Overview

Test Case

A rectangular beam is loaded in pure bending. For an elastic-perfectly-plastic stress-strain behavior, show that the beam remains elastic at M = M_yp = σ_ypbh² / 6 and becomes completely plastic at M = M_ult = 1.5 M_yp.

Figure 32: Problem Sketch

Figure 33: Stress-Strain Curve

Figure 34: Workbench Model

Mesh Controls and Symmetry

For each mesh control, the settings shown in Figure 35 and Figure 36 are used. Inflation mesh control is added to the body using the top and bottom faces as the boundaries.

Figure 35: Inflation Settings

For the MultiZone Mesh Method, Hexa is used for the Mapped Mesh Type. For Element Order, Quadratic (Higher Order) is used.

Figure 36: MultiZone Method Settings

A symmetric boundary condition is applied in the global Z direction on the vertical face of the beam.

Figure 37: Inflation Image

Figure 38: Symmetry Image

Figure 39: Mesh Image

Analysis

Manual Mesh Control is set to Geometry, and Full Brick Integration Scheme is selected for the analysis. Two Remote Points are created, one on each end face with Rigid behavior for applying the load and for setting the boundary conditions. One end of the beam is fixed by applying Remote Displacement scoped to Remote Point. Moment load is applied on the other end using Remote Point in four steps: M1 = 24000 lbf-in, M2 = 28000 lbf-in, M3 = 32000 lbf-in and M4 = 36000 lbf-in. Analysis settings for Force and Displacement Convergence are set to On.

Figure 40: Loading and Boundary Condition

Results Comparison

Moment load is applied in four steps, and Directional Deformation in the Y direction on the center node of the free face (on which Moment load is applied) is compared.

Because solid elements do not calculate node rotation at the free end, directional deformation is used as the target for validating results.

This model is not robust at M/M_yp = 1.5, often resulting in an unconverged solution. Invalid results can also occur due to a plastic strain discontinuity at the neutral plane of the beam.