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fe_mk, fe_mknl

• Init
• Assemble [ , NoT]
• MatType
• Opt

 [m,k,mdof] = fe_mknl(model);
 model      = fe_mk(model,'Options',Opt)
 [m,k,mdof] = fe_mk( ... ,[0       OtherOptions])
 [mat,mdof] = fe_mk( ... ,[MatType OtherOptions])
 [Case,model.DOF]=fe_mknl('init',model); 
 mat=fe_mknl('assemble',model,Case,def,MatType);

• model a model data structure describing nodes, elements, material properties, element properties, and possibly a case.
  
  
• Case a data structure describing loads, boundary conditions, etc. This may be stored in the model and be retrieved automatically using fe_case(model,'GetCase').
  
  
• def a data structure describing the current state of the model for model/residual assembly using fe_mknl. def is expected to use model DOFs. If Case DOFs are used, they are reexpanded to model DOFs using def=struct('def',Case.T*def.def,'DOF',model.DOF). This is currently used to by the *b.m element family for geometrically non-linear matrices.
  
  
• MatType or Opt describing the desired output, appropriate handling of linear constraints, ect.

• model with the additional field model.K containing the matrices. The corresponding types are stored in model.Opt(2,:). The model.DOF field is properly filled.
• [m,k,mdof] returning both mass and stiffness when Opt(1)==0
• [Mat,mdof] returning a matrix with type specified in Opt(1), see MatType below.

 femesh('reset');
 model =femesh('testubeam');
 model.DOF=[];% an non empty model.DOF would eliminate all other DOFs
 model =fe_case(model,'fixdof','Base','z==0');
 model = fe_mk(model,'Options',[0 2]); 
 [k,mdof] = fe_mk(model,'options',[0 0]); 
 fprintf('With constraints %i DOFs\n',size(k,1)); 
 fprintf('Without          %i DOFs',size(model.K{1},1));
 Case=fe_case(model,'gett');
 isequal(Case.DOF,mdof) % mdof is the same as Case.DOF

Init

• Generation of a complete list of DOFs using the feutil('getdof',model) call.
• get the material and element property tables in a robust manner. Generate node positions in a global reference frame.
  
  
• For each element group, build the GroupInfo data (DOF positions).
• For each element group, determine the unique pairs of [MatId ProId] values in the current group of elements and build a separate integ and constit for each pair. One then has the constitutive parameters for each type of element in the current group. pointers rows 6 and 7 give for each element the location of relevent information in the integ and constit tables.
  
  
• For each element group, perform other initializations as defined by evaluating the callback string obtained using elem('GroupInit'). For example, intialize integration rule data structures, define local bases or normal maps, allocate memory for internal state variables...
  
  
• If requested (call without NoCon), preallocate a sparse matrix to store the assembled model. This topology assumes non zero values at all components of element matrices so that it is identical for all possible matrices and constant during non-linear iterations.

Assemble [ , NoT]

 femesh('reset');
 model =femesh('test hexa8 divide 100 10 10');
 % traditional FE_MK assembly
 tic;[m1,k1,mdof] = fe_mk(model);toc

 % Multi-step approach for NL operation
 tic;[Case,model.DOF]=fe_mknl('init',model);toc
 tic;
 m=fe_mknl('assemble',model,Case,2);
 k=fe_mknl('assemble',model,Case,1);
 toc

MatType

• 0 mass and stiffness assembly. 1 stiffness, 2 mass, 3 viscous damping, 4 hysteretic damping, 5 tangent stiffness in geometric non-linear mechanics. Gyroscopic coupling and stiffness are supported in fe_cyclic;
• 100 volume load, 101 pressure load, 102 inertia load, 103 initial stress load. Note that some load types are only supported with the mat_og element family;
• 200 stress at node, 201 stress at element center, 202 stress at gauss point
• 251 energy associated with matrix type 1 (stiffness), 252 energy associated with matrix type 2 (mass), ...
• 300 compute initial stress field associated with an initial deformation. This value is set in Case.GroupInfo{jGroup,5} directly (be careful with the fact that such direct modification INPUTS is not a MATLAB standard feature). 301 compute the stresses induced by a thermal field.

Opt