Geometric NonlinearityIntroduction This tutorial was created using ANSYS 7.0 The purpose of this tutorial is to outline the steps required to do a simple nonlinear analysis of the beam shown below.

There are several causes for nonlinear behaviour such as Changing Status (ex. contact elements), Material Nonlinearities and Geometric Nonlinearities (change in response due to large deformations). This tutorial will deal specifically with Geometric Nonlinearities . To solve this problem, the load will added incrementally. After each increment, the stiffness matrix will be adjusted before increasing the load. The solution will be compared to the equivalent solution using a linear response.

Preprocessing: Defining the Problem 1. Give example a Title Utility Menu > File > Change Title ...2. Create Keypoints Preprocessor > Modeling > Create > Keypoints > In Active CS We are going to define 2 keypoints (the beam vertices) for this structure to create a beam with a length of 5 inches: KeypointCoordinates (x,y)

1(0,0)

2(5,0)

3. Define Lines Preprocessor > Modeling > Create > Lines > Lines > Straight Line Create a line between Keypoint 1 and Keypoint 2.4. Define Element TypesPreprocessor > Element Type > Add/Edit/Delete... For this problem we will use the BEAM3 (Beam 2D elastic) element. This element has 3 degrees of freedom (translation along the X and Y axis's, and rotation about the Z axis). With only 3 degrees of freedom, the BEAM3 element can only be used in 2D analysis.5. Define Real ConstantsPreprocessor > Real Constants... > Add... In the 'Real Constants for BEAM3' window, enter the following geometric properties: i. Cross-sectional area AREA: 0.03125 ii. Area Moment of Inertia IZZ: 4.069e-5 iii. Total beam height HEIGHT: 0.125 This defines an element with a solid rectangular cross section 0.25 x 0.125 inches.6. Define Element Material Properties Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic In the window that appears, enter the following geometric properties for steel: i. Young's modulus EX: 30e6 ii. Poisson's Ratio PRXY: 0.3 If you are wondering why a 'Linear' model was chosen when this is a non-linear example, it is because this example is for non-linear geometry, not non-linear material properties. If we were considering a block of wood, for example, we would have to consider non-linear material properties. 7. Define Mesh Size Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines... For this example we will specify an element edge length of 0.1 " (50 element divisions along the line).8. Mesh the frame Preprocessor > Meshing > Mesh > Lines > click 'Pick All'LMESH,ALL

Solution: Assigning Loads and Solving 1. Define Analysis TypeSolution > New Analysis > StaticANTYPE,02. Set Solution Controls Select Solution > Analysis Type > Sol'n Control... The following image will appear:

Ensure the following selections are made (as shown above) A. Ensure Large Static Displacements are permitted (this will include the effects of large deflection in the results) B. Ensure Automatic time stepping is on. Automatic time stepping allows ANSYS to determine appropriate sizes to break the load steps into. Decreasing the step size usually ensures better accuracy, however, this takes time. The Automatic Time Step feature will determine an appropriate balance. This feature also activates the ANSYS bisection feature which will allow recovery if convergence fails. C. Enter 5 as the number of substeps. This will set the initial substep to 1/5 th of the total load. The following example explains this: Assume that the applied load is 100 lb*in. If the Automatic Time Stepping was off, there would be 5 load steps (each increasing by 1/5 th of the total load): 20 lb*in 40 lb*in 60 lb*in 80 lb*in 100 lb*in Now, with the Automatic Time Stepping is on, the first step size will still be 20 lb*in. However, the remaining substeps will be determined based on the response of the material due to the previous load increment. D. Enter a maximum number of substeps of 1000. This stops the program if the solution does not converge after 1000 steps. E. Enter a minimum number of substeps of 1. F. Ensure all solution items are writen to a results file. NOTEThere are several options which have not been changed from their default values. For more information about these commands, type help followed by the command into the command line. Function Command Comments

Load Step KBC Loads are either linearly interpolated (ramped) from the one substep to another (ie - the load will increase from 10 lbs to 20 lbs in a linear fashion) or they are step functions (ie. the load steps directly from 10 lbs to 20 lbs). By default, the load is ramped. You may wish to use the stepped loading for rate-dependent behaviour or transient load steps.

