Using statistics in the post-process of FEA results


When we are solving a model using Finite Element Analysis, the results are obtained via a distribution map. These internal distributions of the forces  ̶ called stress ̶  appear in the inner regions of the models due to the action of external forces. To model how different forces act on a biological structure, as a bone for example, computational models are created. These models are subdivided in small pieces called “elements” using a mesh. Then, theoretical forces are applied to the model and the stress values of each element are recorded and mapped in a coloured map called stress distribution which enables a qualitative comparison between different models. Of course, this “coloured map” is related with values. Specifically,. with the values obtained from the solving in each element of the mesh.

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To analyse these stress values in a quantitative framework could be complicated, as these elements have different size in the same mesh. for this reason, we published recently the work: ” Accounting for differences in element size and homogeneity when comparing Finite Element models: Armadillos as a case study” in Palaeontologia Electronica. In this work we propose a method to obtain the average mean and median of the distribution of these stresses in a Finite Element model weighting for the differences in elements size. On the other hand we propose a procedure to check whether the meshes used to generate the elements provide accurate results to be used later in statistical analysis. Therefore the stress values can be used as a proxy of the relative strength of vertebrate structures in a comparative framework and allow comparing the obtained mechanical results of different models.

This figure is an example: Box-plots of Von Mises stress distributions when Quasi-Ideal Meshes (QUIM) are assumed for the 20 Cingulata mandibles analysed in the work enabling a qualitative comparison between species and diets.

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Citation: Marcé-Nogué, J., Esteban-Trivigno, S. de, Escrig, C., & Gil, L. (2016). Accounting for differences in element size and homogeneity when comparing Finite Element models: Armadillos as a case study. Palaeontologia Electronica, 19(2), 1–22

Read more: http://goo.gl/2wFCSL

 

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