3.1.9.1. Lobatto

This command is used to create a Gauss-Lobatto beamIntegration object. Gauss-Lobatto integration is the most common approach for evaluating the response of ForceBeamColumn (`Neuenhofer and Filippou 1997`_) because it places an integration point at each end of the element, where bending moments are largest in the absence of interior element loads.

Two input forms are supported:

Prismatic – One section for all integration points:

beamIntegration Lobatto tag secTag N

Non-prismatic – One section tag per integration point (section tags are mapped to Lobatto point locations in order from node I to node J):

beamIntegration Lobatto tag N secTag1 secTag2 ... secTagN

Note

The non-prismatic form allows different sections along the element length (e.g. different reinforcement or cross-sections) without using FixedLocation or plastic-hinge integration. Same option exists for Legendre, Radau, NewtonCotes, Trapezoidal, CompositeSimpson, and other distributed plasticity methods.

Example

Prismatic: 6 integration points, one section (tag 1). Non-prismatic: 3 sections (tags 1, 2, 1) at the 3 Lobatto points.

  1. Tcl Code

beamIntegration Lobatto 2 1 6
beamIntegration Lobatto 3 3 1 2 1

  1. Python Code

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