Output OUTRES This command controls the solution data written to the database. By default, all of the solution items are written at the end of each load step. You may select only a specific iten (ie Nodal DOF solution) to decrease processing time.

Stress Stiffness SSTIF This command activates stress stiffness effects in nonlinear analyses. When large static deformations are permitted (as they are in this case), stress stiffening is automatically included. For some special nonlinear cases, this can cause divergence because some elements do not provide a complete consistent tangent.

Newton Raphson NROPT By default, the program will automatically choose the Newton-Raphson options. Options include the full Newton-Raphson, the modified Newton-Raphson, the previously computed matrix, and the full Newton-Raphson with unsymmetric matrices of elements.

Convergence Values CNVTOL By default, the program checks the out-of-balance load for any active DOF.

3. Apply ConstraintsSolution > Define Loads > Apply > Structural > Displacement > On Keypoints Fix Keypoint 1 (ie all DOFs constrained).4. Apply LoadsSolution > Define Loads > Apply > Structural > Force/Moment > On Keypoints Place a -100 lb*in moment in the MZ direction at the right end of the beam (Keypoint 2)5. Solve the SystemSolution > Solve > Current LSSOLVEThe following will appear on your screan for NonLinear Analyses

This shows the convergence of the solution.

General Postprocessing: Viewing the Results 1. View the deformed shape General Postproc > Plot Results > Deformed Shape... > Def + undeformedPLDISP,1

2. View the deflection contour plot General Postproc > Plot Results > Contour Plot > Nodal Solu... > DOF solution, UYPLNSOL,U,Y,0,1

3. List Horizontal Displacement If this example is performed as a linear model there will be no nodal deflection in the horizontal direction due to the small deflections assumptions. However, this is not realistic for large deflections. Modeling the system non-linearly, these horizontal deflections are calculated by ANSYS.General Postproc > List Results > Nodal Solution...> DOF solution, UX Other results can be obtained as shown in previous linear static analyses.

Material NonlinearityAnsys Lab Material nonlinearityPurpose To learn how to use ANSYS to solve elastic-plastic structural problem.BackgroundWhen ductile metals are loaded beyond elastic range, the initial linear stress response will giveway to a complicated nonlinear response, characterized by a much-reduced modulus and differentstress behavior along load and unloading path. An idealized stress-strain curve in uniaxial tensionis depicted in the figure below. The turning point is called elastic limit, the corresponding stressy is called the yield stress. In 3D case, the elastic limit is characterized by some measures ofstress, for example, if the von Mises stress reaches a critical value.Finite element elastic-plastic analysis is much more delicate than simple elastic analysis. For one,the FEM equation is no longer linear, but a set of nonlinear equations that needs to be solvediteratively. Typically, we divide the applied load into small increments so as to have a betternumerical performance.Lab exerciseA 36x20 rectangular plate with a circular hole in its center is subjected to a tensile pressure forcealong two end sides into the plastic range. Bilinear isotropic hardening is used. Small strain planestress condition is assumed. Note that only 1/4th domain is needed for analysis because ofsymmetry.Consider the hole dimensions

(You can also consider it as a complete model if you dont want to solve it symmetrically.)

