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Membrane and Bending stress extraction from NASTRAN solids elements(4)
Hi all!!
I am working on a heat exchanger analysis with NASTRAN. The sheet plate is modeled with CHEXA elements. As the analysis results must be checked with the ASME code, I need to extract the MEMBRANE and BENDING stresses from these solid elements. Does anybody know how to? Thank you!!
PPD 

40818 (Aerospace) 
28 Jun 07 14:50 
Why are you modelling a thin sheet with solid elements?? Not even sure if you can get membrane stresses developed within solid elements. Also depending upon the geometry/constraint system you might not be able to develop membrane stresses anyway. 

Ah, the idiocy of automeshing a 3D CAD solid. Thin plates/shells should be modelled with shell elements (or at least solid shell elements available in some codes).
You can calculate "membrane" and "bending" stress by pairing up stress results from the nodes on the top and bottom of the plate. Membrance stress is the average of the top and bottom surface stresses and the bending stress is the difference of the the top and bottom surface stresses. However the results from the CEXA element for a plate bending case are likely to be rubbish unless you have a lot of element through the place thickness. You should run a simple beam bending case to check your mesh density and element selection, and to test your postprocessing method.


TGS4 (Mechanical) 
28 Jun 07 18:25 
I would highly recommend that you obtain a copy of WRC Bulletin 429. I provides all the details with which you need in order to perform an analysis to ASME Section VIII, Division 2, Appendix 4, using 3D solid finite elements.
Once you have obtained that and read it, if you have any more questions, please feel free to come back to the forum and we will try to help you. 

I did not get the WRC Bulletin 429 yet, so I try on with solid modelling (There is a specific geometry between plate and shell to be evaluated) I put shells (CQUAD4) with very low thickness on the top and bottom of my solidmodeled plate, sharing nodes with HEXA element faces, and with the same material. Is this OK to get membrane stresses of the plate section? ¿is the membrane stress corresponding with Tresca values at this shells? Would it be correct to get bending as the differenc of this two membrane stresses?
Thank you!


The thin shells on surface will just give you the surface stress. I once wrote a program that could extract bending moments, axial and torsion load going through any planar crosssection of a solid mesh. I wish most FEA programs came with this tool as it is very useful for doing equilibrium checks. Principal  http://www.OnlineFEASolver.com General FEA Consulting Services 

40818 (Aerospace) 
2 Jul 07 16:07 
You should probably look for VonMises stresses on the tension face skin, and minprincipal stresses on the compression face skin. Check your core shears also
Again, be carefull with your "membrane" stresses if thats what your looking for. Your loading and structural setup might mean that you cannot generate membrane stresses especially with linear FE, think of a cantelever beam.
The bending properties of a plate depend greatly on its thickness as compared with its other dimensions. Plates can be summariased into three kinds: (1) thin plates with small deflections, (2) thin plates with large deflections, (3) thick plates.
Thin plates with small deflection. If deflections of a plate are small in comparison with its thickness (or to be more exact deflections small in comparison to its radius of curvature), a very satisfactory approximate theory of bending of the plate by lateral loads can be developed by making the following assumptions: 1. There is no deformation in the middle plane of the plate. This plane remains neutral during bending. 2. Points of the plate lying initially on a normaltothemiddle plane of the plate remain on the normaltothemiddle surface of the plate after bending. 3. The normal stresses in the direction transverse to the plate can be disregarded.
Using these assumptions, all stress components can be expressed by deflection of the plate, which is a function of the two coordinates in the plane of the plate. This function has to satisfy a linear partial differential equation, which, together with the boundary conditions, completely defines the deflection. Thus the solution of this equation gives all necessary information for calculating stresses at any point of the plate. The second assumption is equivalent to the disregard of the effect of shear forces on the deflection of plates. This assumption is usually satisfactory, but in some cases (for example, in the case of holes in a plate) the effect of shear becomes important and some corrections in the theory of thin plates should be introduced. If, in addition to lateral loads, there are external forces acting in the middle plane of the plate, the first assumption does not hold any more, and it is necessary to take into consideration the effect on bending of the plate of the stresses acting in the middle plane of the plate. This can be done by int.oducing some additional terms into the differential equation of plates.
Thin plates with large deflection. The first assumption is completely satisfied only if a plate is bent into a developable surface. In other cases bending of a plate is accompanied by strain in the middle plane, but calculations show that the corresponding stresses in the middle plane are negligible if the deflections of the plate are small in comparison with its thickness. If the deflections are not small, these supplementary stresses must be taken into consideration in deriving the differential equation of plates. In this way we obtain nonlinear equations and the solution of the problem becomes much more complicated. In the case of large deflections we have also to distinguish between immovable edges and edges free to move in the plane of the plate, which may have a considerable bearing upon the magnitude of deflections and stresses of the plate. Owing to the curvature of the deformed middle plane of the plate, the supplementary tensile stresses, which predominate, act in opposition to the given lateral load; thus, the given load is now transmitted partly by the flexural rigidity and partly by a membrane action of the plate. Consequently, very thin plates with negligible resistance to bending behave as membranes, except perhaps for a narrow edge zone where bending may occur because of the boundary conditions imposed on the plate. The case of a plate bent into a developable, in particular into a cylindrical, surface should be considered as an exception. The deflections of such a plate may be of the order of its thickness without necessarily producing membrane stresses and without affecting the linear character of the theory of bending. Membrane stresses would, however, arise in such a plate if its edges are immovable in its plane and the deflections are sufficiemly large. Therefore, in “plates with small deflection” membrane forces caused by edges immovable in the plane of the plate can be practically disregarded.
When discussing "Thick Plates". The approximate theories of thin plates, discussed above, become unreliable in the case of plates of considerable thickness, especially in the case of highly concentrated loads. In such a case the thickplate theory should be applied. This theory considers the problem of plates as a threedimensional problem of elasticity. The stress analysis becomes, consequently, more involved and, up to now, the problem is completely solved only for a few particular cases. Using this analysis, the necessary corrections to the thinplate theory at the points of application of concentrated loads can be introduced. The main suppositions of the theory of thin plates also form the basis for the usual theory of thin shells. There exists, however, a substantial difference in the behavior of plates and shells under the action of external loading. The static equilibrium of a plate element under a lateral load is only possible by action of bending and twisting moments, usually accompanied by shearing forces, while a shell, in general, is able to transmit the surface load by “membrane” stresses which act parallel to the tangential plane at a given point of the middle surface and are distributed uniformly over the thickness of the shell. This property of shells makes them, as a rule, a much more rigid and a more economical structure than a plate would be under the same conditions. In principle, the membrane forces are independent of bending and are wholly defined by the conditions of static equilibrium. The methods of determination of these forces represent the socalled “membrane theory of shells.” However, the reactive forces and deformation obtained by the use of the membrane theory at the shell’s boundary usually become incompatible with the actual boundary conditions. To remove this discrepancy the bending of the shell in the edge zone has to be considered, which may affect slightly the magnitude of initially calculated membrane forces. This bending, however, usually has a very localised character and may be calculated on the basis of the same assumptions which were used in the case of small deflections of thin plates. But there are problems, especially those concerning the elastic stability of shells, in which the assumption of small deflections should be discontinued and the “large deflection theory” should be used. If the thickness of a shell is comparable to the radii of curvature, or if we consider stresses near the concentrated forces, a more rigorous theory, similar to the thickplate theory, should be applied.
A bit long and laborious, but Timoshenko (plates and shells) knew a bit about the theory. Just thought i try to emphasise some details about the thoery, which need to be understood before being taken for gospal.


