Abstract
This paper presents an analytic formula for the theoretical stress concentration factor kt for cylindrical tubes with transverse circular holes, loaded in traction or in flexion. The study is based on modern finite element (FEM) techniques, which allow for appreciating with great accuracy the phenomenon of stress concentration. A comparison between the FEM results of this paper and those that were obtained by the existing analytic formulas shows the need of an update, as some discrepancies may be noticed. Our results are the fruit of a wide campaign of numerical FEM simulations that have been conducted analyzing numerous geometric configurations of the tube. Moreover, these configurations are defined in a wider two-dimensional (2-D) domain than the one valid for previous analytic formulas published in literature. Finally, these FEM results have been approximated with great accuracy by means of a fourth degree double polynomial regression that led to the new analytic formula that is proposed in this paper.
Highlights
Stress concentration phenomena occur whenever a structure charged with loads, which should normally cause a uniform stress distribution, presents strong stress gradients in a few localized very small areas instead.If in proximity of the sudden variations of a mechanical component’s geometry, a regular stress distribution becomes very perturbed, and high stress peaks may be generated there
Simulations that have been conducted analyzing numerous geometric configurations of the tube. These configurations are defined in a wider two-dimensional (2-D) domain than the one valid for previous analytic formulas published in literature. These finite element (FEM) results have been approximated with great accuracy by means of a fourth degree double polynomial regression that led to the new analytic formula that is proposed in this paper
In order to quantify the effect that is produced by generic stress concentrators, a theoretical stress concentration factor kt is commonly defined as: kt =
Summary
Stress concentration phenomena occur whenever a structure charged with loads, which should normally cause a uniform stress distribution, presents strong stress gradients in a few localized very small areas instead. The accurate determination of the stress concentration factor always requires proper and careful investigation This can be carried out following two different approaches: through experimental techniques of structural investigation (such as, for instance, photoelasticity or extensometry), or by means of numerical calculations, which always provide approximate results, the level of approximation can be improved more and more, reaching very high precision. A recent book [12] considers the ESDU3 ofwork of 1989 as an up to date FEM analysis For this reason, we believe that a new investigation that was element codes could treat with great practical difficulties, so complex three-dimensional (3-D). FEM model able to(double describe polynomial a family of different geometrical configurations traction or inof the numerical elaboration regression technique) that allowloaded for theinformulation flexion, all being generated fromour the results same basic.
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