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fe_load

• DofLoad, DOFSet
• FVol
• FSurf

Purpose

Interface for the assembly of distributed and multiple load patterns

Syntax

 Load = fe_load(model)
 Load = fe_load(model,Case)
 Load = fe_load(model,'NoT')
 Load = fe_load(model,Case,'NoT')

Description

fe_load is used to assemble loads (left hand side vectors to FEM problems). Simple point loads are easily built using fe_c and reciprocity (transpose of output shape matrix) but fe_load is needed for more complex cases.

Loads are associated with cases which are structures with at least Case.DOF and Case.Stack fields.

 Case1.DOF = model.DOF; % default is model.DOF
 Case1.Stack = [{'LoadType','Name',TypeSpecificData}];

Taking the example of a point load with type specific data given by

 data=struct('DOF',365.03,'def',1);

you can create a case using low level commands

 Case1=struct('DOF',model.DOF,'Stack',{{'DofLoad','PointLoad',data}});

or with the easier case creation format (using SDT function fe_case)

 Case1=fe_case('DofLoad','PointLoad',data); 

or add a new load to a case defined in the model.Stack field

 model=fe_case(model,'DofLoad','PointLoad',data); 

To compute the load, the model (a structure with fields .Node, .Elt, .pl, .il) must generally be provided with the syntax Load=fe_load(model,Case). If the case is not provided, fe_load uses the first case in model.Stack.

The optional 'NoT' argument is used to require loads defined on the full list of DOFs rather than after constraint eliminations computed using Case.T'*Load.def.

The rest of this manual section describes supported load types and the associated type specific data.

DofLoad, DOFSet

Loads at DOFs and DofLoad and prescribed displacements DofSet entries are described by the following data structure

 femesh('reset');
 model = femesh('testubeam plot');
 data=struct('DOF',365.03,'def',1.1); % 1.1 N at node 365 direction z 
 data.lab=fe_curve('datatype',13);
 model=fe_case(model,'DofLoad','PointLoad',data);
 % alternate format to declare unit inputs
 model=fe_case(model,'DofLoad','ShortTwoInputs',[362.01;258.02]); 
 Load = fe_load(model);
 feplot(model,Load); fecom(';scaleone;undefline;ch1 2') % display

FVol

FVol entries use data is a structure with fields

Each cell of Case.dir can give a constant value, a position dependent value defined by a string FcnName that is evaluated using
fv(:,jDir)=eval(FcnName) or fv(:,jDir)=feval(FcnName,node) if the first fails. Note that node corresponds to nodes of the model in the global coordinate system and you can use the coordinates x,y,z for your evaluation. The transformation to a vector defined at model.DOF is done using vect=elem0('VectFromDir',model,r1,model.DOF), you can look the source code for more details.

For example

 femesh('reset');model = femesh('testubeam');
 data=struct('sel','groupall','dir',[0 32 0]);
 data2=struct('sel','groupall','dir',{{0,0,'(z-1).^3.*x'}});
 model=fe_case(model,'FVol','Constant',data, ...
                     'FVol','Variable',data2);
 Load = fe_load(model); 
 feplot(model,Load);fecom(';colordataz;ch2'); % display

Volume loads are implemented for all elements, you can always get an example using the elements self tests, for example [model,Load]=beam1('testload').

Gravity loads are not explicitly implemented (care must be taken considering masses in this case and not volume). You should use the product of the mass matrix with the rigid body mode corresponding to a uniform acceleration.

FSurf

FSurf entries use data a structure with fields

 if isfield(data,'eltsel'); 
  mo1.Elt=feutil('selelt',mo1,data.eltsel);
 end
 elt=feutil('seleltinnode',mo1, ...
     feutil('findnode',mo1,r1.sel));

Surface loads are defined by surface selection and a field defined at nodes. The surface can be defined by a set of nodes (data.sel and possibly data.eltsel fields. One then retains faces or edges that are fully contained in the specified set of nodes. For example

 femesh('reset');
 model = femesh('testubeam plot');
 data=struct('sel','x==-.5', ... 
             'eltsel','withnode {z>1.25}','def',1,'DOF',.19);
 model=fe_case(model,'Fsurf','Surface load',data);
 Load = fe_load(model); feplot(model,Load);

Or an alternative call with the cell array format for data.sel

 data=struct('eltsel','withnode {z>1.25}','def',1,'DOF',.19);
 NodeList=feutil('findnode x==-.5',model);
 data.sel={'','NodeId','==',NodeList};
 model=fe_case(model,'Fsurf','Surface load',data);
 Load = fe_load(model); feplot(model,Load);

Alternatively, one can specify the surface by referring to a set entry in model.Stack, as shown in the following example

 femesh('reset');
 model = femesh('testubeam plot');

 % Define a face set
 [eltid,model.Elt]=feutil('eltidfix',model);
 i1=feutil('findelt withnode {x==-.5 & y<0}',model);i1=eltid(i1);
 i1(:,2)=2; % fourth face is loaded
 data=struct('ID',1,'data',i1);
 model=stack_set(model,'set','Face 1',data);

 % define a load on face 1
 data=struct('set','Face 1','def',1,'DOF',.19);
 model=fe_case(model,'Fsurf','Surface load',data);
 Load = fe_load(model); feplot(model,Load)

The current trend of development is to consider surface loads as surface elements and transform the case entry to a volume load on a surface.

See also

fe_c, fe_case, fe_mk