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fe_case

Purpose

UI function to handle FEM computation cases

Syntax

  Case = fe_case(Case,'EntryType','Entry Name',Data)
  fe_case(model,'command' ...)

Description

FEM computation cases contains information other than nodes and elements used to describe a FEM computation. Currently supported entries in the case stack are


cyclic(SDT) used to support cyclic symmetry conditions
DofLoadloads defined on DOFs (handled by fe_load)
DofSet(SDT) imposed displacements on DOFs
FixDofused to eliminated DOFs specified by the stack data
FSurfsurface load defined on element faces (handled by fe_load). This will be phased out since surface load elements associated with volume loads entries are more general.
FVolvolume loads defined on elements (handled by fe_load)
infoused to stored non standard entries
KeepDof(obsolete) used to eliminated DOFs not specified by the stack data. These entries are less general than FixDof and should be avoided.
mapfield of normals at nodes
mpcmultiple point constraints
rbe3a flavor of MPC that enforce motion of a node a weighted average
parare used to define physical parameters (see upcom Par commands)
rigidlinear constraints associated with rigid links
SensDof(SDT) Sensor definitions

fe_case is called by the user to initialize (when Case is not provided as first argument) or modify cases (Case is provided).

Accepted commands are

Get, Set, Remove, Reset

Commands for advanced constraint generation

AutoSPC

Analyses the rank of the stiffness matrix at each node and generates a fixdof case entry for DOFs found to be singular:

 model = fe_case(model,'autospc')

Assemble

Calls used to assemble the matrices of a model. See fe_mknl Assemble and section 4.4.8 for optimized assembly strategies.

Build Sec epsl d

model = fe_cyclic('build (N) epsl (d)',model,LeftNodeSelect) is used to append a cyclic constraint entry in the current case.

ConnectionEqualDOF

fe_caseg('Connection EqualDOF',model,'name',DOF1,DOF2) generates a set of MPC connecting each DOF of the vector DOF1 to corresponding DOF in DOF2. DOF1 and DOF2 can be a list of NodeId, in that case all corresponding DOF are connected, or only DOF given as a -dof DOFs command option.

Following example defines 2 disjointed cubes and connects them with a set of MPC between DOFs of the given nodes:

cf1=feplot; cf1.mdl=femesh('testhexa8');
cf1.mdl=feutil('repeatsel 2 0.0 0.0 1.5',cf1.mdl);
cf1.mdl=fe_caseg('Connection EqualDOF -id56',cf1.mdl, ...
    'link1',[5:8]',[9:12]');
fecom(cf1,'promodelviewon');fecom(cf1,'curtab Cases','link1');

The option -id i can be added to the command to specify a MPC ID i for export to other software.

ConnectionPivot

This command generates a set of MPC defining a pivot connection between two sets of nodes. The command specifies the DOFs constraint at the pivot (in the example DOF 6 is free), the local z direction and the location of the pivot node. One then gives the model, the connection name, and node selections for the two sets of nodes.

 model=demosdt('demoTwoPlate');
 model=fe_caseg('Connection Pivot 12345 0 0 1 .5 .5 -3 -id 1111', ...
  model,'pivot','group1','group2');
 def=fe_eig(model);feplot(model,def)

The option -id i can be added to the command to specify a MPC ID i for export to other software.

ConnectionSurface

This command implements node to surface connections trough constraints or penality. fe_caseg('ConnectionSurface DOFs',model,'name',NodeSel1,Eltsel2) generates a set of MPC connecting of DOFs of a set of nodes selected by NodeSel1 (this is a node selection string) to a surface selected by EltSel2 (this is a element selection string). The following example links x and z translations of two plates

 model=demosdt('demoTwoPlate');
 model=fe_caseg('Connection surface 13 -MaxDist0.1',model,'surface', ...
   'z==0', ...                          % Selection of nodes to connect
   'withnode {z==.1 & y<0.5 & x<0.5}'); % Selection of elements for matching
 def=fe_eig(model);feplot(model,def)

Accepted command options are

Warning volume matching requires that nodes are within the element. To allow exterior nodes, you should add a & selface at the end of the element selection string for matching.

ConnectionScrew

fe_caseg('Connection Screw',model,'name',data)

This command generates a set of RBE3 defining a screw connection. Nodes to be connected are defined in planes from their distance to the axis of the screw. The connected nodes define a master set enforcing the motion of a node taken on the axis of the screw with a set of RBE3 or rigid links ring for each plane.

