The main disadvantages of solid element in FEM with linear approximations for bending type problems is

LOCKING - phenomenon during bending -- the solid element will show the bending behavior much stiffer in comparison with analytical solution.

LOCKING is higher if the solid element looks like shell (thickness is smaller than two other sizes).

It can be resolved for solid element only by taking many elements for the thickness, therefore, leading to many FE's.

In order to eliminate the locking problems the Solid-Shell FE is introduced, in which

EAS or ANS methods to remove locking are implemented is presented even for FE with quadratic shape functions, because the locking phenomena can be found also for FE quadratic shape functions.

Shell elements are used to model structural elements in which two dimensions are much greater than the third one and when the change of the analysed feature across this third direction can be neglected. It is reasonable for static analysis of panel/planar elements such as slabs or walls as well as thin-walled spatial elements such as shells. The advatnages of the use of shell elements, as you said, results mainly from time-saving due to reduced number of finite elements (and consequently the equations to solve). So, anytime you can reduce the problem to planar problem and neglect what happens at the thickess of the element I don't see the reason to use solid elements. The results from the following simple analysis: http://www.javelin-tech.com/blog/2012/10/shell-vs-solid-elements/ suggest that it is when the third dimension is at least 20 times smaller than the other ones.

However, if the change of the analysed feature is on a comparable level in all directions of the analysed element, solid elements should be used. It is the case e.g. in block elements, like massive concrete elements which are among my interests. In such elements, the observed thermal and moisture fields are highly non-stationary and the resulting thermal and moisture gradients lead to formation of the internal restraint in the elements which, in turn, is the origin of (self-induced) stresses in the element. If that fact was neglected, we would not be able to analyse this phenomenon.

Be careful with the term "planar problem" and shell elements. Planar problems often correspond to the 2D modeling space, and usage of plain-stress and plain-strain elements. Their topology is identical with the shell elements, but equations are completely different.

Your question is very general and hard to answer.

A few main practical differences: shell-solid (besides of mentioned by Agnieszka)

1. Geometrical model

- solid model is often available, while shell has to be created

- problems in precise connection of the surfaces for shell model

- problems in proper connection (or contact) of multi-layered surfaces

2. Mesh

- shell mesh much is easier to create, if you need good quality elements (box instead of tetrahedron elements in solid)

- more realistic boundary conditions for solid (faces instead of edges)

3. Analysis

- less problems with stability with shell model

- shell needs much less disk space for results, important for nonlinear/nonstationary analysis and big models

- postprocesing of shells is faster (again for big model)

I recommend to take a look at the third possibility: continuous shell element, available in some codes, ex. ABAQUS. The geometry (topology) of element is like solid, but equations are like for shell elements. In some applications is better than shell and solid.

3D shell elements are prefered when the structure has one dimension (say z direction) much smaller that the two others (say x and y). The thickness (z direction) could also be a variable in x,y.

Mindlin-Reisner theory is needed for thicker shells and Kirchoff theory will suffice for a much thinner shell (this is related the the rotational degree of freedom)

If there is no feature in the model through the thickness than modelling teh structure by shell elements is preferered (CPU, problem size). Otherwise, a full 3D will be needed to capture feature through the thickness.

Artur, you are right about the term "planar" and thanks for pointing that out. The use of this term was not precise here. Of course saying planar we refer to 2D elements, which is true in the examples of slabs/walls that I made, but shell elements are also used for modelling of 3D structures when the thickness of the element is neglected. I should rather refer to them as surface elements but the commonly used term "shell elements" is just about right and will suffice.

When choosing between shell or solid element (in addition to one dimension -z- being much smaller to the two others - x,y) will depend on the loading conditions.

If the loading is the shell plan (tangent to the surface). The shell will respond under a membrane effect (only two dof are excited: displacemets in x and y directions) and the 2D plane-stress element could be used or a 3D solid with only one layer through the thickness (a C0 continiuity element).

If the loading in normal to the shell surface, here the shell elemnt is prefered, and depending on the thickness (Kirchoff or Mindlin element could be used, depending on the curvature). The element formulation is more complex as it needs a C1 contuiuity for rotations. One might used the 3D solid element to model the bending (load componenent normal to shell surface) but here at least 3 layers of 3D solids are needed.

