3.1.9.9. LowOrder

beamIntegration('LowOrder', tag, N, *secTags, *locs, *wts)

Create a LowOrder beamIntegration object. This option is a generalization of the FixedLocation and UserDefined integration approaches and is useful for moving load analysis (`Kidarsa, Scott and Higgins 2008`_). The locations of the integration points are user defined, while a selected number of weights are specified and the remaining weights are computed by the method of undetermined coefficients.

\[\sum_{i=1}^{N_f}x_{fi}^{j-1}w_{fi}=\frac{1}{j}-\sum_{i=1}^{N_c}x_{ci}^{j-1}w_{ci}\]

Note that FixedLocation integration is recovered when Nc is zero.

tag |int|	tag of the beam integration
N |int|	number of integration points along the element.
secTags |listi|	A list previous-defined section objects.
locs |listf|	Locations of integration points along the element.
wts |listf|	weights of integration points.

locs = [0.0, 0.2, 0.5, 0.8, 1.0]
wts = [0.2, 0.2]
secs = [1, 2, 2, 2, 1]
beamIntegration('LowOrder',1,len(secs),*secs,*locs,*wts)

Places N integration points along the element, which 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. The wts at user-selected integration points are specified on [0, 1], which can be of length Nc equals 0 up to N. These specified weights are assigned to the first Nc entries in the locs and secs, respectively. The order of accuracy for Low Order integration is N-Nc-1.

Note

Nc is determined from the length of the wts list. Accordingly, FixedLocation integration is recovered when wts is an empty list and UserDefined integration is recovered when the wts and locs lists are of equal length.