Overview

Test Case

A long bar 1 m x 1 m x 24 m with simply supported ends is subjected to lateral load of 1000 N at a distance of 8 m from one end. Find the deformation in the Y direction at 8 m from the simply supported end. As shown in Figure 112, the study considers two cases: In the first test case, both loads act in the same direction (symmetric). In the second, one load acts in one direction along the Y-axis, and the other load acts in the opposite direction (antisymmetric). Figure 112 shows the external forces and supports for each case.

This test case also appears in the Workbench Verification Manual. See VM-WB-MECH-040.

Figure 112: Problem Sketch

Analysis Assumptions and Modeling Notes

For case 1, considering symmetry, the following formula is used for the displacement in the Y-direction:

(1)

For case 2, considering anti-symmetry, the following formula is used for the displacement in the Y-direction:

(2)

where

is the force applied

is the length of the bar

is the Young's modulus

is the inertia

Figure 113: Problem setup for symmetric case

Figure 114: Problem setup for anti-symmetric case

In LS-DYNA, a beam-type model (using the SECTION_BEAM keyword) is used by selecting the section type with a value for ELFORM of 1 (using the Hughes-Liu formulation with cross-section integration) and a value for QR/IRID of 2 (2 x 2 Gauss quadrature). As shown in the figures below, the mesh has been divided for each of the cases.

Figure 115: Model with elements per bar and loads for symmetric case

Figure 116: Model with elements per bar and loads for anti-symmetric case

Results Comparison

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