VM-LSDYNA-BENCHMARK-002
VM-LSDYNA-BENCHMARK-002
Elastic Beam, Nonlinear Deflection under Cantilever Load
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 |
| Input Files | Link to Input Files Download Page |
Test Case
A long beam with a square cross-section is fixed at one end. A cantilever load is applied to the free end. Determine the beam projective length and beam deflection at the loaded end.
| Material Properties | Geometric Properties | Loading |
|---|---|---|
|
E = 3x107 psi ν = 0.3 |
L= 50 in B = 1 in H = 1 in |
P = 2000 lbf |
Analysis Assumptions and Modeling Notes
The projective length of the deformed beam (l) was found by numerical integration of ds/dy shown below, where s is the distance along the deformed beam and l is the y-value where s = L (total length of the beam).
 |
From this process, ℓ = 41.97 in.
The beam deflection (δ) was found by numerical integration of dx/dy shown below and δ is the x-value where y = ℓ.
 |
From this process, δ = 24.68 in.
The LS-DYNA Explicit settings were selected to minimize solution running time but ensure that the output deflection reached a steady state free from vibrations. The load application was defined over 0.3 s (force was ramped from 0 to 2000 N over 0.15 seconds then held constant for 0.15 seconds).
The Global Damping was defined to be 100.
The element used was LS-DYNA Explicit Hex 1 with an element size of 0.25 in.
Results Comparison values are reported for the Windows 11 platform.