Preprocessing1.1. Define estimated reference pressure at yield.We define a parameter Pres to be assigned to the pressure applied on the edge. ANSYS Utility Menu > Parameters > Scalar Parameters Scalar ParametersSelection [ Pres=-100] > Accept Parameters > Save Parameters > OK Scalar Parameters > Close ANSYS Toolbar > SAVE_DB1. 2. Begin the model creation.Create a solid model of a square with a quarter of a circular hole. Use any of your favoritemethod. The easiest way is perhaps through Boolean operations.1.3. Define the element type (PLANE182) and material properties.Plane182 is a 4 node quad element that deals with both small and large strains, with avariety of material options including elasto-plasticity. In ANSYS 18x elements, materialoptions are input separately. In this problem, elasticity is defined by Youngs modulusand Poissons ratio, and plasticity is defined by yield stress and the elastic-plastic tangentmodulus. ANSYS Main Menu Preprocessor > Element Type > Add/Edit/ Delete >AddSolid > [Quad 4node 182] Preprocessor > Material Props > Material Model > Structural > Linear >Elastic > Isotropic> EX [ 7E4 ]> PRXY [ 0.3 ]! define the plastic parameters Preprocessor > Material Props > Material Model > Structural > Nonlinear > Inelastic > RateIndependent > Isotropic Hardening Plasticity > Mises Plasticity > BilinearYield Stss [ 243 ] Tang Mod [ 2E2 ]>Material>Exit ANSYS Toolbar > SAVE_DB1. 4. Mesh the solid model. ANSYS Utility Menu > Plot > Areas ANSYS Main Menu Preprocessor > -Meshing- Size Control-ManualSize-... > -Global- Size > NDIV [ 20 ] ! define the mesh density by # of divisions Preprocessor > -Meshing- Mesh-Areas- Free > Pick All ANSYS Toolbar > SAVE_DBSolution1. Specify load steps and apply force and boundary conditions.Perform two load steps analysis in the solution processor, the first step is a null solution. Thepurpose of this null solution is just to let the graphic display starts from the zero. And second stepused 1.5 * Pres as the applied pressure loading. If the second load step is not large enough to letthe structure go to the plastic range, an even larger load application can be used here. The secondload steps is divided into 10 substeps, which means that in each substep, an increment of 1/10 ofthe total load is applied. ANSYS Utility Menu PlotCtrls > Symbols > [/PBC] [ALL Applied B.C.'s] > [/PSF] [Pressures] Show pres andConvects as [Arrows] > OK ANSYS Main Menu Solution > Analysis Type> Soln Control > Analysis Options [Small Displacement Static]> Time at the end of loadstep [1E-7] > Number of substeps [1] >> Write Items to Result File > All Solution Items> Frequency [Write every N eubstep] where N=[ 1 ]> OK Solution > -Loads- Apply-Structural- Displacements > -Symmetry B.C.- On Lines> [ Left vertical line] > Apply> [ Both Bottom lines] > OK Solution > -Define Loads- Apply-Structural- Pressure > On Lines> [The right vertical line where the forces applied] > OK > VALI [ 0 ] > OK Solution > Load Step Options> Write LS File > [ 1 ] > OK! Load Step 2. The essential boundary conditions carry over to the next stepunless explicitly modified here. Solution > -Define Loads- Apply-Structural- Pressure > On Lines[The right vertical line where the forces applied] > OK > VALI [ 1.5*Pres ] > OK> Soln Control > Time at the end of load step [1.5] > Number of Substeps [10]> Write Items to Result File > Frequency [Write Every N Substep] where N =[ 2 ]> OK Solution > Write LS File > [ 2 ] > OK ANSYS Main Menu > Solution-Solve- From LS Files > LSMIN [ 1 ] LSMAX [ 2 ] > OKIt might take a few minutes to complete the solution.Postprocessing1. Review the results using the time history postprocessor (POST26).We want to plot the time history of the x-displacement at a chosen point. In order to plot the loaddisplacementplot, we need to specify two sets of variables. The first set is time (ANSYS default NVAR1. In this problem, the time is not the physical time but the load factor). The second is the displacementhistory UX at a point, say the left-lower corner of the plate. In the following commands, we assignNVAR 2 for this displacement set. ANSYS main Menu TimeHist Postproc> Settings > Graph... > [XVAR] [Single variable] Single Variable no. [ 2 ] > OK> Define Variables... > Add > Nodal DOF > [Pick the left lower node] > OK> NVAR [ 2 ]Name User-Specified label [ UX ]Item, Comp [ DOF solution ] [ Translation UX ] > OK > Close> List Variables... > NVAR1 [ 2 ] > OK ! to check if this variable is defined. ANSYS Utility Menu PlotCtrls > Style > Graph > Modify Axes > [/AXLAB] X-axis label [ Displacement ][/AXLAB ] Y-axis label [ Load Factor ] > OK TimeHist Postproc >Graph Variables... > NVAR1 [ 1 ] > OKYou can get the displacement-load factor curve here, which is part of your report.

