plane stress vs generalized plane strain vs plane strain

Posted 2024年6月12日 GMT-4 00:54 Structural Mechanics, Physics Interfaces, User Interface Version 6.0 1 Reply

Jung Tae Lee

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When solving 2D plane stress problem, the results are different in generalized plane strain (GPS) and plane strain (PS) both cases with external strain node applied. Which seems quite obvious because two conditions have different geverning equations. But I would like to know what exactly the plane strain does with the external strain node applied (under each linear elastic material node). Also I would like to know why the GPS results are not consistent with the 3D midplane results.

As an example, let us look at a simple solenoid case comparing the 3D midplane results with 2D plane_PS(PS+external strain) and 2D plane_GPS(GPS+external strain). All three models have the same loading condition which results from Lorentz force by applying 200 A/mm^2 in phi-direction. For 2D models, the force in z-direction is zero so this effect was accounted for by giving the resultant strain in z-direction (-0.0001464) obtained from the 3D model.

Thre results comparison for three models are shown in the figures in the image link-> https://postimg.cc/gallery/H851c4p 3D model and 2D_PS model shows consistent results with only difference in z-direction strain. It seems that the 2D_PS model solves the problem ignoring the external stress at first then recalculate the stress in z-direction with the given external strain. But then external strain value is not reflected in the final result (just displays 0 just as default value for typical PS condition). While 2D_GPS shows about 10% of difference in strain as well as in displacement, the stress in x and y-direction are consistent with other models. But then the strain and stress in z-direction shows entirely different results! This is where my mind is blowing.

My guess for this situation for now is that there should be an additional contraint to the 2D_GPS model (maybe some kind of weak constraint). This may do some trick in reformulating the problem so that the resultant strain match the given external strain. So I searched about this and found a blog from 2017 about GPS problem: https://www.comsol.com/blogs/how-to-model-generalized-plane-strain-with-comsol-multiphysics. But this has a Singular matrix problem and cannot be solved by any means.

Does anybody have a clue on why this kind of deviation occurs in 2D_GPS model and a way to resolve?

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1 Reply Last Post 2024年6月12日 GMT-4 02:45

Henrik Sönnerlind COMSOL Employee

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Posted: 2 weeks ago

Updated: 2 weeks ago

Without looking at your problem in detail, the general behaviour of the 2D formulations is based on the full 3D Hooke's law, expressed as

Whatever plane conditions that are imposed, are imposed on this equation.

Please note that the blog post you mention was written before generalized plane strain was a built-in option.

A more recent blog post discussing the various 2D options:

https://www.comsol.com/blogs/what-is-the-difference-between-plane-stress-and-plane-strain

Here, the effects of an imposed out-of-plane strain (in terms of thermal expansion) is discussed in some detail.

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Henrik Sönnerlind
COMSOL

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