abaqus user element implementation of nurbs based isogeometric...

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Abaqus User Element implementation ofNURBS based Isogeometric Analysis

T. Elguedj1, A. Duval1, F. Maurin1, H. Al Akhras1

1Universite de Lyon, CNRSINSA-Lyon, Laboratoire de Mecanique des Contacts et des Structures, France

6th European Congress on Computational Methods in Applied Science andEngineering

Vienna, Austria – Sep. 10th - Sep. 14th 2012

1 / 22

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Outline

1 Introduction

2 ImplementationFEA vs. IGAMultiple patchesInput filesProcedure and GUI

3 Numerical examplesLinear elasticityNonlinear material models

4 Conclusions and future work

2 / 22

Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity

Nonlinear materialmodels

Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Outline

1 Introduction




3 / 22

Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

IntroductionIsogeometric Analysis is based on thegeometric primitives of CAD: NURBS andT-splines. It includes standard FEA as aspecial case, but offers other possibilities:

Precise and efficient geometricmodeling

Simplified mesh refinement

Smooth basis functions with compactsupport

Superior approximation properties

Accurate derivatives and stresses

Integration of design and analysis

Application in industry requires itsimplementation in commercial soft-ware

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Introduction

Several commercial FE packages provide user element capabilities.

Abaqus User ELement and User ELement with abaqus MATerialsubroutine offers the possibility to introduce arbitrary elements intoabaqus using user defined material models (UEL) or most of thematerial models available in the software (UELMAT).

UEL can be defined with arbitrary shape functions, node numbers,polynomial order and integration points.

All the standard finite element data can be passed in the .inp inputfile.

Additional data can be passed as common variables using UserEXTERNAL DataBase (UEXTERNALDB) routines.

5 / 22

Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Outline

1 Introduction




6 / 22

Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Single patch implementation

P1: ABC/ABC P2: c/d QC: e/f T1: gc03 JWBK372-Cottrell May 20, 2009 15:22 Printer Name: Yet to Come

NURBS as a Basis for Analysis 95

Start

Read inputdata

Build connectivities and allocateglobal arrays

Loop through elements

Loop through quadraturepoints

Add contributions toKe and Fe

Assemble Ke Kand Fe F

Evaluate basis functionsand derivatives

Solve Kd=F

Stop

Ke=0 and Fe=0

K=0 and F=0

Writeoutput data

Figure 3.15 Flowchart of a classical finite element code. Such a code can be converted to a single-patchisogeometric analysis code by replacing the routines shown in green.

use the connectivity information to add their contributions to the global stiffness matrix andforce vector, and then move on to the next element. After all of the elements are assembled,the global arrays are complete. We then solve the system, write the result to a file, postprocess,and we are finished. See Hughes, 2000 for further details.To convert an existing finite element code to a single-patch isogeometric analysis code, the

only portions of the code that require modification are the ones shown in green in Figure 3.15.Clearly, the input will change as the file format will depend on the specific element technologybeing used. The precise forms of the connectivity arrays and the global matrices also dependon the basis. The structured nature of the NURBS mesh means that the IEN array (see Section3.3.1.4) can be calculated automatically from the knot vectors and polynomial orders. Next,the “black box” that evaluated the basis functions must be updated to evaluate the NURBSfunctions. This is why we emphasized the modular nature of this routine previously: the typeof information about the basis that it provides to the routine that calls it is exactly the same,but that information should now correspond to the NURBS basis. Lastly, the output must bewritten, and the format of that output will be specific to the NURBS basis.

J.A. Cottrell, T.J.R. Hughes, Y. Bazilevs Isogeometric Analysis, 2009.7 / 22

Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

FEA vs. IGA data

Finite Element Analysis

node coordinates

element type

element connectivity (ID, IENand LM)

integration rule

NURBS based IGA

control points coordinates

polynomial degree

element connectivity (ID, IEN,LM, INC)

integration rule

control points weights

knot vectors

Common data can be passed in the .inp abaqus input file. We only

consider same polynomial order in all parametric directions, therefore

element type defines the degree. Gauss quadrature is defined a priori based

on element type.

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Connectivity

Given a basis function (i.e. control point) number and a parametricdirection, the INC array returns the NURBS coordinate.

Given a local basis function number and element number, the IENarray returns the global basis function number.

Given a global basis function number and degree of freedom number,the ID array returns the equation number.

The IEN array is directly passed in the .inp file with the standardelement connectivity.

The ID array is generated by abaqus based on the boundaryconditions and number of DOF per CP.

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Connectivity

Given a basis function (i.e. control point) number and a parametricdirection, the INC array returns the NURBS coordinate.

