Target OpenFEM is meant to let you use it’s components to build your application • General purpose FEM solver • Multi-physic support • Toolbox flexibility and state of the art performance OpenFEM An open source finite element toolbox SDTools : Etienne Balmes, Jean Michel Leclere INRIA : D. Chapelle, C. Delforge, A. Hassim, M. Oscar : catenary-pantograph interaction Vidrascu, … SDTools/SNCF-DIR Dynavoie SDTools/SNCF-DIR 3D model explicit integration, 1 million of time step in 2 hours Applications OpenFEM history Start in 2001 from • Structural dynamics toolbox .m file elements limited library • MODULEF large library but no longer a convenient prototyping environment Phase I -> OpenFEM 1.0 & 2.0 Heart simulation Internal ear modeling INRIA, Zapadoceska Univerzita University Hospital Zuerich • Port of MODULEF elements (2D and 3D volumes, MITC4) • Translation to SCILAB (Claire Delforge) Phase II (current) ECP/MSSMat MISS3D • Efficient non-linear operation (generic compiled elements, geometric non-linear mechanics, … ) ECP/MSSMat Gefdyn Design criteria A Matlab/Scilab Toolbox, why ? • Be a toolbox (easy to develop, debug, • Development is easier (interactive optimization only should take time) mode, debugger) • Optimize ability to be extended by • Students (non experts) understand it users and can rapidly prototype variations • Performance identical to good fully from standard code compiled code • Performance is not worse (can be • Solve very general multi-physics FE better than poor compiled code) problems • One can easily link into most external • Be suitable for application deployment libraries 1 Easy user extensions OpenFEM architecture • Object oriented concepts (user object provides its methods) Preprocessing FEM core Postprocessing • But non typed data structures (avoid need to declare • Mesh • Shape function utilities • Stress computations inheritance properties) manipulations • Element functions • Signal processing •Structured • Matrix and load assembly • 3D visualization (major meshing • Factored matrix object extension , optimized, Example user element • Property/boundary (dynamic selection of sparse object based) condition setting library) Export • Linear static and time •MEDIT Import response (linear and non • Element name of .m file (beam1.m) • Nastran, IDEAS, • Modulef, GMSH, linear) SAMCEF • Must provide basic methods (node, DOF, face, parent, …) GID • Real eigenvalues • Ensight, MISS3D, • Nastran, IDEAS, • Optimized solvers for large • Self provide calling format. Eg : beam1(‘call’) Gefdyn ANSYS, PERMAS, problems, superelements, [k1,m1]=beam1(nodeE, elt(cEGI(jElt),:), pointers(:,jElt), integ, constit, SAMCEF, MISS, and system dynamics, model elmap, node); GEFDYN reduction and optimization • Drive other software (NASTRAN, MISS) Other self extensions : property functions OpenFEM, SDTools, MSSMat Meshing 1 : example Meshing 2 : femesh/feutil femesh • Structured meshing • Add FEeli FEelj, AddSel • ObjectBeamLine i, ObjectMass i • AddNode [,New] [, From i] • ObjectHoleInPlate FEelt=[]; • Mapped divisions • Object[Quad,Beam,Hexa] MatId ProId FEnode = [1 0 0 0 0 0 0;2 0 0 0 0 0 .15; • AddTest [,NodeShift,Merge] • Objects (beam, circle, • Divide