Mesh refinement is also tricky when using shell elements as a reduced size (x,y) will make the assumption of thickness -z- being much smaller than the other 2 dimensions -x,y, more difficult to sustain. This is not the case for 3D solid elements.

Fawzi,

It's true, but term "... to model the bending (load component normal to shell surface)"

The bending is not necessarily caused by normal (out of plane) force. It can be caused as well by bending moment applied to the edge (shell) or pair of in-plane forces (solid).

The mesh refinement for shell element is in practice not a problem. Even if element size is smaller than it's thickness (so assumption of thickness being much smaller than the other 2 dimensions is not true) results can be correct.

The mentioned assumption is the common opinion that in fact it' s not true. The shell element applicability doesn't depend on ratio L/t, but on ratio R/t

(where L- element length, t - element thickness, R - curvature radius of surface)

For constant R and t (the same geometry) ratio R/t is constant, so refining the mesh is possible even for quite small L. If R/t is high enough, refinement is OK.

The main disadvantages of solid element in FEM with linear approximations for bending type problems is

LOCKING - phenomenon during bending -- the solid element will show the bending behavior much stiffer in comparison with analytical solution.

LOCKING is higher if the solid element looks like shell (thickness is smaller than two other sizes).

It can be resolved for solid element only by taking many elements for the thickness, therefore, leading to many FE's.

In order to eliminate the locking problems the Solid-Shell FE is introduced, in which

EAS or ANS methods to remove locking are implemented is presented even for FE with quadratic shape functions, because the locking phenomena can be found also for FE quadratic shape functions.

Solid-shell FE is what I've mentioned before as continuous shell (Abaqus name)

Dear Artur Iluk,

You mentioned "The mentioned assumption is the common opinion that in fact it's not true. The shell element applicability doesn't depend on ratio L/t, but on ratio R/t (where L- element length, t - element thickness, R - curvature radius of surface)".

I haven't seen this opinion before and I don't think I understand the meaning of "R - curvature radius of surface". For example, an air-blast loading is applied on the surface of a thin rectangular plate (dimension 400*400*3mm) with its edges clamped. What's the meaning of R? And how can you get this opinion? Is there any example?

XinFengDuan

Dear Alexander Konyukhov,

You mentioned "The main disadvantages of solid element in FEM with linear approximations for bending type problems is LOCKING - phenomenon during bending -- the solid element will show the bending behavior much stiffer in comparison with analytical solution. LOCKING is higher if the solid element looks like shell (thickness is smaller than two other sizes). It can be resolved for solid element only by taking many elements for the thickness ".

I have heard this opinion many times, however I don't understand it. Suppose a large pressure is applied on a thin plate (dimension 400*400*1mm) with its edges clamped and the plate will bend. In my opinion, the bending behaviour of the plate will mainly depend on the mesh size of the plate surface not the thickness even the solid element is used. If the mesh size of the plate surface is small enough (for example 1mm) and only one element is used in the thickness direction, I think a good result can be gotten.

So how to understand this question? Or how to validate your opinion about locking during bending with solid element?

XinFengDuan

Dear Fawzi Belblidia,

You mentioned "If the loading in normal to the shell surface, here the shell elemnt is prefered, and depending on the thickness (Kirchoff or Mindlin element could be used, depending on the curvature). The element formulation is more complex as it needs a C1 contuiuity for rotations. One might used the 3D solid element to model the bending (load componenent normal to shell surface) but here at least 3 layers of 3D solids are needed ".

I have heard this opinion many times, however I don't understand it. In my opinion, the bending behaviour of a shell surface will mainly depend on the mesh size of the plate surface not the thickness even the solid element is used. If the mesh size of the plate surface is small enough and only one element is used in the thickness direction, I think a good result can be gotten.

So how to understand this question? Or how to validate your opinion about at least 3 elements are needed in the thickness direction during bending with solid element?

