DEMO_febio_0004_beam_twist
Below is a demonstration for:
- Building geometry for a beam with hexahedral elements
- Defining the boundary conditions
- Coding the febio structure
- Running the model
- Importing and visualizing the displacement results
Contents
- Keywords
- Plot settings
- Control parameters
- Creating model geometry and mesh
- Create rigid body end plate for rotation constraint
- Defining the boundary conditions
- Defining the FEBio input structure
- Quick viewing of the FEBio input file structure
- Exporting the FEBio input file
- Running the FEBio analysis
- Import FEBio results
Keywords
- febio_spec version 4.0
- febio, FEBio
- beam torsion twist loading
- prescribed displacement boundary condition
- hexahedral elements, hex8, hex20
- beam, rectangular
- static, solid, multi-step
- hyperelastic, Ogden
- displacement logfile
- stress logfile
clear; close all; clc;
Plot settings
fontSize=20; faceAlpha1=0.8; markerSize=40; markerSize2=20; lineWidth=3;
Control parameters
% Path names defaultFolder = fileparts(fileparts(mfilename('fullpath'))); savePath=fullfile(defaultFolder,'data','temp'); % Defining file names febioFebFileNamePart='tempModel'; febioFebFileName=fullfile(savePath,[febioFebFileNamePart,'.feb']); %FEB file name febioLogFileName=[febioFebFileNamePart,'.txt']; %FEBio log file name febioLogFileName_disp=[febioFebFileNamePart,'_disp_out.txt']; %Log file name for exporting displacement %Specifying dimensions and number of elements beamWidth=10; sampleWidth=beamWidth; %Width sampleThickness=4*beamWidth; %Thickness sampleHeight=beamWidth; %Height pointSpacings=3*ones(1,3); %Desired point spacing between nodes numElementsWidth=round(sampleWidth/pointSpacings(1)); %Number of elemens in dir 1 numElementsThickness=round(sampleThickness/pointSpacings(2)); %Number of elemens in dir 2 numElementsHeight=round(sampleHeight/pointSpacings(3)); %Number of elemens in dir 3 elementType='hex20'; %'hex8' %Define applied torsion angle alphaRotTotal=2*pi;%0.5*pi; %Total twist angle numSteps=50; %Number of steps %Material parameter set c1=1e-3; %Shear-modulus-like parameter m1=2; %Material parameter setting degree of non-linearity k_factor=1e2; %Bulk modulus factor k=c1*k_factor; %Bulk modulus % FEA control settings numTimeSteps=30; %Number of time steps desired max_refs=25; %Max reforms max_ups=0; %Set to zero to use full-Newton iterations opt_iter=6; %Optimum number of iterations max_retries=5; %Maximum number of retires dtmin=(1/numTimeSteps)/100; %Minimum time step size dtmax=1/numTimeSteps; %Maximum time step size symmetric_stiffness=1; runMode='external';% 'internal' or 'external'
Creating model geometry and mesh
A box is created with tri-linear hexahedral (hex8) elements using the hexMeshBox function. The function offers the boundary faces with seperate labels for the top, bottom, left, right, front, and back sides. As such these can be used to define boundary conditions on the exterior.
