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SIF analytic Solution (Mode I and/or II) for Tubes

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I was wondering if anyone knows of an analytic Solution for KI and/or KII in tubes.

I´ve seen an infinite number of equations, shape functions, FEM simulations, standards, etc. But one closed solution for tubes?, an analog to Williams series but for cilindirical surfaces?

I am trying to fit experimental displacement data to Williams series. I´ve done it succesfully for flat specimens (kind of easy actually). But now, we have to do the same for tubes. When cracks are long, you can´t approximate the tube surface to an infinite plate anymore.

modelling a 3D composite tube

Hi guys,

I deal with modal analysis of  3D 'both clmaped' composite tube in ANSYS. I use solid elements and orthotropic model of material. Constants of this material are homogenized values of composite tube. So I meshed the tube and set the element coord system ESYS as cylindrical. The problem is with results, becasue after solving I get very low eigenfrequncies, i.e. first 100 eigenfrequencies are from 0 to 10 Hz  with step 1 Hz and it seems a bit weird.


Do you have any tips where the problem could be?




J integral variation through thickness in tubes with through-wall circumferential crack, calculated with Abaqus/CAE

Dear friends: I am a PhD candidate studying fracture problems in tubes. I am doing J integral calculations in Abaqus, for tubes with through-wall circumferential cracks subjected to tensile and bending loads. I am using quadratic 20 nodes isoparametric elements with reduced integration (C3D20R), ranging from two to five elements through the wall thickness mesh.

Bending and wrinkling as competing relaxation pathways for strained free-hanging films

A thin film subject to compressive strain can either bend (for large strain gradient) or wrinkle (for small strain gradient). The bending is traditionally used in thermostats (bimetal stripes), but couple of years ago, it was extended to the nanoscale thin films which can bend and roll-up to tubes with defined number of rotations. The wrinkles are also rather common in macro- and microscale thin films.
Here, we developed an equilibrium phase diagram for the shape of
compressively strained free-hanging films by total strain energy

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