Given a local basis function number and element number, the IENarray returns the global basis function number.

Given a global basis function number and degree of freedom number,the ID array returns the equation number.

The INC array is used in the pre-processing step to construct IEN butonly a part of it is necessary in the shape function routine. For eachelement and parametric direction we only need the NURBScoordinate of the first local basis function. We replace INC by a newarray called NIJK.

Given an element number and a parametric direction, the NIJK arrayreturns the NURBS coordinate of the first local basis function.

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Multi-patch implementation


96 Isogeometric Analysis: Toward Integration of CAD and FEA

3.6.1.1 A multiple patch code

A “multi-patch” isogeometric analysis code can be made to conform with the flowchart inFigure 3.15. In practice, however, it makes more sense to consider the slight modificationshown in Figure 3.16. In this case, we begin by inputting enough global information to buildthe global connectivities, as before. This information includes the polynomial orders and theknot vectors for each of the patches, but it does not require the control points. We can savetime and memory by not reading the control points until they are needed. If local refinement

Start

Read globalinput data

Build connectivities and allocateglobal arrays

Loop through elementson the current patch

Loop through quadraturepoints

Add contributions toKe and Fe

Assemble Ke Kand Fe F

Evaluate basis functionsand derivatives

Solve Kd=F

Stop

Ke=0 and Fe=0K=0 and F=0

Writeoutput data

Loop through patches

Read patchinput data

Figure 3.16 Flowchart of a multi-patch isogeometric analysis code. The routines in green representdifferences from the single-patch code.

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Multi-patch implementation

The outer loop on patches cannot be used within abaqus.

For simplicity we only support C0 coupling with conforming meshes.

The connectivity arrays for all patches are generated in thepre-processing step.

Then a global reordering of the elements and control points is donewith a merging of CP on patch interfaces.

The .inp file is generated for the whole domain as for a single patch.

Patch data is passed in the .NB file.


NURBS as a Basis for Analysis 87

which we insert into (3.58) along with w|!D = 0 to arrive at

−∫

"

∇w · ∇u d" +∫

"

w f d" +∫

!R

wr d! − β

∫

!R

wu d! = 0. (3.61)

Though we have replaced one expression involving the unknown u for another, we haveenforced the relationship between them weakly.

3.5 Multiple patches revisited3.5.1 Local refinementIn Section 3 of Chapter 2 we discussed the need for modeling domains using multiple patches.We always assume compatible discretizations for the geometry, meaning that on the coarsestmesh, mappings and parameterizations on the adjoining patch faces are identical. Each controlpoint on a face is in one-to-one correspondence with a control point from the adjoining face,likewise for the control variables of the solution. In many instances, this relationship will bepreserved as we refine. To make the assembly of the stiffness matrices and force vectors assimple as possible, the connectivity array will identify the equivalent local control variableson each face with a single control variable in the global array. By identifying them as a singleentity for analysis purposes, we simplify the logic and decrease the total amount of workneeded. The result is that the two patches are joined as though they were one.Identifying two control points at the same location in physical space as being a single entity

is fairly trivial. Slightly subtler is what this implies for the basis functions. The situation isshown in Figure 3.7. When two bases generated using open knot vectors are brought together,the effect is indistinguishable from the case of one knot vector with a knot repeated p times,as long as the coefficients of the two joining functions are the same. This is, of course, exactlywhat we have assured by identifying the two control variables as one.

Figure 3.7 If two knot vectors formed from open knot vectors are brought together, they can be madeto act as one if the coefficients (i.e., control variables) of the two functions on their interface are alwaysequal to each other. The result is indistinguishable from the case of a single knot vector with a C0boundary at the interface.

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

.inp file

*HEADING

**Job name:test.txt

**abqNURBS - Laboratoire de Mecanique des Contacts et des Structures - INSA-Lyon

*Part, name=Piece

*USER ELEMENT, NODES=ncpelt, TYPE=Up, COORDINATES=d, variables=size of SVARS,

INTEGRATION=ngelt, TENSOR=PSTRAIN or THREED

1,2 for 2D, 1,2,3 for 3D

*Node,nset=AllNode ->list of control points

cpnb, X-coordinate, Y-coordinate, Z-coordinate

*Element, type=Up, elset=AllEls -> list of elements

eltnb, CP1, CP2, CP3, ...

