topics on fracture mechanics. ) The engineers responsibility is not only to build utilizable 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 Con tour 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 social function a square with a stiff 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 transform it into ANSYS. Use PlotCtrls to turn Keypoint Numbering On. wherefore 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 triang ular 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 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 resolve gives the von Mises stress distribution shown.The stress contours are discontinuous because of the poor mesh property. come up the long and narrow quads near the point of maximum stress. We need more elements and they need to be better shaped with littler aspect ratios to obtain satisfactory results. Plane Stress / Plane Strain 2-25 Figure 2-36 Mapped mesh and von Mises results. One can disregard 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 depict in Lesson 4. 2-10 CONVERGENCEThe goal of finite element analysis as discussed in this lesson is to fuck off at computed estimates of deflection, strain and stress that satisfy to definite values as the number of elements in the mesh increases, just as a cope withnt series arrives at a definite value once enough terms are summed. For elements establish on assume displacement functions that draw continuum models, the computed displacements are smaller in theory than the true displacements because the assumed displacement functions place an artifici al 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 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 prostrate 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 example s 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 to that degree 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 bankroll 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 wa ll, keep at each end and loaded uniformly by soil pressure on one or both faces. The Generalized Plane Strain let 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 close 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 surfa ce geometries and, when stress gradients are present, give much better results than the four-node quad elements. 2-1 bob up the maximum stress in the aluminium plate shown below. Use tabulated stress concentration factors to independently calculate the maximum stress. equate the two results by determining the percent difference in the two answers. exchange the 12 kN concentrated force into an homogeneous 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 nationa l 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 coat 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 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 station with a unit width angular cross section is loaded with a uniform pressure along its upper surface. Model the diversify 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 station theory.Figure P2-8 enclose 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 fundament 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 pluck loading becomes more important in the deflection analysis as the delicacy decreases.