XinFengDuan

Hello XinFeng Duan,

It is agreed that shells provide less computational time in contrast to solids. This is mainly due to the number of elements to be used in the model. For shell elements the plane (x,y) dimensions are usually much larger than the thickness (Z) dimension. To achieve similar accuracy, solid elements have to have similar size (element ratio) in all directions, thus necessitating a smaller size solids (as you mentioned). Moreover, with solids and to be able to mimic the bending effect of the structure (in the z-direction of plate/shell structure), it is necessary to model through the structure thickness with more than one solid element. While, the shell element has already the bending effect within it formulation (as rotation dof according to Mindlin or Kirchoff theory).

Dear Fawzi Belblidia,

Thank you for your reply. I want to validate this conclusion with a simple example, however I don't know how to do it. Is it possible to validate it with a simple example?

That will be great. You can use any standard text book in elasticity to check these assumptions. See for examples attachment or: http://www.roymech.co.uk/Useful_Tables/Mechanics/Plates.html

Use solid and plate element to model one of these examples and compare finding to given analytical solution.

Hope this helps.

Dear Fawzi Belblidia,

Thank you for the useful information. What's the expecting results according to the theory? If less than 3 elements are used through the thickness, does the maximum stress and deflection smaller than the results with shell elements? 

Dear all.

I also got same problem with solid and shell elements.

Now, I am analyzing very thin shells with ratio between thickness(t) and overall size(D) of shell is 1/5000  I used different element types to compare the strength and stiff of structures. The result is so interesting. The models are meshed by shell elements, solid-shell elements are not sensitive with element size but the output result is low even lower than experiment while models meshed by solid elements is stiffer and much higher mech properties( 10 times results gained by shell elements) but they is sensitive with element size. And because of very large ratio D/t, i don't know what element size is good enough and the analysis result is correct or not?

Could you give me your recommendation in this case?

Thanks

I think multi-layers of solid element is better than shell element.

how can i create shell element in hypermesh  and what material property should give as a input to solve in ansys.

I think this link will answer your question:

http://www.javelin-tech.com/blog/2012/10/shell-vs-solid-elements/#.WNlfsfkrLIU

If you have to model shells, especially in geometrically nonlinear problems, in my opinion solid-shell elements present same advantages, first of all the use of only translational DOFs. Among the other proposals I have very good experiences with the element proposed by professors Sze, Chan and Pian. The thickness locking is eliminate using a generalized constitutive matrix, which permits to model also composites, shear and trapezoidal lockings using ANS.

Sze, K.Y. and Chan, W.K. and Pian, T.H.H., An eight-node hybrid-stress solid-shell element for geometric non-linear analysis of elastic shells, International Journal for Numerical Methods in Engineering, 2002, 55, 7, 853-878, doi={10.1002/nme.535}

You can also read someone of my recent papers.

In this article (https://msp.org/jomms/2010/5-3/jomms-v5-n3-p09-s.pdf) details of an hybrid FEM formulation is discussed using solid elements. Only one element in thickness direction is enough to model very thin structure. Brick type and shell type structure can be model without using complicated interfacing (solid and shell degree of freedoms are different) if solid and shell type geometry has to be model together. The rotation degree of freedom makes shell formulation very complicated and reducing general nonlinear constitutive relation for shell formulation complicate the situation further.

Other than computational time, one advantage is that Shell allows rotation (Conventional Shell). Shell has both Translation as well as Rotation degrees of freedom. To note : In some software, you have two types of shells - Continuum as well as Conventional shell. Though both are modeled as shells, Continuum shells may not allow rotational D.O..F. Shell elements are more efficient in modelling bending behavior. I believe with shell elements, you also get the option to choose whether to consider Shear deformation or not as well in addition to bending on application of a transverse load. That is you have the option of whether to include Kirchoff theory or not in your model.

Visualization (Post processing of results) is also much more easier in a shell model. You can request an output variable and the software displays output contours more easily and faster even for a big size shell model.

Good question.. Please share me the best answer might you trust...

Regards…

Since shell elements allow the modelling of thin features with fewer elements than solid elements, they need low computational time. They are also easier to mesh and less prone negative Jacobian errors which might occur when using extremely thin solid features. However, the shell elements are limited to features which are really thin. A good approximate is if the thickness of the body is at least 20 times less than the span.