Thermal TransientANSYS Example: Transient Thermal Analysis of a Pipe Support BracketThe section of pipe shown below is a representative section of a longer pipe carrying a hot fluid under pressure. The pipe is supported every 400 mm by a bracket that is welded to the pipe and subsequently attached to the wall. The pipe and bracket are made of 2024-T6 aluminum. The pipe has an outer and inner diameter of 50 mm and 38 mm, respectively. The bracket is attached to the wall with an insulating pad along the base, so there is no heat transfer between the wall and bracket. All dimensions in the figure below are given in mm.The air temperature surrounding the pipe and bracket is 300 K, and the heat transfer (film) coefficient between the air and pipe/bracket is h = 200 W/(m2-K). The pipe and bracket also have a uniform initial temperature of 300 K. Fluid at a temperature of 450 K then begins flowing through the pipe, and the heat transfer (film) coefficient between the pipe and fluid ish = 1200 W/ (m2-K).In this example, ANSYS will be used to perform a transient thermal analysis on the pipe and bracket. The temperature in the pipe and bracket will be examined over a period of 20 seconds after the fluid begins flowing through the pipe. A contour plot of the temperature distribution can be generated at any point in time, and temperature vs. time plots can be generated for any node. Animation can also be used to display the temperature distribution in the entire part as a function of time. The analysis will be performed using 10 node, 3D thermal elements (SOLID 87).

The following thermal properties of 2024-T6 aluminum are required for the analysis.