% Create a box with hexahedral elements beamDimensions=[sampleWidth sampleThickness sampleHeight]; %Dimensions beamElementNumbers=[numElementsWidth numElementsThickness numElementsHeight]; %Number of elements outputStructType=2; %A structure compatible with mesh view [meshStruct]=hexMeshBox(beamDimensions,beamElementNumbers,outputStructType); %Access elements, nodes, and faces from the structure E=meshStruct.elements; %The elements V=meshStruct.nodes; %The nodes (vertices) Fb=meshStruct.facesBoundary; %The boundary faces Cb=meshStruct.boundaryMarker; %The "colors" or labels for the boundary faces elementMaterialIndices=ones(size(E,1),1); %Element material indices if strcmp(elementType,'hex20') [E,V,~,Fb]=hex8_hex20(E,V,{},Fb); meshStruct.elements=E; meshStruct.nodes=V; meshStruct.Fb=Fb; quadType='quad8'; else quadType='quad4'; end
Plotting model boundary surfaces and a cut view
hFig=cFigure; subplot(1,2,1); hold on; title('Model boundary surfaces and labels','FontSize',fontSize); hp=gpatch(Fb,V,Cb,'k',faceAlpha1); hp.Marker='.'; hp.MarkerSize=markerSize2; colormap(gjet(6)); icolorbar; axisGeom(gca,fontSize); hs=subplot(1,2,2); hold on; title('Cut view of solid mesh','FontSize',fontSize); optionStruct.hFig=[hFig hs]; meshView(meshStruct,optionStruct); axisGeom(gca,fontSize); drawnow;
Create rigid body end plate for rotation constraint
Fr=Fb(Cb==3,:); %The faces for the beam end %Nodes part of the rigid body indRigid=unique(Fr(:));
Defining the boundary conditions
The visualization of the model boundary shows colors for each side of the cube. These labels can be used to define boundary conditions.
%Define supported node set bcSupportList=unique(Fb(Cb==4,:)); %Node set part of selected face
Visualizing boundary conditions. Markers plotted on the semi-transparent model denote the nodes in the various boundary condition lists.
hf=cFigure; title('Boundary conditions','FontSize',fontSize); xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on; gpatch(Fb,V,'w','k',0.5); hl(1)=plotV(V(bcSupportList,:),'k.','MarkerSize',markerSize); hl(2)=gpatch(Fr,V,'rw','k',1); plotV(V(indRigid,:),'r.','MarkerSize',markerSize); legend(hl,{'BC support','Rigid body'}); axisGeom(gca,fontSize); camlight headlight; drawnow;
Defining the FEBio input structure
See also febioStructTemplate and febioStruct2xml and the FEBio user manual.
%Get a template with default settings [febio_spec]=febioStructTemplate; %febio_spec version febio_spec.ATTR.version='4.0'; %Module section febio_spec.Module.ATTR.type='solid'; %Control section febio_spec.Control.analysis='STATIC'; febio_spec.Control.time_steps=numTimeSteps; febio_spec.Control.step_size=1/numTimeSteps; febio_spec.Control.solver.max_refs=max_refs; febio_spec.Control.solver.qn_method.max_ups=max_ups; febio_spec.Control.solver.symmetric_stiffness=symmetric_stiffness; febio_spec.Control.time_stepper.dtmin=dtmin; febio_spec.Control.time_stepper.dtmax=dtmax; febio_spec.Control.time_stepper.max_retries=max_retries; febio_spec.Control.time_stepper.opt_iter=opt_iter; %Material section materialName1='Material1'; febio_spec.Material.material{1}.ATTR.name=materialName1; febio_spec.Material.material{1}.ATTR.type='Ogden'; febio_spec.Material.material{1}.ATTR.id=1; febio_spec.Material.material{1}.c1=c1; febio_spec.Material.material{1}.m1=m1; febio_spec.Material.material{1}.c2=c1; febio_spec.Material.material{1}.m2=-m1; febio_spec.Material.material{1}.k=k; materialName2='Material2'; febio_spec.Material.material{2}.ATTR.name=materialName2; febio_spec.Material.material{2}.ATTR.type='rigid