VM-LSDYNA-SOLVE-025

VM-LSDYNA-SOLVE-025
Laterally Loaded Tapered Support Structure

Overview

Reference: Crandall, S.H. & Dahl, N.C. (1959). An introduction to the mechanics of solids. McGraw-Hill Book Co. p.342.
Analysis Type(s): Implicit Analysis
Element Type(s): Shell

Test Case

A cantilever beam of thickness t and length 𝓁 has a depth d which tapers uniformly from d at the tip to 3d at the wall. It is loaded by a force F at the tip, as shown. Find the maximum bending stress at the fixed end of the beam.

This problem is also presented in test case VM5 in the Mechanical APDL Verification Manual.

Figure 96: Problem Sketch: Cantilever Beam

Problem Sketch: Cantilever Beam

Material PropertiesGeometric PropertiesLoading

E = 3e7 psi

ν = 0

t = 2 in

d = 3 in

𝓁 = 50 in

F = 4000 lb

Analysis Assumptions and Modeling Notes

The tapered cantilever beam is modeled with shell element elform 1, 12, and 16. The nodes at the fixed end of the beam are constrained in x, y, z, rx, ry, and rz directions. And a point load is applied at the free tip node of the beam with *LOAD_NODE_POINT. An implicit analysis is performed to find out the maximum x stress at the fixed end, and the results are compared among different element formations.

The beam is meshed with a 0.2 in element size, as shown in Figure 97.

Figure 97: Cantilever Beam Mesh

Cantilever Beam Mesh

Results Comparison

ResultsTarget LS-DYNA SolverError (%)
Stress at fixed end (psi) elform = 1 74077759.34.8
Stress at fixed end (psi) elform = 12 74077758.74.7
Stress at fixed end (psi) elform = 16 74077753.24.7