The above discussions are relevant. Just to put a cap on this thread, I would like to add the following: The correct mesh distribution has to deal with the order of the displacement function being assumed and the method of numerical integration being used.
In the early development of FEM...
Feddozz:
The Dialog function in Intel 9.0 or higher and CVF 6.6c permits the dialog to be introduced as mode or modeless dialogs. There is a starting procedure dlgint(Idd_Dialog_Name,dlg). To close the dialog the procedure is dlgUnint(dlg).
There may be other commands from a dialog system...
Engleosun:
There are two types of instability: structural instability and dynamic instability. The first is usually the condition when a member of a structure bifurcates ( a sudden change in the position to a lower energy state). The load can either be static or dynamic. The second is a more...
Vato: The structure you are now describing is either a curved plate or a shell. Discontinuity stresses can occur when there is a sudden change in the radii of curvature. 1/rphi for a flat plate is zero. You need to separate the curved corrugation and flat plate into two distinct elements...
Prost: Your identification of the ref. Grioli is correct. See pg 107 of that ref. Fichera had posed three classical problems of elasticity. One is the mixed boundary value problem--a displacement specified on one surface and zero stress tractions on the adjacent surface. Grioli presents the...
Any structure that has a re-entrant corner will produce a very large stress concentration. The peak stress of a 90 deg. corner is infinite based upon M. L. Williams' study (JAM ~ 1957). Any FEM based on classical elasticity will predict larger and larger peak stresses as the radius of the...
The circumferential wave number of Fourier no., n, is different for each shell configuration and boundary condition. That is why several computer programs have been written to assist the analyst. For simply supported shells, the lowest harmonic pattern usually follows a sin function.
The...
Oops, I forgot the other real world component--the stainless material being used. Some SS are really non-linear. Their stress-strain curve follows what is called the Ramberg-Osgood Law and bends so you can not determine a true Elastic modulus for any strain level. A tangent modulus may be...
Ah, the real world. I would look very closely to the true bounday condition. If you have just clamped one end and not buried the end into a very stiff material, the BCs are not fixed (but close). The "clamp" may be over only a portion of the circumference something like a shop vise).
Now...
Shell behavior is when the cross section deforms with angular variations at one station. The general pattern can be expressed of the form An(Sin pi*k*L)*(Sin pi*n*theta) + (Cos pi*n*theta) + Bn(Cos pi*k*L)*(Sin pi*n*theta) + (Cos pi*n*theta)). An and Bn are functions of the natural frequency...
The vibration of cylindrical shells has been exhaustively studied. One of the better collection of data for shells of various shapes and boundary conditions is by A.W. Leissa, "Vibration of Shells", NASA SP-288, 1973. And its free. Leissa provides summaries of shell responses, particularly...
The over 200 discussions presented thus far cover a great deal of points of view. One of the questions I have, how do we learn from this experience? And how do we apply this experience to other bridges having similar conditions?
It is my view that the two in-depth inspections should be used...
Darkwing888 is absolutely correct. If you review the 2001 report by Univ Mn., it points out that cracks had been observed in 1990. As a "fix", holes were drilled at the end of the cracks to stop their propagation. I could not examine the details of the "fix."
The questions that I had brought...
It appears that some of the earlier investigtions included a fatique evaluation. Three basic members were determine critical. These evaluations were using Miner's rule. Does anyone know the material and its transition temperature of the basic truss?
I did not see any K1c evaluations, only...
MintJulep: To gain an understanding of the bifurcation process for cylindrical shells of revolution subjected an external pressure into another state, may I suggest that you examine: Paragraph 83, Timoshenko, Theory of Elastic Stability, Eng. Soc Monographs.
Quicker: I do not think that your...