body'; febio_spec.Material.material{2}.ATTR.id=2; febio_spec.Material.material{2}.density=1; febio_spec.Material.material{2}.center_of_mass=mean(V(indRigid,:),1); %Mesh section % -> Nodes febio_spec.Mesh.Nodes{1}.ATTR.name='nodeSet_all'; %The node set name febio_spec.Mesh.Nodes{1}.node.ATTR.id=(1:size(V,1))'; %The node id's febio_spec.Mesh.Nodes{1}.node.VAL=V; %The nodel coordinates % -> Elements partName1='Part1'; febio_spec.Mesh.Elements{1}.ATTR.name=partName1; %Name of this part febio_spec.Mesh.Elements{1}.ATTR.type=elementType; %Element type febio_spec.Mesh.Elements{1}.elem.ATTR.id=(1:1:size(E,1))'; %Element id's febio_spec.Mesh.Elements{1}.elem.VAL=E; %The element matrix partName2='Part2'; febio_spec.Mesh.Elements{2}.ATTR.name=partName2; %Name of this part febio_spec.Mesh.Elements{2}.ATTR.type=quadType; %Element type febio_spec.Mesh.Elements{2}.elem.ATTR.id=size(E,1)+(1:1:size(Fr,1))'; %Element id's febio_spec.Mesh.Elements{2}.elem.VAL=Fr; %The element matrix % -> NodeSets nodeSetName1='bcSupportList'; febio_spec.Mesh.NodeSet{1}.ATTR.name=nodeSetName1; febio_spec.Mesh.NodeSet{1}.VAL=mrow(bcSupportList); %MeshDomains section febio_spec.MeshDomains.SolidDomain.ATTR.name=partName1; febio_spec.MeshDomains.SolidDomain.ATTR.mat=materialName1; febio_spec.MeshDomains.ShellDomain.ATTR.name=partName2; febio_spec.MeshDomains.ShellDomain.ATTR.mat=materialName2; %Boundary condition section % -> Fix boundary conditions febio_spec.Boundary.bc{1}.ATTR.name='zero_displacement_xyz'; febio_spec.Boundary.bc{1}.ATTR.type='zero displacement'; febio_spec.Boundary.bc{1}.ATTR.node_set=nodeSetName1; febio_spec.Boundary.bc{1}.x_dof=1; febio_spec.Boundary.bc{1}.y_dof=1; febio_spec.Boundary.bc{1}.z_dof=1; %Rigid section %Rigid section % ->Rigid body fix boundary conditions febio_spec.Rigid.rigid_bc{1}.ATTR.name='RotFix_1'; febio_spec.Rigid.rigid_bc{1}.ATTR.type='rigid_fixed'; febio_spec.Rigid.rigid_bc{1}.rb=2; febio_spec.Rigid.rigid_bc{1}.Rx_dof=1; febio_spec.Rigid.rigid_bc{1}.Ry_dof=1; febio_spec.Rigid.rigid_bc{1}.Rz_dof=1; febio_spec.Rigid.rigid_bc{1}.Ru_dof=1; % febio_spec.Rigid.rigid_bc{1}.Rv_dof=1; febio_spec.Rigid.rigid_bc{1}.Rw_dof=1; % ->Rigid body prescribe boundary conditions febio_spec.Rigid.rigid_bc{2}.ATTR.name='RigidPrescribe'; febio_spec.Rigid.rigid_bc{2}.ATTR.type='rigid_rotation'; febio_spec.Rigid.rigid_bc{2}.rb=2; febio_spec.Rigid.rigid_bc{2}.dof='Rv'; febio_spec.Rigid.rigid_bc{2}.value.ATTR.lc=1; febio_spec.Rigid.rigid_bc{2}.value.VAL=alphaRotTotal; febio_spec.Rigid.rigid_bc{2}.relative=0; %LoadData section % -> load_controller febio_spec.LoadData.load_controller{1}.ATTR.name='LC_1'; febio_spec.LoadData.load_controller{1}.ATTR.id=1; febio_spec.LoadData.load_controller{1}.ATTR.type='loadcurve'; febio_spec.LoadData.load_controller{1}.interpolate='LINEAR'; %febio_spec.LoadData.load_controller{1}.extend='CONSTANT'; febio_spec.LoadData.load_controller{1}.points.pt.VAL=[0 0; 1 1]; %Output section % -> log file febio_spec.Output.logfile.ATTR.file=febioLogFileName; febio_spec.Output.logfile.node_data{1}.ATTR.file=febioLogFileName_disp; febio_spec.Output.logfile.node_data{1}.ATTR.data='ux;uy;uz'; febio_spec.Output.logfile.node_data{1}.ATTR.delim=',';
Quick viewing of the FEBio input file structure
The febView function can be used to view the xml structure in a MATLAB figure window.
