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Subsubsection 4.3.4.1: Gauss-Kronrod Trapezoidal Rule Up Subsection 4.3.4: Scheme Subsubsection 4.3.4.3: Trapezoidal Rule

#### 4.3.4.2 Finite Element Integration Rule

The scheme type for the finite element integration rule is “fibers-3d-fei” for unconstrained and uncoupled continuous fiber distributions. This integration rule should only be used with 3D fiber density distributions. This scheme discretizes the unit sphere into a set of spherical triangles of nearly identical surface areas. The unit normal passes through the centroid of each surface element. The integration is performed as a summation over . For each direction the stress is evaluated only if the fiber bundle is in tension along that direction. The following material parameters need to be defined:
 the number of integration points [ ]
The parameter <resolution> must be one of the values 20, 34, 60, 74, 196, 210, 396, 410, 596, 610, 796, 810, 996, 1010, 1196, 1210, 1396, 1410, 1596, 1610, and 1796. A recommended combination is nph=7 and nth=31. A conservative choice for producing accurate results under general loading conditions is 1610. Increasing values of require increasing computational time.
Example :
<scheme type="fibers-3d-fei">
<resolution>1610</resolution>
</scheme>


Subsubsection 4.3.4.1: Gauss-Kronrod Trapezoidal Rule Up Subsection 4.3.4: Scheme Subsubsection 4.3.4.3: Trapezoidal Rule