In the case where rigid links are defined, the command appends a group of rigid elements to the model.

Real screw can be represented by beams connecting all the axis slave nodes.

data defining the screw is a data structure with following fields:


Origina vector [x0 y0 z0] defining the origin of the screw.
axisa vector [nx ny nz] defining the direction of the screw axis.
radiusdefines the radius of the screw.
planesa matrix with as many lines as link rings. Each row is of the form [z0 type ProId zTol rTol] where z0 is the distance to the origin along the axis of the screw, type is the type of the link (0 for rigid and 1 for rbe3), ProId is the ProId of the elements containing nodes to connect, and zTol and rTol are tolerance of the positions of these nodes respectively for distance along the axis and distance to the axis.
 One can also define more generally planes as a cell array whose each row defines a plane and is of the form {z0 type st} where z0 and type are defined above and st is a FindNode string. st can contain $FieldName tokens that will be replaced by corresponding data.FieldName value (for example 'cyl<= $radius o $Origin $axis & inElt{ProId $ProId}' will select nodes in cylinder of radius data.radius, origin data.Origin and axis data.axis, and in elements of ProId data.ProId).
rigidOptional. This field (in lower case) must be added if a rigid link is created (type 0), containing the value [ Inf abs('rigid')].
MatProIdOptional. If present beams are added to connect slave nodes at the center of each link ring. It is a vector [MatId ProId] defining the MatId and the ProId of the beams.
MasterCelasOptional. It defines the celas element which is added if this field is present. It is of the form [0 0 -DofID1 DofID2 ProID EltID Kv Mv Cv Bv]. The first node of the celas is the slave node of the rbe3 ring and the second is added at the same location. This can be useful to reduce a superelement keeping the center of the rings in the interface.
NewNodeOptional. If it is omitted or equal to 1 then a new slave node is added to the model at the centers of the link rings. If it equals to 0, existent model node can be kept.
NnodeOptional. Gives the number of points to retain in each plane.

Following example creates a test model, and adds 2 rbe3 rings in 2 planes.

model=demosdt('demoscrew layer 0 40 20 3 3 layer 0 40 20 4'); % create model
r1=struct('Origin',[20 10 0],'axis',[0 0 1],'radius',3, ...
          'planes',[1.5 1 111 1 3.1;
                    5.0 1 112 1 4;], ...
          'MasterCelas',[0 0 -123456 123456 10 0 1e14], ...
          'NewNode',0);
model=fe_caseg('ConnectionScrew',model,'screw1',r1);
cf=feplot(model); % show model 
fecom('promodelviewon');fecom('curtab Cases','screw1');

Entries

The following paragraphs list available entries not handled by fe_load or upcom.

cyclic (SDT)

cyclic entries are used to define sector edges for cyclic symmetry computations. They are generated using the fe_cyclic Build command.

FixDof

FixDof entries correspond to rows of the Case.Stack cell array giving {'FixDof', Name, Data}. Name is a string identifying the entry. data is a column DOF definition vector (see section 7.10) or a string defining a node selection command. You can also use
data=struct('data',DataStringOrDof,'ID',ID) to specify a identifier.

You can now add DOF and ID specifications to the findnode command. For example 'x==0 -dof 1 2 -ID 101' fixes DOFs x and y on the x==0 plane and generates an data.ID field equal to 101 (for use in other software).

The following command gives syntax examples. An example is given at the end of the fe_case documentation.

 model = fe_case(model,'FixDof','clamped dofs','z==0', ...
    'FixDof','SimpleSupport','x==1 & y==1 -DOF 3', ...
    'FixDof','DofList',[1.01;2.01;2.02], ...
    'FixDof','AllDofAtNode',[5;6], ...
    'FixDof','DofAtAllNode',[.05]);

map

map entries are used to define maps for normals at nodes. These entries are typically used by shell elements or by meshing tools. Data is a structure with fields

MPC

MPC (multiple point constraint) entries are rows of the Case.Stack cell array giving {'MPC', Name, Data}. Name is a string identifying the entry. Data is a structure with fields Data.ID positive integer for identification. Data.c is a sparse matrix whose columns correspond to DOFs in Data.DOF. c is the constraint matrix such that [c] {q} = {0} for q defined on DOF.

Data.slave is an optional vector of slave DOFs in Data.DOF. If the vector does not exist, it is filled by feutil FixMpcMaster.

