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## Finite Elements

by: Miss Leatha Gottlieb

41

0

4

# Finite Elements ME EN 6510

Miss Leatha Gottlieb
The U
GPA 3.76

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
4
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KARMA
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## Popular in Mechanical Engineering

This 4 page Class Notes was uploaded by Miss Leatha Gottlieb on Monday October 26, 2015. The Class Notes belongs to ME EN 6510 at University of Utah taught by Staff in Fall. Since its upload, it has received 41 views. For similar materials see /class/230018/me-en-6510-university-of-utah in Mechanical Engineering at University of Utah.

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Date Created: 10/26/15
University of Utah ME EN 65105510 Introduction to Finite Elements Fall 2005 2D ELASTICITY Using ANSYS for 2D planar elasticity problems Introduction Planar elasticity problems are either plane stress or plane strain Both categories of problems use the same elements defaults to plane stress In the Ansys program plane42 is a 4 node isoparametric element with 2 degrees of freedom at each node This element is a workhorse element and is widely used The ANSYS program permits internal degrees of freedom with incompatible modes in this element This feature usually leads to faster convergence ie better accuracy but can be suppressed if desired The following problem will illustrate how to use the program for planar problems ANSYS also provides an advanced version of the plane 42 element These are the Plane 82 elements with 8 nodes 4 at the element corners and 4 on the element midsides Example Hole in a plate The problem to be worked is shown in Fig 1 It is a typical stress concentration problem consisting of a hole in an aluminum plate It will be desired to calculate the maximum stress around the hole which can then be used to calculate the stress concentration factor Note that symmetry reduces the calculation to 14 of the actual plate Using symmetry where appropriate is essential Symm X llllll Symm y 05 55 Figure 1 Hole in a at plate problem ANSYS model geometry The code required to build and solve this problem is given on the following pages It can be typed into a prepared input file inp or entered directly into the command line When you finish you might want to also play with the GUI menus on your own and see if you can do the problem using that method as well Ansys input le Comments title your title et142 mpex110e6 mpprxy133 k 1 0 5 0 k2400 k3 60 k464 k 544 k604 k7005 csys1 k80545 csys L121010 L851010 L761010 csys1 L185 L875 csys L255 L565 L234 L345 L454 a1258 a8567 a2345 ameshall nselslocx00 dsymsymmx nselslocy00 dsymsymmy element plane42 a 4 node isoparametric planar element sets modulus sets Poisson s ratio a key point a key point a key point a key point a key pointquot note that the point is at 0010 changes from xy the default to r 9 global cylindrical coordinate system Use on line help for other options places key point no 8 at r05 945 degrees changes active system to the global coordinate system default option for csys command Note csys0 is also correct puts a line with 10 segments between pts 1 amp 2 The last segment is 10 times larger than the first This is done to obtain proper mesh which is sufficiently refined at regions of high stress gradients and less refined at low gradient areas It takes a few trials to get the right mesh depending on the complexity of the given problem I cyl coord so that the lines below match the hole 5 segments from 1 to 8 equally spaced the default 5 segments from 8 to 7 equally spaced the default changes active system to the global coordinate system creates an area with key pts as corners order is important creates an area with key pts as corners This creates the element mesh select nodes on y axis x0 define a symmetry bc for these nodes same as constraining ux displacements using d command select nodes on x axis y0 from all nodes define a symmetry bc for these nodes nselslocx66 select nodes on right side of plate from all nodes sfallpress 1000 apply tension of P1000 units to right side of plate nselall reselect all nodes psfpress2 show pressure as arrows on plots pbcu1 show disp constraints on plots rep replot similar to refresh screen Once the input file has been prepared as above check to see that it is ok by typing in the following commands to ANSYS prep7 the input phase of ansys show x11 necessary if you are going to do plots inputfilenameinp Filenameinp is the name of your input file 8 letters max for filename All of the commands in the input file will be executed The following commands are then used to examine your model to see that it is correct and what you want klist lists all keypoints lplot gives a plot of the line segments aplot plots the area The divisions are not elements eplot gives a plot of elements a good diagnostic tool pbcu1 1 shows the bc s in plots 0 turns this feature off pnumnode1 1 shows the node no s in plots 0 turns this off nplot plots the nodes If the model is not correct go to the editor and fix the input file and re enter it as above If correct proceed as follows wsorty used to minimize bandwidth good for larger problems For large problems you need to try a sort in each direction ansys will use the smallest bandwidth finish exits from prep7 solu initiates solution phase solve runs the solution finish after solution exits from solution phase post1 this enters the post processing phase to examine answers showx11 for x windows display set required directive edge11 Plots model edges optional pldisp1 plots the original and deformed mesh an important diagnostic plnsolsx plots a contour plot of stresses in the x direction Other options sxsysxy Good diagnostic plnsols1 plots a contour plot of sig1 principal stress csys1 change back to polar coordinates nselslocx02 selects only nodes Within a radius of 2 from the origin restore all nodes With nselall eslns select all elements attached to selected nodes csys plnsols1 contour plot near the region of high stresses pnumnode1 1 shows the node no s in plots 0 turns this off nplot Plots the node numbers Note Which numbers are along the cross section Where the stress is highest edge10 turns the edge feature off Necessary for the next plot lpath7278 defines a path for detailed plotting based on node numbers pdefsig1s1 labels the principal stress along the defined path as sig1 plpathsig1 plots sig1 along the path from node 72 to node 78 The numbers were obtained from the node plot prpathsig1 prints the sig1 values if you want to see them finish exits from post1 When you are done type eof exits from Ansys

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