== Problem Description == A simple composite laminated beam as shown in Fig.1 is clamped at x=0, and subjected to a 10 kN point force in x-direction and a 10 kN∙mm moment in y-direction at x=1m. Dimensions of the beam and layup of the laminate are given in Fig.1. The laminate is made of 8 layers, each of a continuous fiber reinforced composite. The lamina constants are E_1 = 110.5 \text{GPa}, E_2 = E_3 = 13.64 \text{GPa}, G_{12} = G_{13} = 3.92 \text{GPa}, G_{23} = 3.26 \text{GPa}, \nu_{12} = \nu_{13} = 0.329, \nu_{23} = 0.400. [[Image(Fig1_8layerBeam.png, 600px)]] ---- == Software Used == This wiki page is based on [https://cdmhub.org/tools/scstandard/ Gmsh4SC] version 2.0. [[br]] A previous resource ([https://cdmhub.org/resources/1280 Gmsh4SC Tutorial #1]) including documents and Gmsh files, and the video are based on Gmsh4SC version 1.3.[[br]][[br]] '''__Updates in tutorial for Gmsh4SC ver. 2.0:__''' [[br]] • Draw point and line elements using commands [[br]] • !CalculiX boundary conditions [[br]] ---- == Companion Video == Please refer to the !YouTube video by [https://cdmhub.org/members/1776 Xin Liu] showing the solution procedure using '''Gmsh4SC version 1.3'''. [[Video(https://www.youtube.com/watch?v=iyybuMYxGhA&list=PLGwp8OYDfmxF2fgn3p2KZZscnVX4c8Vve&index=1)]] ---- == Solution Procedure == Below describes the step-by-step procedure you followed to solve the problem. It is better to accompany this document with the companion youtube video. === 1. Input Laminate Geometry and Lamina Material Properties === The structure genome (SG) for this laminated beam is the cross section of the laminate beam, because there is no heterogeneity along beam reference line. Here we input material properties of each layer using orthotropic model, and geometry information directly generated by laminate layup code. ==== 1.1 Create a new .geo file ==== * Click `File` - `New` * Change the filename in `/path/to/current/session/Filename.geo` (give a name other than Untitled) [[Image(Fig2_newfile.png, 400px)]] ==== 1.2 Input lamina properties ==== * Click `Material` - `Thermoelastic` - `Orthotropic` * Input the 9 lamina constants * Click `Add` - `Close` - `Exit` [[Image(Fig3_MaterialProp.png, 600px)]] ==== 1.3 Input laminate geometry by composite layup ==== * Click `Geometry` - `Common SG` - `2D SG` - `Beam sections` * Click `Composites` - `layup define` - `Fast generate` [[Image(Fig4_GenLaminate.png, 530px)]] * Material: `1 -- MAT1` (for lamina) * Layup: `[0/90/0/90]s` (as shown in Fig.1) * ply thickness: `5` (unit: mm, as total thickness for 8 layers is 0.04m) [[File(Fig5_GenLaminate_cont.gif)]] * Click `Add` - `Close`, and get back to the previous window showing Beam Section - Composites * Width: `180` (unit: mm, as shown in Fig.1), and click `Add` [[Image(Fig6_Width.png, 270px)]] The geometry of the 8-layer laminate is generated. [[br]] [[Image(Fig7_8layerGeofinished.png, 600px)]] === 2. Homogenization: Effective SG Properties Calculation === Now consider the 8 layers as a homogeneous material, we calculate the effective stiffness matrix of the SG by Homogenization command. ==== 2.1 Mesh ==== * Click `Mesh` - `Mesh control` * In the `General` tab, tick `Recombine all triangular meshes`, input Element size factor: `0.1`, then close this window [[Image(Fig8_MeshCtrl.png, 380px)]] * Click `Generate 2D mesh` - `Generate`, and you'll see the mesh generated for 8 layers * Click `Set order 2` [[Image(Fig9_8layersMeshed.png, 600px)]] [[br]]If you want to change mesh properties, e.g., change element size factor, you may reopen Mesh control, input the new number, and then click `Generate` again to get the new mesh. ==== 2.2 Homogenization ==== * Click `SwiftComp` - `Homogenization` - `Beam Model` * No need to change or input anything in this case * Click `Save`, wait for ~10 seconds, click `Run` [[Image(Fig10_homogenization.png, 500px)]] ==== 2.3 Check results and save files ==== * Once the homogenization finishes, a plain text file `Filename.msh.k` containing effective stiffness and compliance matrices of the laminate will pop up. [[Image(Fig11_8layerResults.png, 580px)]] * You may download the files for your own record by the following methods. # __Use Import/Export tool on cdmhub.