# 4.13.10. MidDistance¶

beamIntegration('MidDistance', tag, N, *secTags, *locs)

Create a MidDistance beamIntegration object. This option allows user-specified locations of the integration points. The associated integration weights are determined from the midpoints between adjacent integration point locations. $$w_i=(x_{i+1}-x_{i-1})/2$$ for $$i=2...N-1$$, $$w_1=(x_1+x_2)/2$$, and $$w_N=1-(x_{N-1}+x_N)/2$$.

 tag (int) tag of the beam integration N (int) number of integration points along the element. secTags (list (int)) A list previous-defined section objects. locs (list (float)) Locations of integration points along the element.
locs = [0.0, 0.2, 0.5, 0.8, 1.0]
secs = [1,2,2,2,1]
beamIntegration('MidDistance',1,len(secs),*secs,*locs)


Places N integration points along the element, whose locations are defined in locs on the natural domain [0, 1]. The force-deformation response at each integration point is defined by the secs. Both the locs and secs should be of length N. This integration rule can only integrate constant functions exactly since the sum of the integration weights is one.

For the locs shown above, the associated integration weights will be [0.15, 0.2, 0.3, 0.2, 0.15].