The density of the aluminum alloy is 2770 kg/m3, which is constant within the temperature range considered here.ANSYS Analysis:Start ANSYS Product Launcher, set the Working Directory to C:\temp, define Job Name as Pipe_Bracket, and click Run. Then define Title and Preferences.Utility Menu .. File .. Change Title .. Enter Transient Thermal Analysis of a Pipe Bracket .. OKANSYS Main Menu .. Preferences .. Preferences for GUI Filtering .. Select Thermal and h-method .. OKEnter the Preprocessor to define the model geometry:Define Element Type and Material Properties. Since many of the Material Properties are temperature-dependent, we must specify the temperature units and define the properties at several temperatures.ANSYS Main Menu .. Preprocessor .. Element Type .. Add/Edit/Delete .. Add .. Thermal Solid Tet 10 node 87 (define Element type reference number as 1) .. OK .. CloseANSYS Main Menu .. Preprocessor .. Material Props .. Temperature Units .. Kelvin or RankinANSYS Main Menu .. Preprocessor .. Material Props .. Material Models .. Double Click Thermal .. Conductivity .. Isotropic .. Add Temperature .. Enter 100 for T1, 65 for KXX .. Enter 200 for T2, 163 for KXX .. Add Temperature .. Enter 300 for T3, 177 for KXX .. Add Temperature .. Enter 400 for T4, 186 for KXX .. Add Temperature .. Enter 600 for T5, 186 for KXX .. OK .. Double Click Specific Heat .. Repeat the process with values of 473, 787, 875, 925, and 1042 for C at each Temperature .. OK .. Double Click Density .. Enter 2770 for DENS without specifying a temperature (density is constant) .. OK .. Click Exit (under Material)Begin creating the geometry by defining a Hollow Cylinder (Volume) for the pipe.ANSYS Main Menu .. Preprocessor .. Modeling .. Create .. Volumes .. Cylinder .. Hollow Cylinder .. Enter 0 for WP X, 0 for WP Y, 0.019 for Rad-1, 0.025 for Rad-2 and 0.4 for Depth .. OKChange to an Isotropic View using the Plot Menu.The support bracket will be created by defining two Rectangles (Areas), deleting the Area that overlaps the Cylinder, and then extruding the Areas into a Volume. First, the WorkPlane must be moved.Utility Menu .. WorkPlane .. Offset WP to XYZ Locations + .. Type 0, 0, -0.1625 in the Command Line of the Offset WP window (Global Cartesian coordinates) .. OKANSYS Main Menu .. Preprocessor .. Modeling .. Create .. Areas .. Rectangle .. By Dimensions .. Enter 0.0075 and 0.0075 for X1 and X2, and 0.02 and 0.085 for Y1 and Y2, respectively .. Apply .. Enter 0.0075 and 0.0325 for X1 and X2, and 0.085 and 0.1 for Y1 and Y2, respectively .. OKANSYS Main Menu .. Preprocessor .. Modeling .. Operate .. Booleans .. Divide .. Area by Area .. Select (with the mouse) the rectangular Area to be divided .. OK .. Select the outer Area of the Cylinder .. OKANSYS Main Menu .. Preprocessor .. Modeling .. Delete .. Area and Below .. Select the remaining Area to be deleted .. OKUtility Menu .. Plot .. ReplotANSYS Main Menu .. Preprocessor .. Modeling .. Operate .. Booleans .. Add .. Areas .. Select (with the mouse) the two rectangular Areas .. OKANSYS Main Menu .. Preprocessor .. Modeling .. Operate .. Extrude .. Areas .. By XYZ Offset .. Select the Area that defines the bracket .. OK .. Enter 0.075 for DZ .. OKUtility Menu .. Plot .. ReplotANSYS Main Menu .. Preprocessor .. Modeling .. Operate .. Booleans .. Add .. Volumes .. Select Pick AllUtility Menu .. Plot .. ReplotThe component will now be Free Meshed with Tetrahedral Elements using a Global Size (Element edge length) of 6 mm. Then save the Database.ANSYS Main Menu .. Preprocessor .. Meshing .. MeshTool .. Under Size Controls: Global click Set .. Enter 0.006 for Element edge length .. OK .. Under Mesh: select Volumes, Tet and Free .. Click Mesh .. Select (with the mouse) the Volume .. OKANSYS Toolbar .. SAVE_DBEnter the Solution Menu to define boundary conditions and loads and run the analysis:ANSYS Main Menu .. Solution .. Analysis Type .. New Analysis .. Select Transient .. OK .. Select Full for Solution method .. OKThe initial temperature of the pipe/bracket must first be defined.ANSYS Main Menu .. Solution .. Define Loads .. Apply .. Initial Condition .. Define .. Select Pick All .. Select Temp for DOF to be specified.. Enter 300 for VALUE .. OKNow apply the Thermal Loads (Convections) to the pipe and bracket. The Film Coefficient on the inside of the pipe is 1200 (fluid temperature is 450), and the Film Coefficient on the outside of the pipe is 200 (air temperature is 300). Be careful to select the correct Areas when applying