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Structural Element - Example

void
StructuralElement ::  giveCharacteristicMatrix (FloatMatrix& answer, 
                      CharType mtrx, TimeStep *tStep) 
// 
// returns characteristic matrix of receiver according to mtrx
//
{
  if (mtrx == TangentStiffnessMatrix) 
    this -> computeStiffnessMatrix(answer, TangentStiffness, tStep);
  else if (mtrx == SecantStiffnessMatrix) 
    this -> computeStiffnessMatrix(answer, SecantStiffness, tStep);
  else if (mtrx == MassMatrix) 
    this -> computeMassMatrix(answer, tStep);
  else if 
  ....
}

void
StructuralElement :: computeStiffnessMatrix (FloatMatrix& answer, 
                     MatResponseMode rMode, TimeStep* tStep)
// Computes numerically the stiffness matrix of the receiver.
{
  int j;
  double      dV ;
  FloatMatrix d, bj, dbj;
  GaussPoint  *gp ;
  IntegrationRule* iRule;

  // give reference to integration rule
  iRule = integrationRulesArray[giveDefaultIntegrationRule()];
     
  // loop over integration points
  for (j=0 ; j < iRule->getNumberOfIntegrationPoints() ; j++) {
     gp = iRule->getIntegrationPoint(j) ;
     // compute geometrical matrix of particular element 
     this -> computeBmatrixAt(gp, bj) ;  
     //compute material stiffness
     this -> computeConstitutiveMatrixAt(d, rMode, gp, tStep); 
     // compute jacobian
     dV = this -> computeVolumeAround(gp) ; 
     // evaluate stiffness
     dbj.beProductOf (d, bj) ;
     answer.plusProductSymmUpper(bj,dbj,dV) ; 

  }
 
  answer.symmetrized() ;
  // transform into global coordinate system if necessary
  if (this->updateRotationMatrix()) 
     answer.rotatedWith(*this->rotationMatrix) ;
  return  ;
}

The element strain and stress vectors at a given integration point are computed using computeStrainVector and computeStressVector services. The element strain vector can be evaluated using , where is the geometrical matrix and is element local displacement vector. The stress evaluation is rather simple, since the stress evaluation from a given strain increment and actual state (kept within the integration point) is done at the cross section description level (integration over cross section volume) and material model level (stress evaluation).

void
StructuralElement :: computeStrainVector (FloatArray& answer, 
                     GaussPoint* gp, TimeStep* stepN)
// Computes the vector containing the strains 
// at the Gauss point gp of the receiver, 
// at time step stepN. The nature of these strains depends
// on the element's type.
{
  FloatMatrix b;
  FloatArray  u ;
  
  this -> computeBmatrixAt(gp, b) ;
  // compute vector of element's unknowns
  this -> computeVectorOf(DisplacementVector,
                          UnknownMode_Total,stepN,u) ;
  // transform global unknowns into element local c.s.
  if (this->updateRotationMatrix()) 
     u.rotatedWith(this->rotationMatrix,'n') ;
  answer.beProductOf (b, u) ;
  
  return ;
}


void
StructuralElement :: computeStressVector (FloatArray& answer, 
                     GaussPoint* gp, TimeStep* stepN)
// Computes the vector containing the stresses 
// at the Gauss point gp of the receiver, at time step stepN. 
// The nature of these stresses depends on the element's type.
{

  FloatArray Epsilon ;
  StructuralCrossSection* cs = (StructuralCrossSection*) 
                                this->giveCrossSection();
  Material *mat = this->giveMaterial();
  
  this->computeStrainVector (Epsilon, gp,stepN) ;
  // ask cross section model for real stresses 
  // for given strain increment 
  cs -> giveRealStresses (answer, ReducedForm, gp, Epsilon, stepN);

  return  ;
}

The StructuralElement class overloads also services for context storing/restoring, calling corresponding services for all integration rules (and thus on all integration points belonging to an element).

For further reference see OOFEM library reference manualand files ``structuralelement.h'' and ``structuralelement.C''.

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Next: Isoparametric Truss 2d element Up: Analysis specific element classes Previous: Analysis specific element classes   Contents