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Geometric Properties of an Elliptical Tube

Summary

In the analysis of elliptical tube secstions, we need to divide the tube section into a number of segments. The forces acted over the segment are then distributed onto the nearest finite element nodes.

The Problem

In the figure below, there is an elliptical tube of radius (a,b) and thichness t. For a segment from a1 to a2, we need to find its area and centroid. The solution may not have to be exact.

The solution



Accuracy Analysis

Test Example 1
  a = 180
  b = 120
  t = 10
Applied forces : N=1000, Mx=100000, My=100000.

The forces are distributed onto the section using plane theory to get the stress plane. The tube section is divided into 200 segements. The force on each segment is then calculated as
     F = SegmentArea * StressAtCentroid
     Mx = F * Ycentroid
     My = F * Xcentroid

Sum over all segments gives the total

     N = 999(0.1%)     Mx=98250 (1.75%)     My=101919(1.92%)

Test Example 2

  a = 180
  b = 180
  t = 10

Therefore, it is actually a circular tube. But the load is distributed as an elliptical tube to check its accuracy.

Results:
  N = 1000(0.00%)  Mx=99987(0.13%)      My=99987(0.13%)