3.15.2 Meshing and analyzing a two-dimensional model of a beam cross-section

Product: ABAQUS/Standard

Elements tested

WARP2D3 WARP2D4

Features tested

The special-purpose two-dimensional elements WARP2D3 (3-node triangular) and WARP2D4 (4-node quadrilateral) are used to create two-dimensional beam cross-section models. The *BEAM SECTION GENERATE procedure is used to numerically calculate the geometric, stiffness, and inertia properties of the section, including the warping function and shear center location (see “Meshed beam cross-sections,” Section 3.5.6 of the ABAQUS Theory Manual). The calculated properties are written to the jobname.bsp text file.

Problem description

Model:

Several cross-section shapes are considered. Two-dimensional finite element models of an I-section, an I-section with nodal offset, a rectangular section, a pipe section with a cut, a C-section, and an airfoil section (see Figure 3.15.2–1) are included.

Figure 3.15.2–1 An airfoil cross-section.

Mesh:

All the cross-sections are meshed using WARP2D3 and/or WARP2D4 elements.

Material:

Only elastic materials, using either the *ELASTIC, TYPE=ISOTROPIC or *ELASTIC, TYPE=TRACTION option, can be used for the two-dimensional model.

Boundary conditions:

Boundary conditions are not meaningful when generating beam section properties and are ignored.

Loading:

Loads are not meaningful when generating beam section properties and are ignored.

Results and discussion

The beam cross-section properties for each of the meshed cross-sections are written to the jobname.bsp text file. The integrated values of the properties for the meshed beam cross-sections are compared to the analytical solutions or solutions generated for a section from the predefined library. The warping function shapes of the two-dimensional cross-sections compare well with the solutions for the solid element models of the beam subjected to a unit twist.