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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). Loads are associated with case structures with at least a Case.Stack field giving all the case entries. Addition of entries to the cases, it typically done using fe_case.

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). In general simultaneous assembly of matrices and loads detailed in section 4.8.8 is preferable.

The option 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.

The frequency or time dependence of a load can be specified as a data.curve field in the load case entry. This field is a cell array specifying the dependence for each column of the applied loads.

Each entry can be a curve data structure, or a string referring to an existing curve (stored in the model.Stack), to describe frequency or time dependence of loads.

Units for the load are defined through the .lab field (in {F}=[B]{u} one assumes u to be unitless thus F and B have the same unit systems).

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

data.DOF | column vector containing a DOF selection |

data.def | matrix of load/set for each DOF (each column is a load/set case and the rows are indexed by Case.DOF ). With two DOFs, def=[1;1] is a single input at two DOFs, while def=eye(2) corresponds to two inputs. |

data.name | optional name of the case |

data.lab | optional cell array giving label, unit label , and unit info (see fe_curve DataType) for each load (column of data.def) |

data.curve | see fe_load curve |

Typical initialization is illustrated below

% Applying a load case in a model model = femesh('testubeam plot'); % Simplified format to declare unit inputs model=fe_case(model,'DofLoad','ShortTwoInputs',[362.01;258.02]); % General format with amplitudes at multiple DOF % At node 365, 1 N in x and 1.1 N in z data=struct('DOF',[365.01;365.03],'def',[1;1.1]); data.lab=fe_curve('datatype',13); model=fe_case(model,'DofLoad','PointLoad',data); Load = fe_load(model); feplot(model,Load); fecom(';scaleone;undefline;ch1 2') % display

When sensors are defined in SDT, loads collocated with sensors can be defined using sensor DofLoadSensDof.

FVol entries use data is a structure with fields

data.sel | an element selection (or amodel description matrix but this is not acceptable for non-linear applications). |

data.dir | a 3 by 1 cell array specifying the value in each global direction x, y, z. Alternatives for this specification are detailed below . The field can also be specified using .def and .DOF fields. |

data.lab | cell array giving label, unit label , and unit info (see fe_curve DataType) for each load (column of data.def) |

data.curve | see fe_load curve |

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

% Applying a volumic load in a model 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 entries use data a structure with fields

data.sel | a vector of NodeId in which the faces are contained (all the nodes in a loaded face/edge must be contained in the list). data.sel can also contain any valid node selection (using string or cell array format). |

the optional data.eltsel field can be used for an optional element selection to be performed before selection of faces with feutil('selelt innode',model,data.sel). The surface is obtained using% Surface selection mechanism performed for a FSurf input if isfield(data,'eltsel'); mo1.Elt=feutil('selelt',mo1,data.eltsel); end elt=feutil('seleltinnode',mo1, ... feutil('findnode',mo1,r1.sel)); | |

data.set | Alternative specification of the loaded face by specifying a face set name to be found in model.Stack |

data.def | a vector with as many rows as data.DOF specifying a value for each DOF. |

data.DOF | DOF definition vector specifying what DOFs are loaded. Note that pressure is DOF .19 and generates a load opposite to the outgoing surface normal. Uniform pressure can be defined using wild cards as show in the example below. |

data.lab | cell array giving label, unit label ,and unit info (see fe_curve DataType) for each load (column of data.def) |

data.curve | see fe_load curve |

data.type | string giving 'surface' (default) or 'edge' (used in the case of 2D models where external surfaces are edges) |

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

% Applying a surfacing load case in a model using selectors 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

% Applying a surfacing load case in a model using node lists 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

% Applying a surfacing load case in a model using sets 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

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