*ELSET,ELSET=EltPAtch1 -> set of all the elements

list of elements nb

*NSET,NSET=SetCPFacei -> set of control points used for Dirichlet BC

list of control points lying on the i-th face

*ELSET, ELSET=SetEltFacei -> set of elements used for Neumann BC

list of elements belonging to the i-th face

*UEL PROPERTY, ELSET=EltPatch1, MATERIAL=MAT ->assign the material to the set of all elements

*End Part

** ASSEMBLY

*Assembly, name=Assembly

*Instance, name=I1, part=Piece

*End Instance

*End Assembly

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

.inp file

**MATERIAL

*MATERIAL,NAME=MAT

*Elastic

Young’s modulus value, Poisson’s ratio value

*STEP,extrapolation=NO,NLGEOM=YES or NO

*Static

** BOUNDARY CONDITIONS ->list of Dirichlet boundary conditions

*Boundary

I1.SetCPFacei, direction of the imposed BC, direction of the imposed BC, value imposed.

** LOADS ->list of Neumann boundary conditions

*Cload

I1.SetFacei, key for selecting element face, value imposed.

** OUTPUT REQUESTS

*node file, frequency=1

U,RF,CF

*el file, frequency=1

SDV

*End Step

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

.NB file

*DIMENSION

2 or 3

* total nb of elements

nelt

*nb of patches

nbpatch

*nb of elements per patch

neltp1, neltp2, ...

*data for patch i

number of knots for parametric direction j

knot vector for parametric direction j

*NIJK array based on global domain element numbering

eltnb, nijk1, nijk2, nijk3

*list of CP weights based on global domain CP numbering

CPnb, weight

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Procedure

1 Pre-processing

Matlab pre-processor based on Geopdes. Handles 2D, 3D single

and multi-patch cases.

Rhino plugin for multi-patch 2D cases (imposition of BC,

material definition).

2 Analysis

3 Post-processing

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Procedure

1 Pre-processing

2 Analysis

GUI for selecting IGA input files.

Interactive job execution using our IGA user element.

3 Post-processing

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Procedure

1 Pre-processing

2 Analysis

3 Post-processing

Request output of the results in a raw ASCII file .fil (CP data,

internal variables).

GUI user interface for selecting input and output files and

post-processing parameters.

Abaqus python and C++ scripting interface to perform

projection on a finer FE mesh. (Internal variables are first

projected onto CP using global least-square if needed).

Generate a projected output database binary file .odb readable

in abaqus CAE.

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Graphical User Interface

movie

14 / 22

Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Outline

1 Introduction




15 / 22

Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Linear elasticity: single patch horseshoe

E= 100 000MPa, ν = 0.3, imposed displacement of ud = +/− 1ex.

T.J.R. Hughes, J.A. Cottrell, Y. BazilevsIsogeometric analysis: CAD, finite elements, NURBS, exact geometry andmesh refinement. Computer Methods in Applied Mechanics andEngineering, vol. 194, p. 4135–4195, 2005.

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Linear elasticity: single patch horseshoe (cont’d)

σzz on initial configuration σzz on deformed configuration

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Linear elasticity: multipatch cylinder

Cylinder submitted to internal pressure, geometry defined with 4 patches.R = 2m, r = 1m, E = 100000MPa, ν = 0.3, p=10MPa.

Von Mises stress on deformedconfiguration

undeformed geometry and mesh.

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Small strain plasticity: plane strain cylinder

Cylinder submitted to internal pressure, elastic vs. perfectly plastic case.R = 2m, r = 1m, E=200000MPa, ν = 0.3, σy=200MPa, p=145MPa.

Von Mises stress pure elastic case(σmin

vm = 85MPa ; σMAXvm =335MPa)

Von Mises stress perfectly plasticcase (σmin

vm = 116MPa ;σMAXvm =200MPa)19 / 22

Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Outline

1 Introduction




20 / 22

Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Conclusions

We have a proposed an implementation of NURBS based IGA in theabaqus FEA commercial package.

The implementation is able to handle single and multiple patches (C0continuity across compatible patch boundaries).

Thank to UELMAT we can directly use most material modelsavailable in abaqus for small and large deformation (NLGEOM).

Post processing capabilities are available directly into abaqus CAEusing Python/C++ scripting interface.

Preliminary work on pre-processing allow us to provide a GUI for 2Dcases and matlab for 3D.

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Introduction

Implementation

FEA vs. IGA

Multiple patches

Input files

Procedure and GUI

Numericalexamples

Linear elasticity


Conclusions

T. Elguedj

abqNURBS

09/12/2012

ECCOMAS 2012

Future work

Improve the way necessary extra data can be passed on (i.e. outsidethe .inp file).

Introduce Bezier extraction as an alternative.

Include temperature for thermal or thermo-mechanical analysis,further test NLGEOM and material models as well as dynamics.

Released as open source under the CeCILL license in a few days.

http://abqnurbs.insa-lyon.fr

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abaqus user element implementation of nurbs based isogeometric...

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