__ The tool is launched by default for every !SwiftComp session. [[br]] [[Image(Fig12_download.png, 130px)]] # __Use any FTP tool__ * host: `cdmhub.org` * username: if you forgot your username, it can be found in many ways. For example, if you're logged on cdmhub webpage, on the upper right corner says "Logged in (`your_Username`)". Or, in any launched swiftcomp session, click the bottom grey bar or click `Tools` - `Message Console`, to show message console. On the 9th line it says "Info: Home directory: /home/cdmhub/ `your_Username` /". * password: same as your log in password to cdmhub webpage. * remote site address: `/home/cdmhub/your_Username/data/sessions/5-digit_current_session_number` * current session number can be found above the !SwiftComp window, or in the title of the webpage, or in Dashboard - Activity. # __Use `sftp` command line__ (the following commands work for Mac - Terminal) * `sftp your_Username@cdmhub.org` * `get /home/cdmhub/your_Username/data/sessions/5-digit_current_session_number/Filename.msh.k local_folder_path` * feel free to use `help` or `?` to check all available commands * I usually download these files after homogenization: *`Filename.geo`: geometry without mesh *`Filename.msh`: geometry and mesh informations *`Filename.msh.k`: results after homogenization === 3. Macroscopic Analysis for the Beam === ==== 3.1 Create beam geometry ==== * Click `File` - `New`, and input a different filename, e.g., `/home/.../Beam.geo`, same as in Fig.2 * For Gmsh4SC version 2.0, you need to input the beam geometry by commands * Click `Input control` - `Edit file` * Manually add the following three lines: [[br]] `Point(1) = {0,0,0,1.0}`: create a point of position {x,y,z} = {0,0,0}, mesh size = 1.0 [[br]] `Point(2) = {0,0,1000,1.0}`: create a point at x=1000 (unit: mm) [[br]] `Line(1) = {1,2}`: create a line connecting the two points.[[br]] * Click `Save`, then close text editor [[Image(Fig13_BeamgeoCmd.png, 400px)]] * Click `Reload`, and you will see the beam geometry on the screen. [[Image(Fig14_Beamgeo.png, 430px)]] ==== 3.2 Input effective SG properties for the beam ==== * Click `Geometry` - `Assign structural properties` - `Beam`, Click `Close` [[Image(Fig15_AssignBeamProp.png, 400px)]] * Click on the red line, Press `e` and `q` [[Image(Fig16_AssignBeamProp_2.png, 350px)]] * In the pop-up browser window, choose `Filename.msh.k` (the results file in Fig.11 after Homogenization step) [[Image(Fig17_AssignBeamProp_3.png, 400px)]] [[br]]Now the beam is considered as a homogeneous material with effective material properties given in Fig.11. ==== 3.3 Generate mesh for the beam ==== * Change the elementary mesh size back to 1.0: Click `Mesh` - `Mesh control`, input Element size factor: `1.0` * Click `Mesh` - `Generate 1D mesh` - `Generate` [[Image(Fig18_BeamMesh.png, 400px)]] ==== 3.4 Input file for !CalculiX ==== * Click `CalculiX` - `Write INP file`, to create the input file (Filename.inp) for [http://www.dhondt.de CalculiX] [[Image(Fig19_INPfile.png, 400px)]] * Click `Import structural properties`, to input mesh information in the INP file [[Image(Fig20_importstruct.png, 400px)]] * Click `Define step`, to check the input file and add boundary conditions manually [[Image(Fig21_openINPfile.png, 600px)]] [[br]] These are the {x,y,z} values for each mesh node. Notice that Node#1 and Node#2 are the two ends, x=0 and x=1000, while other nodes are increasing by step 1 since the size factor is 1. * Input the following 8 lines at the end of the opened file: {{{ *BOUNDARY 1,1,6 *STEP *STATIC *CLOAD 2,1,10000 2,5,10000 *END STEP }}} [[Image(Fig22_inputBC.png, 600px)]] * Click `Save`, close Geany editor, click `Run`. [[Image(Fig23_RunCCX.png, 400px)]] [[br]] * If you're not familiar with !CalculiX, the commands you just input have the following meanings: * `*BOUNDARY`[[br]] `1,1,6`[[br]] `1,_,_` means Node#1 (x=0) [[br]] `_,1,6` means fixed degree of freedom 1 through 6. [[br]] Degree of freedom 1,2,3: translation in x,y,z direction; [[br]] Degree of freedom 4,5,6: rotation about x,yz, axis. [[br]] * `*CLOAD`[[br]] `2,1,10000`[[br]] `2,5,10000` [[br]] `CLOAD` means concentrated load [[br]] `2,_,_` means Node#2 (x=1000) [[br]] `_,1,10000` means degree of freedom 1 (translation in x direction), 10000N force [[br]] `_,5,10000` means degree of freedom 5 (rotation