Overview

Test Case

A long, rectangular plate is fixed along the longitudinal face, and the opposite face is subjected to a moment of 5000 lbf-in about the Z axis. To get accurate results, the advanced mesh control element size is set to 0.5 inches. The goal is to find the X normal stress at a distance of 0.5 inches from the fixed support as well as the total deformation and reaction moment.

This test case also appears in the Workbench Verification Manual. See VM-WB-MECH-030.

Figure 108: Problem sketch

Figure 109: Problem setup

Analysis Assumptions and Modeling Notes

Since the loading is uniform and in one plane (the X-Y plane), the test case can be analyzed as a plane strain problem. Therefore, the moment applied will be per unit length (5000/1000 = 5 lbf-in). The analysis takes into account the unit length in the Z-direction.

In LS-DYNA, a shell-type model (using the SECTION_SHELL keyword) has been used by selecting the section type, with a value for ELFORM of 13 (using Plane strain) and a value for NIP of 4 (2 x 2 Gauss quadrature with fully integrated two-dimensional elements). To achieve good results, the problem requires a very fine mesh, as shown in Figure 111.

Figure 110: Plane Strain Model (analyzing any cross section (40" x 1") along the length)

Figure 111: Plane Strain Model (analyzing any cross section (40" x 1") along the length)

Results Comparison

The LS-DYNA results are nearly identical to the theoretical results.