Disagreement of eigenvalues of tangent stiffness among shell and solid elements

[hustzjy312]

Dear all,

I conducted a quasi-static snap-through buckling analysis of a circular cylindrical panel in rectangular base via arc-length solver, subjected to a central point load. Only geometric nonlinearity is considered and two type of elements were used. One is a a finite deformation shell element from J.C. Simo ( shl3df.f ). The other is a finite deformation solid element( fld3d1.f ).

I got almost the same load-deflection response from the two elements. However, the eigenvalues of the tangent stiffness from the two elements have the same shape but with very different values. The load-deflection curve and the smallest eigenvalues of the tangent stiffness are attached. In addition, I verified that the eigenvalues of the solid element are correct. Therefore I think there is a scaling problem in the corresponding shell element ( shl3df.f ). Could you please help me to figure out the problem?

My FEAP is version 83, and I used the solution commands 'tang identity subs' in the batch to obtain the eigenvalues.

Thanks,

Yang

[FEAP_Admin]

It is not clear why you think the eigenvalues should come out to be the same.  The zero crossings are the same as they represent the instabilities but beyond that you are looking at two completely different formulations of the physics (totally different dofs).

[hustzjy312]

Thanks for you kindly reply. I agree that they have totally different dofs. But I formulate the same panel under the same boundary conditions. Physically, for the same linear mode, I think that they should give me the same frequency. Thus, at least for the first load step, we should obtain same frequency. But in the figure of the eigenvalue, we can see very different eigenvalues. Even when I plot the generalized eigenvalues ('Tang Mass Subs'). For the same linear mode, two elements still give me different frequencies.  Therefore, I think there might be a scaling problem when FEAP computes the eigenvalues for that shell element( shl3df.f ).

[Prof. R.L. Taylor]

Can you do a simpler problem so you can understand more about the differences. 

Use the shell element to create a strip one element wide (unit width) by several in the length direction.  Set boundary conditions to get cylindrical bending behavior (a 1-d response for length direction).

Do the same problem with 2-d plane strain and 3-d elements.

Do with ident and with mass  -- you should get a match between the 2-d and 3-d solid elements.   What does the shell give now?

Repeat for linear elements.

[hustzjy312]

Dear Prof. Taylor,

Thanks very much for your kindly reply. I set up several simulations according to your suggestion.

The 'tang iden subs' gave me close results for the large and small deformation shell elements. However, the 'tang mass subs' gave me totally different results for the two shell elements. Therefore, I think that the diference comes from the mass. 

I also modeled the panel with 8-node solid element and 27-node solid element. Both the 'tang iden subs' and the 'tang mass subs' of both solid elements give me totally different results from the two shell elements. Moreover, the results from the 8-node solid element are also different from the ones from 27-node solid element. However, close results are obtained from the small and large deformation 8-node solid elements. Also, close results are obtained from the small and large deformation 27-node solid elements.

The inputs are attached to this reply. Could you please help me check them?

Thanks very much again.

Yang