Note that the current implementation has no provision for using local coordinates in the definition of MPC (they are assumed to be defined using global coordinates).

par (SDT)

par entries are used to define variable coefficients in element selections. It is nominally used through upcom Par commands but other routines may also use it [45].

RBE3 (SDT)

rbe3 constraints enforce the motion of a slave node as a weighted average of master nodes. Two definition strategies are supported in SDT, either direct or implicit. There are known robustness problems with the current implementation of this constraint.

The direct definition explicitely declares each node with coupled DOFs and weighting in a data field. Several rbe3 constrains can be declared in data.data. Each row of data.data codes a set of constraints following the format

Rbe3ID NodeIdSlave DofSlave Weight1 DofMaster1 NodeId1 ...

DofMaster and DofSlave code which DOFs are used (123 for translations, 123456 for both translations and rotations).

The implicit definition handles Node Selectors described in section 7.11 to define the rbe3. The input is then a structure:

data=struct('SlaveSel','NodeSel',...
            'MasterSel','NodeSel',...
            'DOF', DofSlave,...
            'MasterDOF', DofMaster);

SlaveSel is the slave node selection (typically a single node), MasterSel is the master node selection, DOF is the declaration of the slave node coupling, MasterDOF is the declaration of the master nodes coupling (same for all master nodes).

Grounding or coupling the slave node movement is possible through the use of a celas, as shown in the example below featuring an implicit rbe3 definition. In a practical approach, the slave node is duplicated and a celas element is generated between the two, which allows the definition of global movement stiffnesses. Constraining the rotation of a drilled block around its bore axis is considered using a global rotation stiffness.

% Definition of a drilled block around y
model=feutil('ObjectHoleInBlock 0 0 0   1 0 0   0 1 0  2 2 2 .5 4 4 4'); 
model=fe_mat('DefaultIl',model); % default material properties
model=fe_mat('defaultPl',model); % default element integration properties
% Generation of the bore surface node set
[i1,r1]=feutil('Findnode cyl ==0.5 o 0 0 0 0 1 0',model);
model=feutil('AddsetNodeId',model,'bolt',r1(:,1));
% Generation of the slave node driving the global bore movement
model.Node(end+[1:2],1:7)=[242 0 0 0 0 0 0;244 0 0 0  0 0 0];
% Addition of the celas element between the slave node and its duplicate
model.Elt(end+[1:2],1:7)=[inf abs('celas') 0;242 244 123456 0 0 0 1e11];
model=feutil('AddSetNodeId',model,'ref_rot',244);
% Definition of the RBE3 constraint
data=struct('SlaveSel','setname bolt',...
            'MasterSel','setname ref_rot',...
            'DOF',123,...
            'MasterDOF',123456);
model=fe_case(model,'rbe3','block_mov',data);
% Grounding the global y rotation (leaving the celas stiffness work)
model=fe_case(model,'fixdof','ClampBlockRot',242.05);
% 5 rigid body modes model obtained
def=fe_eig(model,[5 20 1e3]);

rigid

See details under rigid which also illustrates the RigidAppend command.

Sens ... (SDT)

SensDof entries are detailed in  section 4.3. They are stored as rows of the Case.Stack cell array giving {'SensDof', Name, data}. SensStrain entries have been replaced with strain sensors in SensDof.

un=0

model=fe_case(model,'un=0','Normal motion',map); where map gives normals at nodes generates an mpc case entry that enforces the condition {u}T{n}=0 at each node of the map.

Example

Here is an example combining various fe_case commands

 femesh('reset');
 model = femesh('test ubeam plot');
 % specifying clamped dofs (FixDof) 
 model = fe_case(model,'FixDof','clamped dofs','z==0');
 % creating a volume load
 data  = struct('sel','GroupAll','dir',[1 0 0]);
 model = fe_case(model,'FVol','Volumic load',data);
 % assemble active DOFs and matrices
 model=fe_mknl(model);
 % assemble RHS (volumic load)
 Load  = fe_load(model,'Case1');
 % compute static response
 kd=ofact(model.K{2});def.def= kd\Load.def; ofact('clear',kd)
 Case=fe_case(model,'gett'); def.DOF=Case.DOF;
 % plot displacements
 feplot('initdef',def);
 fecom(';undef;triax;showpatch;promodelinit');

See also

fe_mk, fe_case


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