Overview

Test Case

For an elastic beam subjected to pure bending, validate the use of pyramids in a tetrahedron to hexahedron interface. Find the axial stress at the top, midplane, and bottom surfaces.

Figure 331: Tetrahedron to Hexahedron Interface Problem Sketch

Analysis Assumptions and Modeling Notes

The problem is solved in two different ways:

The model is generated using the block primitive which is divided into 8 sub-blocks. The pyramid interface is created by meshing the hexahedra first, followed by the tetrahedra. The working plane describes the hex-tet interface region.

Full displacement constraints placed upon three corners in the model midplane does not allow generation of significant reaction forces. A pure bending condition is created by the application of a pressure gradient on the faces of elements lying in the z = 0 and z = L planes. The linear gradient varies from -0.18979 on the bottom to 0.18979 on the top.

where

σZ = stress in z-direction

Mz = effective moment, z-direction

y = distance from neutral surface

Ic = second moment of area about the horizontal centroidal axis

Results Comparison

Figure 332: Bending of Hex-to-tet Interface