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Re: Vertebrate long bone strength (implications for dinosaurs)

Thanks to Ben for posting this heads up.  I just grabbed the full paper (it's 
free!) and am giving it a read through.  I am quite enjoying the manuscript and 
the topic is of great importance.  My one critique would be that while the MS 
certainly shows that FEA and beam theory get very different answers for 
compressive strength estimation, it isn't clear from the paper how the authors 
know that FEA is getting closer to the right answer.  They presume this is the 
case (so far as I can tell so far) based on violations of assumptions in beam 
theory, but FEA makes assumptions, as well, and it isn't clear how the authors 
are dealing with that side of things.  In the conclusions, they do seem to take 
note of this issue:

"Future studies applying FEA to long bone stress estimation
should proceed with caution, however, particularly when variables
such as applied forces and material properties remain
uncertain. This is necessarily the case in palaeontological
studies, and, therefore, sensitivity analyses should be carried
out in order to quantify the effect of the error introduced by
these unknowns. It must be emphasized that applying an
overly simplified FEA model to a complex biomechanical problem
may result in incorporating just as many assumptions
into the analysis as the application of classic beam theory."


--Mike H.

On Nov 21, 2012, at 12:36 PM, Ben Creisler wrote:

> From: Ben Creisler
> bcreisler@gmail.com
> A new paper. The pdf is free:
> Charlotte A. Brassey Lee Margetts, Andrew C. Kitchener, Philip J.
> Withers, Phillip L. Manning and William I. Sellers (2013)
> Finite element modelling versus classic beam theory: comparing methods
> for stress estimation in a morphologically diverse sample of
> vertebrate long bones.
> Journal of the Royal Society Interface10 (79): 20120823
> doi: 10.1098/rsif.2012.0823
> http://rsif.royalsocietypublishing.org/content/10/79/20120823.abstract
> Classic beam theory is frequently used in biomechanics to model the
> stress behaviour of vertebrate long bones, particularly when creating
> intraspecific scaling models. Although methodologically
> straightforward, classic beam theory requires complex irregular bones
> to be approximated as slender beams, and the errors associated with
> simplifying complex organic structures to such an extent are unknown.
> Alternative approaches, such as finite element analysis (FEA), while
> much more time-consuming to perform, require no such assumptions. This
> study compares the results obtained using classic beam theory with
> those from FEA to quantify the beam theory errors and to provide
> recommendations about when a full FEA is essential for reasonable
> biomechanical predictions. High-resolution computed tomographic scans
> of eight vertebrate long bones were used to calculate diaphyseal
> stress owing to various loading regimes. Under compression, FEA values
> of minimum principal stress (σmin) were on average 142 per cent (±28%
> s.e.) larger than those predicted by beam theory, with deviation
> between the two models correlated to shaft curvature (two-tailed p =
> 0.03, r2 = 0.56). Under bending, FEA values of maximum principal
> stress (σmax) and beam theory values differed on average by 12 per
> cent (±4% s.e.), with deviation between the models significantly
> correlated to cross-sectional asymmetry at midshaft (two-tailed p =
> 0.02, r2 = 0.62). In torsion, assuming maximum stress values occurred
> at the location of minimum cortical thickness brought beam theory and
> FEA values closest in line, and in this case FEA values of τtorsion
> were on average 14 per cent (±5% s.e.) higher than beam theory.
> Therefore, FEA is the preferred modelling solution when estimates of
> absolute diaphyseal stress are required, although values calculated by
> beam theory for bending may be acceptable in some situations.
> ===
> Science magazine Science Shots online news mentions how this study may
> apply to dinosaurs:
> http://news.sciencemag.org/sciencenow/2012/11/scienceshot-curves-are-tough-on-.html
> "The strategy might be especially useful in reconstructing animals
> that are extinct, such as dinosaurs. Overestimating the strength of a
> dinosaur's leg bones by ignoring the effects of bone curvature may, in
> turn, mean overestimating how much weight those bones could have
> supported. Turns out, large dinos like Tyrannosaurus rex and the
> lumbering sauropods might have been somewhat slimmer than previously
> believed."