about y axis), 10000N∙mm moment [[br]] * For other types of boundary conditions, you may refer to [http://www.dhondt.de/ccx_2.14.pdf CalculiX documentation]. * Detailed introduction for !CalculiX commands can be found in Chapter 4 of the [https://cdmhub.org/resources/1342/download/Gmsh4SCManual.pdf Gmsh4SC User Manual]. ==== 3.5 Check results ==== * Click `Results`, and you may navigate the `Filename_sc.dat` file to check global responses of the beam, including Displacement (u_1, u_2, u_3), Rotation (\theta_1, \theta_2, \theta_3, Strain (\gamma_{11}, \kappa_1, \kappa_2, \kappa_3), and Stress (F_1, M_1, M_2, M_3) at nodes (x=0 through 1000) and at Gauss points. [[Image(Fig24_BeamResult.png, 600px)]] * Now you can find the global responses at each position of the beam (e.g., x = 500 mm) referring to the Node number (e.g., Node#502). [[Image(Fig25_Node502.png, 300px)]] * At x = 500 mm (Node#502), the beam global responses are found to be:[[br]] u_1=1.110338E-02, u_2=6.677899E-18(=0), u_3=-1.611413E-02[[br]] \theta_1=-1.770997E-21(=0), \theta_2=6.445670E-05, \theta_3=2.671169E-20(=0), [[br]] \gamma_{11}=2.220675E-05, \kappa_1=-3.542017E-24(=0), \kappa_2=1.289142E-07, \kappa_3=5.342389E-23(=0), [[br]] F_1=1.000000E+04, M_1=3.097452E-23(=0), M_2=1.000000E+04, M_3=-5.376268E-16(=0) [[br]] [[Image(Fig26_displacement.png, 350px)]][[Image(Fig27_rotation.png, 350px)]][[Image(Fig28_strain.png, 400px)]][[Image(Fig29_loading.png, 400px)]] [[br]] * It's more convenient to download the `Filename_sc.dat` file on your local computer and search for these values. See section 2.3 of this wiki page for download instructions. === 4. Dehomogenization: Local Stress Distribution === With the strain at each node given by !CalculiX results, for a specific node (e.g., Node#502 at x=500 mm), we can check the local stresses in the 8 lamina layers. ==== 4.1 Reopen microstructure geometry file ==== * Click `File` - `Open`, and choose the `the_8-layer_laminate_file.geo` [[Image(Fig30_OpenGeo.png, 300px)]] * If the 8 layer laminate geometry does not appear on the screen, it is possible that it's outside the current view. You may bring it back by clicking `Tools` - `Manipulator` - `Reset` [[Image(Fig31_resetview.png, 600px)]] ==== 4.2 Dehomogenization ==== * Click `SwiftComp` - `Dehomogenization` - `Beam Model` * Input displacement (v1, v2, v3) and strain (e11, k1, k2, k3) for Node#502. (values are given in section 3.5) [[Image(Fig32_dehomo.png, 600px)]] * Click `Save` - `Run`, the results are shown on the screen with color bars. You may check the displacement, strain and stress results in the `Post-processing` panel. [[Image(Fig33_dehomoResults.png, 600px)]] * Stress \sigma_{11} of each layer is given in the following figure. [[Image(Fig34_s11.png, 600px)]] * Numerical results can be found in `filenameVIEW.msh`. For example, the \sigma_{11} results are given for each node. [[Image(Fig35_s11numbers.png, 600px)]] ==== 4.3 Check results along a line (optional) ==== * To get the stress values \sigma_{11} along the cross section (e.g., x=0, y varies from -20 to +20), you may use the CutGrid plugin. * Click on the triangle beside S11, then click `Plugin`. * Select `CutGrid`, `View[10]` (S11), and input `X0 = 0, Y0 = -20, Z0 = 0` and `X1 = 0, Y1 = 20, Z1 = 0`. X2 Y2 Z2 can be any number as we only need two points to define a line. * !NumPointsU = `100` which is the number of points from {X0, Y0, Z0} to {X1, Y1, Z1}. * !NumPointsV = `1` which is the number of points from {X0, Y0, Z0} to {X2, Y2, Z2}. * Position of these three points are labeled on the geometry [[Image(Fig36_CutGrid.png, 600px)]] * Click `Run`, and a new view will appear that only contains S11 along x=0, y= -20 to +20. You may export the new view by clicking the triangle - `Export`. Numerical results including {x,y,z} of each node and S11 values are recorded in the exported file. [[Image(Fig37_S11acrossY.png, 600px)]] ---- == References == # Xin Liu; Wenbin Yu (2017), "Gmsh4SC Tutorial #1: Analysis of a Composite Laminated Beam," https://cdmhub.org/resources/1280. # [https://gmsh.info/doc/texinfo/gmsh.html#Geometry-commands Gmsh documentation for geometry commands input] # [https://cdmhub.org/resources/1342/download/Gmsh4SCManual.pdf Xin Liu; Wenbin Yu (2017), Gmsh4SC User Manual]