febView(febio_spec); %Viewing the febio file
Exporting the FEBio input file
Exporting the febio_spec structure to an FEBio input file is done using the febioStruct2xml function.
febioStruct2xml(febio_spec,febioFebFileName); %Exporting to file and domNode
Running the FEBio analysis
To run the analysis defined by the created FEBio input file the runMonitorFEBio function is used. The input for this function is a structure defining job settings e.g. the FEBio input file name. The optional output runFlag informs the user if the analysis was run succesfully.
febioAnalysis.run_filename=febioFebFileName; %The input file name febioAnalysis.run_logname=febioLogFileName; %The name for the log file febioAnalysis.disp_on=1; %Display information on the command window febioAnalysis.runMode=runMode; [runFlag]=runMonitorFEBio(febioAnalysis);%START FEBio NOW!!!!!!!!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
--------> RUNNING/MONITORING FEBIO JOB <-------- 20-Apr-2023 10:38:12
FEBio path: /home/kevin/FEBioStudio2/bin/febio4
# Attempt removal of existing log files 20-Apr-2023 10:38:12
* Removal succesful 20-Apr-2023 10:38:12
# Attempt removal of existing .xplt files 20-Apr-2023 10:38:12
* Removal succesful 20-Apr-2023 10:38:12
# Starting FEBio... 20-Apr-2023 10:38:12
Max. total analysis time is: Inf s
* Waiting for log file creation 20-Apr-2023 10:38:13
Max. wait time: 30 s
* Log file found. 20-Apr-2023 10:38:13
# Parsing log file... 20-Apr-2023 10:38:13
number of iterations : 8 20-Apr-2023 10:38:13
number of reformations : 8 20-Apr-2023 10:38:13
------- converged at time : 0.0333333 20-Apr-2023 10:38:13
number of iterations : 8 20-Apr-2023 10:38:14
number of reformations : 8 20-Apr-2023 10:38:14
------- converged at time : 0.0622455 20-Apr-2023 10:38:14
number of iterations : 7 20-Apr-2023 10:38:14
number of reformations : 7 20-Apr-2023 10:38:14
------- converged at time : 0.0873288 20-Apr-2023 10:38:14
number of iterations : 6 20-Apr-2023 10:38:14
number of reformations : 6 20-Apr-2023 10:38:14
------- converged at time : 0.110576 20-Apr-2023 10:38:14
number of iterations : 6 20-Apr-2023 10:38:14
number of reformations : 6 20-Apr-2023 10:38:14
------- converged at time : 0.133824 20-Apr-2023 10:38:14
number of iterations : 6 20-Apr-2023 10:38:14
number of reformations : 6 20-Apr-2023 10:38:14
------- converged at time : 0.157071 20-Apr-2023 10:38:14
number of iterations : 6 20-Apr-2023 10:38:14
number of reformations : 6 20-Apr-2023 10:38:14
------- converged at time : 0.180318 20-Apr-2023 10:38:14
number of iterations : 6 20-Apr-2023 10:38:15
number of reformations : 6 20-Apr-2023 10:38:15
------- converged at time : 0.203566 20-Apr-2023 10:38:15
number of iterations : 6 20-Apr-2023 10:38:15
number of reformations : 6 20-Apr-2023 10:38:15
------- converged at time : 0.226813 20-Apr-2023 10:38:15
number of iterations : 6 20-Apr-2023 10:38:15
number of reformations : 6 20-Apr-2023 10:38:15
------- converged at time : 0.250061 20-Apr-2023 10:38:15
number of iterations : 6 20-Apr-2023 10:38:15
number of reformations : 6 20-Apr-2023 10:38:15
------- converged at time : 0.273308 20-Apr-2023 10:38:15
number of iterations : 6 20-Apr-2023 10:38:16
number of reformations : 6 20-Apr-2023 10:38:16
------- converged at time : 0.296555 20-Apr-2023 10:38:16
number of iterations : 6 20-Apr-2023 10:38:16
number of reformations : 6 20-Apr-2023 10:38:16
