VM-LSDYNA-BENCHMARK-001

VM-LSDYNA-BENCHMARK-001
Elastic Beam, Linear Deflection under Cantilever Load (small deflection assumption)

Overview

Reference: Chen, L. (2010). An integral approach for large deflection cantilever beams. International Journal of Non-Linear Mechanics, (45), 301-305.
Analysis Type(s): Explicit Dynamics with Workbench LS-DYNA
Element Type(s): Solid

Test Case

A long beam with a square cross-section is fixed at one end. A cantilever load is applied to the other end. Determine the deflection of the beam at the loaded end.

Figure 231: Problem Sketch

Problem Sketch

Figure 232: Ansys Workbench Model

Ansys Workbench Model

Material PropertiesGeometric PropertiesLoading

E = 3x107 psi

ν = 0.3

L= 50 in

B = 2 in

H = 2 in

P = 2000 lbf

Analysis Assumptions and Modeling Notes

The closed form solution for the deflection () of the beam at the loaded end is as follows:

where

Results Comparison values are reported for the Windows 11 platform.

Results Comparison

ResultsTarget Workbench LS-DYNAError (%)
Ux–2.083–2.06280.97