fe_stres

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fe_stres

Purpose

Computation of stresses and energies for given deformations.

Syntax

Result = fe_stres('Command',MODEL,DEF)
  ...  = fe_stres('Command',node,elt,pl,il, ...)
  ...  = fe_stres( ... ,mode,mdof)

Description

You can display stresses and energies directly using fecom ColordataEnergies and ColordataEner commands and use fe_stres to analyze results numerically. MODEL can be specified by four input arguments node, elt, pl and il (those used by fe_mk, see also section 7.1 and following), a structure array with fields .Node, .Elt, .pl, .il, or a database wrapper with those fields.

The deformations DEF can be specified using two arguments: mode and associated DOF definition vector mdof or a structure array with fields .def and .DOF.

ene [m,k]ElementSelection

Element energy computation. For a given shape, the levels of strain and kinetic energy in different elements give an indication of how much influence the modification of the element properties may have on the global system response. This knowledge is a useful analysis tool to determine regions that may need to be updated in a FE model.

The strain and kinetic energies of an element are defined by

E_strain^e=

^TK_element

and E_kinetic^e=

^TM_element

Element energies for elements selected with ElementSelection (see the femesh FindElt commands) are computed for deformations in DEF and the result is returned in the structure array RESULT with fields .data and .EltId which specifies which elements were selected.

For comples frequency responses, one integrates the response over one cycle, which corresponds to summing the energies of the real and imaginary parts and using a factor 1/4 rather than 1/2.

feplot allows the visualization of these energies using a color coding. You can use the high level commands fecom ColorDataK or ColorDataM or compute energies and initialize color with (see also the d_ubeam and gartup demos)

 feplot('ColorDataElt',RESULT);
 fecom(';showpatch;ColorBar')

For backward compatibility, fe_stres returns [StrainE,KinE] as two arguments if no element selection is given. To select all elements, use the 'ener groupall' command.

Note that the element energy and not energy density is computed. This may be misleading when displaying energy levels for structures with uneven meshes. upcom provides a compiled version of fe_stres for the superelements it handles.

stress

out=fe_stres('stress CritFcn Rest',MODEL,DEF,EltSel) returns the stresses evaluated at elements of Model selected by EltSel.

The CritFcn part of the command string is used to select a criterion. Currently supported criteria are

sI, sII, sIII	principal stresses from max to min. sI is the default.
mises	Returns the von Mises stress (note that the plane strain case is not currently handled consistently).
-com i	Returns the stress components of index i.

The Rest part of the command string is used to select a restitution method. Currently supported restitutions are

AtNode	average stress at each node (default). Note this is not currently weighted by element volume and thus quite approximate. Result is a structure with fields .DOF and .data
AtCenter	stress at center or mean stress at element stress restitution points. Result is a structure with fields .EltId and .data
AtInteg	stress at integration points (*b family of elements)
Gstate	returns a case with Case.GroupInfo{jGroup,5} containing the group gstate. This will be typically used to initialize stress states in for non-linear computations. For multiple deformations, gstate the first nElt columns correspond to the first deformation.

The fecom ColordataStress directly calls fe_stres and displays the result. For example, run the basic element test q4p testsurstress, then display various stresses using

 q4p('testsurstress')
 fecom('colordatastress atcenter')
 fecom('colordatastress mises')
 fecom('colordatastress sII atcenter')