4.13.1. Lobatto

beamIntegration('Lobatto', tag, secTag, N)

beamIntegration('Lobatto', tag, N, *secTags)

Create a Gauss–Lobatto beamIntegration object. Gauss–Lobatto is common for forceBeamColumn (Neuenhofer and Filippou 1997) because it places an integration point at each end of the element, where bending is largest if there are no interior element loads.

Prismatic — one section for all points: (tag, secTag, N).

Non-prismatic — one section tag per point, in order from node I to J: (tag, N, secTag1, secTag2, …, secTagN).

tag (int)	unique beam integration tag
secTag (int)	(prismatic) one defined section for all points
N (int)	number of integration points
secTags (list (int))	(non-prismatic) N section tags

Note

The non-prismatic form assigns different sections along the length (e.g. tapering reinforcement) without relying on hinge-only schemes. The same two forms exist for Legendre, Radau, NewtonCotes, Trapezoidal, and CompositeSimpson.

Example

Prismatic: 6 points, section tag 1. Non-prismatic: 3 sections [1, 2, 1] at 3 Lobatto points.

import openseespy.opensees as ops

ops.beamIntegration('Lobatto', 2, 1, 6)
sec_tag_list = [1, 2, 1]
ops.beamIntegration('Lobatto', 3, len(sec_tag_list), *sec_tag_list)