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This and the next image are from:
Luis A. Godoy (1) and Eduardo M. Sosa (2)
(1) Universidad Nacional de Córdoba, FCEFyN, Departamento de Estructuras, and researcher, CONICET Casilla de Correo 916, Correo Central, Córdoba 5000
(2) University of Puerto Rico, Mayaguez, PR 00681-9041, Puerto Rico
“Computational buckling analysis of shells: theories and practice”, Mecanica Computacional, edited by S. R. Idelsohn, V. E. Sonzogni and A. Cardona, Vol. XXI, October, 2002, pp. 1652-1667
ABSTRACT: Shell buckling problems belong to the class of geometrically nonlinear behavior, and may be coupled with material nonlinearity of the shell. There are many general-purpose finite element programs that perform geometric and material nonlinear analysis of shells; however, this does not mean that a user can feed data and collect reliable results without a full understanding of the physics of the problem. This paper discusses the theories involved in the explanation and classification of phenomena, and in the prediction of results. Next, those approaches are considered in the practical analysis of one shell form, namely thin-walled steel tanks used to store oil. Results have been obtained with the general-purpose package ABAQUS, and they tend to show that their interpretation requires the use of Koiter’s theory in order to make sense of what is obtained. Some thoughts on possible ways to implement Croll’s lower bound reduced energy approach in practice are given.
The dynamically deformed roofed tank for normalized pressure, lambda = 2.515, is shown on the next slide.
This is Figure 4 from the paper cited above. In the paper the caption reads:
"Nonlinear dynamic response for a 3-sec wind gust [that is] assumed [to be] constant [with time]. Each curve is for [a slightly] different pressure amplitude. Instability occurs for [normalized] pressure, lambda = 2.515 [the green curve]."
Sudden, relatively large normal displacement occurs at Node 8938 at earlier and earlier times as the normalized pressure is increased slightly above lamda=2.515. No dynamic instability occurs during the 3-second wind gust for normalized pressure less than 2.515.
The next slide shows the deflection pattern for normalized pressure = 2.515 and time = 2.55 seconds.
The nonlinear static buckling pressure for this roofed tank is lambda=2.6107.
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