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Stress averaging between different shell thickness 2
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Note that if you are modelling a component with continuously tapering thickness, but you have to model with plate elements each of which has a discrete thickness, using stress-averaging may be more meaningful than discrete element stresses, because there will be no stress discontinuities in the real system.
Good point Julian !
Alternatively you can use a FE solver that allows varying thickness in shell elements, such as LUSAS.
Alternatively you can use a FE solver that allows varying thickness in shell elements, such as LUSAS.
@ Drej,
When you are designing concrete slabs and shells, the design effects you want are usually moments and shear forces across the whole section thickness, rather than stresses. Plate / shell elements may be the preferred option for such analyses, as brick stresses have to be integrated through the thickness to get the design effects, and you will generally need a much finer mesh using brick elements, to get sufficient elements through the thickness to capture the bending behaviour with any semblance of realism. (Be VERY, VERY careful if you are using the solid automesher in your favourite CAD system to generate FEA models of such structures! Many of them will happily generate a mesh of bricks just one element thick, which will be potentially dangerous if you rely on the FEA results for design.)
E.g. suppose you are modelling a tapered concrete cantilevered slab; 6 m wide; 2 m cantilevered projection; 300 mm thick at the cantilever root; 150 thick at the cantilever free edge. Which modelling approach would you recommend for analysis and design:
a) Use plate elements on say 200 mm x 200 mm grid => 300 quad elements; design moments and shear forces are given directly in the element force / stress recovery post-processor.
b) Use solid brick elements; you will need at least say 4 elements thick to model plate bending behaviours with any semblance of realism, so your mesh size should probably be about 100 mm => 4,800 brick elements, and you will need to post-process the brick stresses to determine the design moments and shears.
What is best for one person doesn't necessarily make it the best for everyone!
(Sorry - couldn't resist!)
When you are designing concrete slabs and shells, the design effects you want are usually moments and shear forces across the whole section thickness, rather than stresses. Plate / shell elements may be the preferred option for such analyses, as brick stresses have to be integrated through the thickness to get the design effects, and you will generally need a much finer mesh using brick elements, to get sufficient elements through the thickness to capture the bending behaviour with any semblance of realism. (Be VERY, VERY careful if you are using the solid automesher in your favourite CAD system to generate FEA models of such structures! Many of them will happily generate a mesh of bricks just one element thick, which will be potentially dangerous if you rely on the FEA results for design.)
E.g. suppose you are modelling a tapered concrete cantilevered slab; 6 m wide; 2 m cantilevered projection; 300 mm thick at the cantilever root; 150 thick at the cantilever free edge. Which modelling approach would you recommend for analysis and design:
a) Use plate elements on say 200 mm x 200 mm grid => 300 quad elements; design moments and shear forces are given directly in the element force / stress recovery post-processor.
b) Use solid brick elements; you will need at least say 4 elements thick to model plate bending behaviours with any semblance of realism, so your mesh size should probably be about 100 mm => 4,800 brick elements, and you will need to post-process the brick stresses to determine the design moments and shears.
What is best for one person doesn't necessarily make it the best for everyone!
(Sorry - couldn't resist!)
The OP referred to averaging across different shell sections. As said, the problems this can create can be avoided if solids are used and hence the structure modelled explicitly. No mention of shear forces or moments in the OP, but these are easily obtained (if required) from most quality COTS codes for solids.
"Slabs" or "tapered slabs" are not natural shell-type structures (even for "thick" shells), and hence shells will not always be relevant for a structure - this will be dependent on the geometry. If a structure is modelled using shells and the geometry is not applicable to shells, then this can have consequences on the results. If the structure is principally in bending then shells for such structures will not accurately capture the bending response, especially localised strains/stresses. Shells will always over-stiffen the structure in this respect, and hence solids would be more appropriate if an accurate resolution is needed. Shells will capture the global stiffness reasonably well (and very well for a natural shell structure) but locally this will not be the case.
Appropriate elements are always required for the right geometry/loading and for the required resolution of results.
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"Slabs" or "tapered slabs" are not natural shell-type structures (even for "thick" shells), and hence shells will not always be relevant for a structure - this will be dependent on the geometry. If a structure is modelled using shells and the geometry is not applicable to shells, then this can have consequences on the results. If the structure is principally in bending then shells for such structures will not accurately capture the bending response, especially localised strains/stresses. Shells will always over-stiffen the structure in this respect, and hence solids would be more appropriate if an accurate resolution is needed. Shells will capture the global stiffness reasonably well (and very well for a natural shell structure) but locally this will not be the case.
Appropriate elements are always required for the right geometry/loading and for the required resolution of results.
