Nonlinear dynamic analisys of reservoir shell with modelled shape imperfections

Abstract

The nonlinear dynamic analysis of imperfect reservoir shell with a variable thickness of wall under pressure was executed. The finite-element model of reservoir in the form of a cylindrical shell in the software NASTRAN was built. The shell wall in the form of the three-cornered finite-element net was presented. Shape imperfection as a lower buckling form of perfect shell (Buckling) was modelled. Value of amplitude of imperfection was set proportionally to a minimum thickness of shell wall. The limits on the radial and tangential displacements of top edge nodes were entered, the nodes of lower edge were fastened. Excitation as external pressure, which linearly depended on time and uniform distributed on all shell elements was presented. The modal analysis of shell with modelled shape imperfections by using computational procedure of task on natural vibrations (Normal Modes) by the Lanczos method was executed. The nonlinear dynamic analysis (Nonlinear Direct Transient) of imperfect reservoir shell under pressure by N’yumark method was executed. Influence of amplitude of modelled imperfection on the shell stress-strain for different time intervals of excitation, the conditionally critical values of dynamic loading and corresponding of shell deformation forms were investigated.
 It was discovered that a modelled shell shape imperfection as a lower buckling form of perfect shell under static pressure in the dynamic analysis of shell under the same type of the loading was effeсtive. Influence of modelled shape imperfections amplitude on the stress-strain state of shell for different time interval of excitation, the conditionally critical values of dynamic loading and appropriate forms of shell deformation was considerable. Presented imperfection model in the modal analysis of shell was not effective. The increase of amplitude of shell imperfection led to insignificant decrease of natural frequencies and amplitudes of appropriate natural forms with the same amount of the semiwaves in the circular direction. In our opinion presented model of shell shape imperfection can be effective in the modal analysis of shell with the stress-strain state from the previous action of static pressure and for the estimation of design reliability of reservoir shell in the case of the dynamic loadings using the Bolotin probabilistic approach.

Natural frequencies and modes of parametric vibrations of reservoir shell with shape imperfections

“…The finite element model of the shell has an infinite number of freedom degrees and natural frequencies, so solving the dynamics problem is difficult. If behavior of natural vibrations of the shell was researched, it is possible to talk about shell internal properties which take a great place at the forced vibrations including parametric one [9][10][11][12][13][14]. It is important to take into account influence of the constant component of parametric load on natural frequencies and modes of shell.…”

Choice of the shape imperfections model in dynamics problems of a long flexible cylindrical shell subjected to force couples

“…It is known that the presence of small shape imperfections of thin-walled shells, which arise in the process of their manufacture, transportation and operation, can significantly reduce the critical value of static or dynamic buckling load and lead to emergency situations [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In the articles [7][8][9][10][11][12][13], the authors presented a numerical technique that made it possible to estimate the effect of geometric imperfections of cylindrical shells on their bearing capacity under static loads. The first bifurcation mode as a model of shell imperfections under the action of one type of load (surface pressure, axial compression) was taken.…”

“…When these shapes do not coincide, it was important to investigate their effect on the dynamic characteristics and the critical dynamic load values. For example, in the article [12], the authors performed a modal and nonlinear dynamic analysis of the stability of the tank shell with variable thickness under surface pressure. The shape imperfections model in the lower bifurcation buckling mode was presented.…”