VM-LSDYNA-SOLVE-020

VM-LSDYNA-SOLVE-020
Elasto-Plastic Analysis of a Rectangular Beam

Overview

Reference: Any solid mechanics textbook
Analysis Type(s): Static Plastic Analysis
Element Type(s): Shell
Input Files:Link to Input Files Download Page

Test Case

This test case also appears in the Workbench Mechanical Verification Manual. See VM-WB-MECH-029.

A rectangular beam is loaded in pure bending. For an elastic-perfectly-plastic stress-strain behavior, show that the beam remains elastic at M = Myp = σypbh2/6 and becomes completely plastic at M = Mult = 1.5 Myp.

Figure 78: Problem Sketch

Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30,000,000 psiLength, L = 10 inM = 1.0 Myp = 24,000 lbf-in
σyp = 36,000 psiWidth, b = 1 inM = 1.25 Myp = 30,000 lbf-in
v = 0.0Height, h = 2 inM = 1.5 Myp = 36,000 lbf-in

Analysis Assumptions and Modeling Notes

The rectangular beam is made of ten shell elements using ELFORM 2 and thickness 2 inches. The number of through thickness integration points is set to eight with NIP in *SECTION_SHELL. Lobatto integration is specified in *CONTROL_SHELL to measure integration point stress on the shell surfaces. Material properties including yield strength are defined in *MAT_PLASTIC_KINEMATIC. ETAN is set to zero to make an elastic-perfectly-plastic model.

*BOUNDARY_SPC_SET creates a fixed support at one end of the beam. The opposite end face was made rigid using a *CONSTRAINED_NODAL_RIGID_BODY. This was necessary to apply a moment to the tip of the beam. The moment was prescribed using *LOAD_RIGID_BODY. Implicit analysis is used with NSOLVER 12. Static analysis is specified with IMASS in *CONTROL_IMPLICIT_DYNAMICS.

The maximum von mises stress is measured from d3plot using the History tool in LS-PrePost.

Results Comparison

Below are three sets of column plots. The first plot shows the maximum von mises stress with respect to time for M = 24000, 30000, and 36000 lbf-in, respectively. The second plot shows the applied moment with respect to time. The rate of applied moment is equal in each test case. Results show that the beam becomes plastic once a stress of 36000 psi is reached.

ResultsTarget LS-DYNAError (%)

Equivalent Stress, psi for

M = 24000 lbf-in

36000360000.0

Equivalent Stress, psi for

M = 30000 lbf-in

36000360000.0

Equivalent Stress, psi for

M = 36000 lbf-in

36000360000.0

Figure 79: Maximum von mises stress with respect to time (M = 24000)

Maximum von mises stress with respect to time (M = 24000)

Figure 80: Applied moment with respect to time (M = 24000)

Applied moment with respect to time (M = 24000)

Figure 81: Maximum von mises stress with respect to time (M = 30000)

Maximum von mises stress with respect to time (M = 30000)

Figure 82: Applied moment with respect to time (M = 30000)

Applied moment with respect to time (M = 30000)

Figure 83: Maximum von mises stress with respect to time (M = 36000)

Maximum von mises stress with respect to time (M = 36000)

Figure 84: Applied moment with respect to time (M = 36000)

Applied moment with respect to time (M = 36000)