div1 div2 div3 •Object[Circle,Cylinder,Disk] 3 0 0 0 0.4 1.0 .176;4 0 0 0 0.4 0.9 0.176]; • Optim [Model, NodeNum, EltCheck] % fuselage tube, …) • DivideInGroups • DivideGroup i ElementSelectors • Orient, Orient i [ , n nx ny nz] [,-neg] femesh('objectbeamline 1 2'); • Plot [Elt, El0] femesh('extrude 0 1.0 0.0 0.0', … •EltId • Extrude nRep tx ty tz • Quad2Tria, quad42quadb, etc. [linspace(0,.55,5) linspace(.65,1.4,6) 1.5]); • RefineBeam femesh('addsel;'); • FindDof ElementSelectors •GetDof • Remove[Elt,El0] ElementSelectors •Renumber % vertical tail • Find [Elt,El0] ElementSelectors • FindNode Selectors • RepeatSel nITE tx ty tz femesh('objectbeamline',femesh('findnode z==.15 & x>=1.4')); • Rev nDiv OrigID Ang nx ny nz femesh(';extrude 3 0 0 .1;addsel;'); • GetEdge[Line,Patch] • GetElemF • RotateSel OrigID Ang nx ny nz % vertical horizontal tail • Sel [Elt,El0] ElementSelectors femesh('objectbeamline',femesh('findnode z==.45')); •GetLine •GetNodeSelectors • SelGroup i, SelNode i femesh('extrude 0 0.0 0.2 0.0',[-1 -.5 0 .5 1]); • SetGroup [i,name] [Mat j, Pro k, EGID e, Name s] femesh('addsel;'); • GetNormal[Elt,Node][,Map] •GetPatch •StringDOF Node: [144x7 double] • Info [ ,FEeli, Nodei] • SymSel OrigID nx ny nz % right drum • TransSel tx ty tz femesh(';objectbeamline 3 4;extrude 1 .4 0 0'); Elt: [100x9 double] • Join [,el0] [group i, EName] •model [,0] • UnJoin Gp1 Gp2 femesh('divide',[0 2/40 15/40 25/40 1],[0 .7 1]); pl: [2x6 double] femesh('addsel;'); • Matid,ProId,MPID il: [4x6 double] % left drum bas: [] femesh(';symsel 1 0 1 0;addsel;'); Stack: {} Generation, Selection, … Meshing 3: unstructured Meshing 4: fe_gmsh FEnode = [1 0 0 0 0 0 0; 2 0 0 0 1 0 0; 3 0 0 0 0 2 0]; Rationale : meshing is a serious femesh('objectholeinplate 1 2 3 .5 .5 3 4 4'); FEelt=FEel0;femesh('selelt seledge');model=femesh('model0'); business that needs to be model.Node=feutil('getnode groupall',model); integrated in a CAD environment. model=fe_gmsh('addline',model,'groupall'); OpenFEM is a computing mo1=fe_gmsh('write temp.msh -lc .3 -run -2 -v 0',model); environment. feplot(mo1); delete('temp.msh') •IMPORT (MODULEF, GMSH, GID, Default element size NASTRAN, ANSYS, SAMCEF, PERMAS, GMSH options IDEAS) • Good functionality for 2D and 3D • Run meshing software : GMSH Driver, • Limited handling of complex surfaces MODULEF • 2D quad meshing, 2D Delaunay OpenFEM, SDTools 2 Meshing 5: selection Element library Recursive node and element selections m-file functions The OpenFEM • 3D lines/points : Bar, Beam, Pre-stressed beam, specification is designed Spring, bush, viscoelastic spring, mass for multiphysics GID ~=i EltId i • Shells 3/4 nodes applications Group ~=i EltInd i • Multilayer shell element Groupa i EltName ~=s mex from MODULEF • 2D, plane stress/strain, axi, linear, quadratic 99 DOF/node InElt{sel} EGID == i Facing > cos x y z • 3D, linear and quadratic, geometric-linear, orthotropy 999 internal DOF/element NodeId > i • Shells (MITC4) NotIn{sel} Group i mex (generic compiled elements) Plane == i nx ny nz InNode i • 2D, plane stress/strain, linear, quadratic rad <=r x y z MatId i • 3D, linear and quadratic, geometric non-linear Setname name ProId i