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Drej said: "Slabs" or "tapered slabs" are not natural shell-type structures (even for "thick" shells), and hence shells will not always be relevant for a structure"
I would contended that typical reinforced / post-tensioned concrete "slabs" and "tapered slabs" are perfect candidates for modelling with plate / shell elements. What about a hyperbolic reinforced concrete cooling tower, as another example? These are classical thin shells in every sense of the word, and generally have a continuously varying thickness (thickest at the top and bottom edges - but still very thin when considered as thickness / diameter - and thinnest at the mid-height where the diameter is also smallest). For such an analysis I would use plate / shell elements, and use stress averaging for all stress extraction.
I would contended that typical reinforced / post-tensioned concrete "slabs" and "tapered slabs" are perfect candidates for modelling with plate / shell elements. What about a hyperbolic reinforced concrete cooling tower, as another example? These are classical thin shells in every sense of the word, and generally have a continuously varying thickness (thickest at the top and bottom edges - but still very thin when considered as thickness / diameter - and thinnest at the mid-height where the diameter is also smallest). For such an analysis I would use plate / shell elements, and use stress averaging for all stress extraction.
Just to make sure I am making myself clear:
If you are analysing a feature which would generate a stress discontinuity, you should generally not be using stress averaging. This would include:
. Discrete changes in thickness, such as at a butt weld between plates of different thickness, or a step change of thickness in a reinforced concrete plate or shell.
. Angular discontinuities in the plane of the plate / shell, such as at an end cap on a pipe nozzle, or a conical reducer, etc.
. Tee-joints an cruciform joints, etc.
For each of these features, the stresses in the elements meeting at the common node will be different, so stress averaging would not be appropriate.
Yes, modelling with solid elements can be one way of resolving the issue, but may not be the most appropriate approach for analysing slender plates and shells with tapering thickness. If plate bending behaviour is a significant component of the structural response (such as for shells of revolution subject to non-uniform pressure loading or concentrated loads, flat plates supported at the edges, etc), you will need to use several elements through the plate / shell thickness to capture the bending response, and this can result in truly enormous models. Using plate / shell elements might be a better approach.
If you are modelling a feature which has no geometric or thickness discontinuities, such as a smoothly tapering plate or shell, then stress averaging may be an appropriate strategy.
Hope this helps!
If you are analysing a feature which would generate a stress discontinuity, you should generally not be using stress averaging. This would include:
. Discrete changes in thickness, such as at a butt weld between plates of different thickness, or a step change of thickness in a reinforced concrete plate or shell.
. Angular discontinuities in the plane of the plate / shell, such as at an end cap on a pipe nozzle, or a conical reducer, etc.
. Tee-joints an cruciform joints, etc.
For each of these features, the stresses in the elements meeting at the common node will be different, so stress averaging would not be appropriate.
Yes, modelling with solid elements can be one way of resolving the issue, but may not be the most appropriate approach for analysing slender plates and shells with tapering thickness. If plate bending behaviour is a significant component of the structural response (such as for shells of revolution subject to non-uniform pressure loading or concentrated loads, flat plates supported at the edges, etc), you will need to use several elements through the plate / shell thickness to capture the bending response, and this can result in truly enormous models. Using plate / shell elements might be a better approach.
If you are modelling a feature which has no geometric or thickness discontinuities, such as a smoothly tapering plate or shell, then stress averaging may be an appropriate strategy.
Hope this helps!
This is all very off topic, but I'm afraid I can only agree to disagree. Whether the structure - or any structure - is applicable to shells is always geometry dependent (with cognisance of the response). You cannot make a generic statement on this like you have.
Also, "If plate bending behaviour is a significant component of the structural response (such as for shells of revolution subject to non-uniform pressure loading or concentrated loads, flat plates supported at the edges, etc), you will need to use several elements through the plate / shell thickness to capture the bending response, and this can result in truly enormous models."
Presumably you mean use several solid elements through-thickness as opposed to shells? In any case, this does not necessarily result in "truly enormous models" if carried out carefully. And if the difference is using shells and obtaining an erroneous answer or using solids to obtain an appropriate response then this has to be considered carefully. An appropriate technique is solid sub-modelling. If you sub-model, model sizes can be manageable. Everything has to be considered on a case-by-case basis.
Hope this helps.
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Also, "If plate bending behaviour is a significant component of the structural response (such as for shells of revolution subject to non-uniform pressure loading or concentrated loads, flat plates supported at the edges, etc), you will need to use several elements through the plate / shell thickness to capture the bending response, and this can result in truly enormous models."
Presumably you mean use several solid elements through-thickness as opposed to shells? In any case, this does not necessarily result in "truly enormous models" if carried out carefully. And if the difference is using shells and obtaining an erroneous answer or using solids to obtain an appropriate response then this has to be considered carefully. An appropriate technique is solid sub-modelling. If you sub-model, model sizes can be manageable. Everything has to be considered on a case-by-case basis.
Hope this helps.
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