the Loads. It may be helpful to list the Areas to determine which Lines define each Area.Utility Menu .. Plot .. AreasUtility Menu .. Plot Ctrls .. Numbering .. Click Area numbers and Line numbers On .. OKANSYS Main Menu .. Solution .. Define Loads .. Apply .. Thermal .. Convection .. On Areas .. Select (with the mouse) the Areas defining the inside of the pipe (A5 and A6 in this case) .. OK .. Enter 1200 for Film coefficient and 450 for Bulk temperature .. OKANSYS Main Menu .. Solution .. Define Loads .. Apply .. Thermal .. Convection .. On Areas .. Select the outside Areas, except the Area which is insulated (A3, A16, A1, A2, A7, A13, A14, A8, A9, A10, and A11) .. OK .. Enter 200 for Film coefficient and 300 for Bulk temperature .. OKSince the problem is nonlinear (in time and temperature), several options must be defined for the nonlinear solver. Specifically, Time Step Options must be defined. The transient solution will be performed for 20 seconds, using an initial Time Step Size of 1 second. Since the temperatures are applied instantly (rather than gradually), they will be applied as Stepped, rather than Ramped Boundary Conditions. Automatic Time Stepping will be activated, as this may reduce the Solution time. Minimum and Maximum Time Step Sizes of 0.5 and 4 seconds will be defined.ANSYS Main Menu .. Solution .. Load Step Opts .. Time/Frequency .. Time Time Step .. Enter 20 for TIME, 1 for DELTIM, select Stepped for KBC, click Automatic time stepping ON, enter 0.5 for Minimum time step size and 4 for Maximum time step size (if the temperature distribution for every second is needed then this number will be set to 1) .. OKDefine the frequency with which results will be written to the Database and Results File. Then save the Database and initiate the Solution.ANSYS Main Menu .. Solution .. Load Step Opts .. Output Ctrls .. DB/Results File .. Select All items to be controlled, and select Every substep for FREQ (File write frequency) .. OKANSYS Toolbar .. SAVE_DBANSYS Main Menu .. Solution .. Solve .. Current LS .. OK .. Close the information window when solution is done .. Close the /STATUS Command windowEnter the General Postprocessor to examine the results:A Contour Plot of the nodal temperatures at any substep (time increment) can be generated by reading the appropriate set of results from the Results File.ANSYS Main Menu .. General Postproc .. Results Summary .. CloseANSYS Main Menu .. General Postproc .. Read Results .. First SetANSYS Main Menu .. General Postproc .. Plot Results .. Contour Plot .. Nodal Solution .. Select DOF Solution and Nodal Temperature .. OKANSYS Main Menu .. General Postproc .. Read Results .. Next SetANSYS Main Menu .. General Postproc .. Plot Results .. Contour Plot .. Nodal Solution .. Select DOF Solution and Nodal Temperature .. OK*** This procedure can be repeated until all desired substeps have been viewed. ***The temperature of a particular node can be viewed on the plot, or the nodal temperatures can be listed and saved to a file for further analysis.ANSYS Main Menu .. General Postproc .. Query Results .. Subgrid Solu .. Select (with the mouse) various Nodes to see the temperaturesANSYS Main Menu .. General Postproc .. List Results .. Nodal Solution .. Select DOF Solution and Nodal Temperature .. OKThe transient temperature distribution can also be Animated over the 20 second time period.Utility Menu .. Plot Ctrls .. Animate .. Over Time .. Set Number of animation frames to the desired value (20 used here), select Current Load Stp (the entire transient solution solved in this example comprises one Load Step), set the Animation time delay to the desired value (0.5 s used here) with Auto contour scaling On, and select DOF solution and Temperature TEMP .. OKA Temperature vs. Time Plot for any node can be generated within the Time History Postprocessor using the following procedure.ANSYS Main Menu .. TimeHist Postpro .. Define Variables .. Add .. Select Nodal DOF result .. OK .. Select (with the mouse) the desired node .. OK .. Click OK to close window .. CloseANSYS Main Menu .. Time Hist Postpro .. Graph Variables .. Enter 2 (since the selected node is set 2) for NVAR1 (1st variable to graph) .. OKThe analysis should be rerun with a finer mesh to check for convergence of the solution. The procedure will be the same, but a smaller Global Element Size will be defined. If the results (nodal temperatures) using the two meshes are in close agreement, the model can be considered to have small discretization error.