mechanics, full anisotropy, mechanical or thermal pre- SelEdge type stress x >a • Acoustic fluids x y z SelFace type • INRIA : hyperelasticity, follower pressure WithNode i • SDTools : piezo volumes and shells with composite WithoutNode i support, poroelasticity Recent, in development Shape function utilities (integrules) User elements elseif comstr(Cam,'node'); out = [1 2]; elseif comstr(Cam,'prop'); out = [3 4 5]; Supported topologies are elseif comstr(Cam,'dof'); out=[1.01 1.02 1.03 2.01 2.02 2.03]'; elseif comstr(Cam,'line'); out = [1 2]; elseif comstr(Cam,'face'); out =[]; • bar1 (1D linear) » integrules('hexa8',3) elseif comstr(Cam,'sci_face'); out = [1 2 2]; elseif comstr(Cam,'edge'); out =[1 2]; • beam1 (1D cubic) elseif comstr(Cam,'patch'); out = [1 2]; elseif comstr(Cam,'parent'); out = 'beam1'; • quad4 (2D bi-linear), quadb (2d quadratic) N: [27x8 double] • tria3 (2D affine), tria6 (2D quadratic) Nr: [27x8 double] Ns: [27x8 double] • tetra4, tetra10 Nt: [27x8 double] [k1,m1]=beam1(nodeE, elt(cEGI(jElt),:), Nw: 27 pointers(:,jElt), integ, constit, elmap, node); • penta6, penta15 NDN: [8x108 double] NDNLabels: {'' ',x' ',y' ',z'} • hexa8, hexa20, hexa27 [ID,pl,il]=deal(varargin); jdet: [27x1 double] pe=pe(find(pe(:,1)==ID(1),3:end); % material properties w: [27x4 double] ie=ie(find(ie(:,1)==ID(2),3:end); Nnode: 8 % E*A nu eta rho*A A lump xi: [8x3 double] constit = [pe(1)*ie(4) 0 pe(3)*ie(4) ie(4) ie(7)]; integ=ID;%matid proid type: 'hexa8' Elmap=[]; out=constit(:); out1=integ(:); out2=ElMap; Generic compiled elements Generic compiled elements During assembly init Objective ease implementation of define • arbitrary multi-physic •D ↔ constit • linear element families • Good compiled speed • ε ↔ EltConst.NDN • provisions for non linear extensions •Ke ↔ D,e (EltConst. Assumptions MatrixIntegrationRule built in integrules MatrixRule) •Strain ε=[B]{q} linear function of N and ∇N • Element matrix quadratic function of strain EltConst=p_solid('constsolid','hexa8',[],[]) p_solid('constsolid','hexa8',[],[]) p_solid('constfluid','hexa8',[],[]) 3 Boundary conditions ofact : gateway to sparse libraries Cases define : Kq=F is central to most FEM problems. Optimal is case/machine boundary conditions, point and distributed loads, dependent. ofact object allows library independent code. physical parameters, ... data=struct('sel','x==-.5', ... 'eltsel','withnode {z>1.25}', ... •Method: dynamic selection of method (OpenFEM, SDTools) 'def',1,'DOF',.19); model = fe_case(femesh('testubeam'),... lu : MATLAB sparse LU solver 'FSurf','Pressure load',data, ... chol : MATLAB sparse Cholesky solver pardiso : PARDISO sparse solver 'FixDof','Fixed boundary condition','x==0'); *umfpack : UMFPACK solver (NOT AVAILABLE ON THIS MACHINE) -> spfmex : SDT sparse LDLt solver mtaucs : TAUCS sparse solver Supported boundary conditions sp_util : SDT skyline solver *psldlt : SGI sparse solver (NOT AVAILABLE ON THIS MACHINE) • KeepDOF, FixDOF • Rigid •Symfact: symbolic factorization (renumbering, allocation) •MPC, Un=0 •Fact: numeric factorization (possibly multiple for single symfact) Handling by elimination : solve Weld spots and damping treatment •Solve: forward backward solve