TGS4 (Mechanical) 
3 Jul 07 12:30 
If you are performing this analysis for an ASME pressure vessel, I cannot emphasize enough the need to actually understand the ASME Code, which is going to require you to obtain and read WRC 429.
The other posts here are useful and helpful, but are not particularly relevant to the ASME Code. For example, 40818's suggestion to check the von Mises stress on the tension face is reasonable, but does not comply with the current ASME Code  therefore, unfortunately, it is a bad suggestion. 

40818 (Aerospace) 
3 Jul 07 15:58 
I totally agree with TGS4, if you have set criteria which you must comply with, then that is what you must check. Unfortunately i'm not familiar with the ASME code, but general engineering principles will still apply and are the foundation on which all these codes and guidlines are based, so i think its a bit harsh to say its a bad suggestion!!, But i take your point about not complying with the code.


cbrn (Mechanical) 
4 Jul 07 3:12 
Hi, 40818, as TGS4 says, not necessarily the "good engineering practice" meets the "codes' requirements". A check using "engineeristic practice" can be useful for your personal purpose, but if you design in compliance with a Norm then it's completely useless since afterwards you will have to repeat your processing in conformity with the Norm, thus doubling the amount of work... If you are at University, it can be interesting to compare different methods for "academic" purposes, but in production it's a waste of time: it's  by far  better to thoroughly study the Norm, to fully understand it and then to apply it. How to apply it is another point, of course (and it's the point of the O.P.), and unfortunately the ASME "B.P.V.C" VIII2 (app.4) is probably the most distant Norm I've ever seen from FE practice. Of course: it was born when FE was nothing but a dream of some mathematical visionary... This doesn't mean a "dumb" application of whatsoever: a good engineer will know "at first sight" of the FE results if a pressure vessel is going to meet the requirements or not, and for that, "alternative" check methods can (must...) be usefully used. SWComposite's reply contains the basic concept at the basis of the "linearized stress" computation, but then in order to apply ASME VIII2,a4 one must also know what is a primary stress, what is secondary, what is general, what is local, what is peak... In fact, the FEM doesn't know anyting about stress categorization (in general), so it's up to you to interprete the data: the same stress linearization will lead, depending on the location, to a "general" or to a "local" set of stresses, for example; or, the data extracted along a similarly oriented path but at different locations can lead one time to a "membraneonly" stress, the other to a "membrane+bending" one... I fear all this is too long and complicated to be discussed "from the scratch" here in full details. As TGS4 said, it's far better for the O.P. to first study the ASME VIII2 plus its "application guide" WRC 429, and then come back with some more specific questions. Just my opinion, though.
Regards 