------- converged at time : 0.319803 20-Apr-2023 10:38:16
number of iterations : 6 20-Apr-2023 10:38:16
number of reformations : 6 20-Apr-2023 10:38:16
------- converged at time : 0.34305 20-Apr-2023 10:38:16
number of iterations : 6 20-Apr-2023 10:38:16
number of reformations : 6 20-Apr-2023 10:38:16
------- converged at time : 0.366297 20-Apr-2023 10:38:16
number of iterations : 6 20-Apr-2023 10:38:17
number of reformations : 6 20-Apr-2023 10:38:17
------- converged at time : 0.389545 20-Apr-2023 10:38:17
number of iterations : 6 20-Apr-2023 10:38:17
number of reformations : 6 20-Apr-2023 10:38:17
------- converged at time : 0.412792 20-Apr-2023 10:38:17
number of iterations : 6 20-Apr-2023 10:38:17
number of reformations : 6 20-Apr-2023 10:38:17
------- converged at time : 0.43604 20-Apr-2023 10:38:17
number of iterations : 6 20-Apr-2023 10:38:17
number of reformations : 6 20-Apr-2023 10:38:17
------- converged at time : 0.459287 20-Apr-2023 10:38:17
number of iterations : 6 20-Apr-2023 10:38:17
number of reformations : 6 20-Apr-2023 10:38:17
------- converged at time : 0.482534 20-Apr-2023 10:38:17
number of iterations : 6 20-Apr-2023 10:38:18
number of reformations : 6 20-Apr-2023 10:38:18
------- converged at time : 0.505782 20-Apr-2023 10:38:18
number of iterations : 6 20-Apr-2023 10:38:18
number of reformations : 6 20-Apr-2023 10:38:18
------- converged at time : 0.529029 20-Apr-2023 10:38:18
number of iterations : 6 20-Apr-2023 10:38:18
number of reformations : 6 20-Apr-2023 10:38:18
------- converged at time : 0.552276 20-Apr-2023 10:38:18
number of iterations : 6 20-Apr-2023 10:38:18
number of reformations : 6 20-Apr-2023 10:38:18
------- converged at time : 0.575524 20-Apr-2023 10:38:18
number of iterations : 6 20-Apr-2023 10:38:18
number of reformations : 6 20-Apr-2023 10:38:18
------- converged at time : 0.598771 20-Apr-2023 10:38:18
number of iterations : 6 20-Apr-2023 10:38:19
number of reformations : 6 20-Apr-2023 10:38:19
------- converged at time : 0.622019 20-Apr-2023 10:38:19
number of iterations : 6 20-Apr-2023 10:38:19
number of reformations : 6 20-Apr-2023 10:38:19
------- converged at time : 0.645266 20-Apr-2023 10:38:19
number of iterations : 6 20-Apr-2023 10:38:19
number of reformations : 6 20-Apr-2023 10:38:19
------- converged at time : 0.668513 20-Apr-2023 10:38:19
number of iterations : 6 20-Apr-2023 10:38:19
number of reformations : 6 20-Apr-2023 10:38:19
------- converged at time : 0.691761 20-Apr-2023 10:38:19
number of iterations : 6 20-Apr-2023 10:38:19
number of reformations : 6 20-Apr-2023 10:38:19
------- converged at time : 0.715008 20-Apr-2023 10:38:19
number of iterations : 6 20-Apr-2023 10:38:19
------- converged at time : 0.738255 20-Apr-2023 10:38:20
number of iterations : 6 20-Apr-2023 10:38:20
number of reformations : 6 20-Apr-2023 10:38:20
------- converged at time : 0.761503 20-Apr-2023 10:38:20
number of iterations : 6 20-Apr-2023 10:38:20
number of reformations : 6 20-Apr-2023 10:38:20
------- converged at time : 0.78475 20-Apr-2023 10:38:20
number of iterations : 6 20-Apr-2023 10:38:20
number of reformations : 6 20-Apr-2023 10:38:20
------- converged at time : 0.807998 20-Apr-2023 10:38:20
number of iterations : 6 20-Apr-2023 10:38:20
number of reformations : 6 20-Apr-2023 10:38:20
------- converged at time : 0.831245 20-Apr-2023 10:38:20
number of iterations : 6 20-Apr-2023 10:38:20
number of reformations : 6 20-Apr-2023 10:38:20
------- converged at time : 0.854492 20-Apr-2023 10:38:20
number of iterations : 6 20-Apr-2023 10:38:21
number of reformations : 6 20-Apr-2023 10:38:21
------- converged at time : 0.87774 20-Apr-2023 10:38:21
number of iterations : 6 20-Apr-2023 10:38:21
number of reformations : 6 20-Apr-2023 10:38:21
------- converged at time : 0.900987 20-Apr-2023 10:38:21
number of iterations : 8 20-Apr-2023 10:38:21
number of reformations : 8 20-Apr-2023 10:38:21
------- converged at time : 0.924235 20-Apr-2023 10:38:21
number of iterations : 6 20-Apr-2023 10:38:21
number of reformations : 6 20-Apr-2023 10:38:21
------- converged at time : 0.944412 20-Apr-2023 10:38:21
number of iterations : 6 20-Apr-2023 10:38:21
number of reformations : 6 20-Apr-2023 10:38:21
------- converged at time : 0.964589 20-Apr-2023 10:38:21
number of iterations : 6 20-Apr-2023 10:38:22
number of reformations : 6 20-Apr-2023 10:38:22
------- converged at time : 0.984767 20-Apr-2023 10:38:22
number of iterations : 6 20-Apr-2023 10:38:22
number of reformations : 6 20-Apr-2023 10:38:22
------- converged at time : 1 20-Apr-2023 10:38:22
Elapsed time : 0:00:09 20-Apr-2023 10:38:22
N O R M A L T E R M I N A T I O N
# Done 20-Apr-2023 10:38:22
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Import FEBio results
if runFlag==1 %i.e. a succesful run
Importing nodal displacements from a log file
dataStruct=importFEBio_logfile(fullfile(savePath,febioLogFileName_disp),0,1);
%Access data
N_disp_mat=dataStruct.data; %Displacement
timeVec=dataStruct.time; %Time
%Create deformed coordinate set
V_DEF=N_disp_mat+repmat(V,[1 1 size(N_disp_mat,3)]);
Plotting the simulated results using anim8 to visualize and animate deformations
DN_magnitude=sqrt(sum(N_disp_mat(:,:,end).^2,2)); %Current displacement magnitude % Create basic view and store graphics handle to initiate animation hf=cFigure; %Open figure gtitle([febioFebFileNamePart,': Press play to animate']); title('Displacement magnitude [mm]','Interpreter','Latex') hp=gpatch(Fb,V_DEF(:,:,end),DN_magnitude,'k',1); %Add graphics object to animate hp.Marker='.'; hp.MarkerSize=markerSize2; hp.FaceColor='interp'; gpatch(Fb,V,0.5*ones(1,3),'k',0.25); %A static graphics object axisGeom(gca,fontSize); colormap(gjet(250)); colorbar; caxis([0 max(DN_magnitude)]); axis(axisLim(V_DEF)); %Set axis limits statically camlight headlight; % Set up animation features animStruct.Time=timeVec; %The time vector for qt=1:1:size(N_disp_mat,3) %Loop over time increments DN_magnitude=sqrt(sum(N_disp_mat(:,:,qt).^2,2)); %Current displacement magnitude %Set entries in animation structure animStruct.Handles{qt}=[hp hp]; %Handles of objects to animate animStruct.Props{qt}={'Vertices','CData'}; %Properties of objects to animate animStruct.Set{qt}={V_DEF(:,:,qt),DN_magnitude}; %Property values for to set in order to animate end anim8(hf,animStruct); %Initiate animation feature drawnow;
end
GIBBON www.gibboncode.org
Kevin Mattheus Moerman, [email protected]
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License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE
GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.
Copyright (C) 2006-2022 Kevin Mattheus Moerman and the GIBBON contributors
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