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A numerical approach to investigation of static and dynamic characteristics of fuel reservoir and surge-protection capacity with cracks in welded joints of their walls has been proposed. Mathematical modeling of the nonlinear behavior of the complex shell structure has been performed under the action of static vertical loading using the software complex of finite element analysis. The models of cracks with different length within vertical and horizontal welded joints of shell walls have been developed. The influence of cracks on the stress-strain state and stability of the fuel reservoir as well as the surge-protection capacity has been investigated. The dynamic characteristics of the structure have been determined, the influence of cracks on the frequencies and the modes of their natural vibrations has been evaluated.

The authors put forward a numerical approach to determination of nonlinear bending stability of a long flexible cylindrical shell with geometrical imperfections. The shell wall imperfection in the form of bulging in long half-wave is modeled using a software package for finite-element analysis. Prebuckling and postbuckling behavior of an imperfect shell in bending is studied. The critical normal stress in the shell compression zone is plotted vs. the imperfection amplitude. The bending stability region is determined for a shell with geometrical imperfections.

A probabilistic approach to reliability analysis for stability of an imperfect supporting shell has been elaborated. The nonlinear stability of the shell under combined loading conditions is analyzed taking into account the shell imperfection. A surface of critical load combinations has been constructed and a field of stability has been defined. The stability reliability has been determined allowing for various types of distribution in frequency of the shell imperfection and its maximum possible preset value through the use of reliability surface. The authors have derived allowable combinations of complex loadings that should be taken into consideration during the design and operation of a supporting shell.

A numerical method for investigating stability of the supported cylindrical shell with account for geometric imperfection in the form of its deformation during in-service loading has been developed. The problem of nonlinear stability of the imperfect supported cylindrical shell under combined loading has been solved. The influence of the imperfection amplitude on the critical combination of loads and stability region of the supported shell has been evaluated. Introduction. Supported cylindrical shells find widespread use in many engineering fields such as industrial engineering, food, chemical and other industries. One of the main features required of these structures is the ensuring of their minimum weight with sufficient strength and stability. It can be fulfilled provided that geometric nonlinearity, which is typical of the structures with openings, stiffening rings or ribs on their surface operating under conditions close to boundary ones, is taken into consideration during the investigation of their load-carrying capacity and stability. The problem of evaluation of the influence of geometric imperfection on the stability of shell structures remains topical (1-9). Use of analytical methods involves the form of geometric imperfection of the supported shell to be expressed as trigonometric functions, which considerably narrows the focus of investigations. With the availability of modern calculation systems it is possible to express geometric imperfections arbitrarily (10-13), which enhances the physical understanding of the behaviour of imperfect shells. Despite widespread use of supported shells in engineering practice, the influence of imperfections on stability, especially under combined loading, has not been fully investigated. The paper is devoted to the solution of the problem of stability of the imperfect supported shell under wind loading with account for alternating pressure from the weight of the tank filled with liquid, which is placed at the top. A numerical approach, which is based on the finite element method and nonlinear analysis of stability of the shell with geometric imperfections in the form of its deformation, has been proposed. The limiting values for stress-strain state of the supported shell as well as critical values of combined loading, under which its overall stability conditions are fulfilled, have been determined. The influence of geometric imperfection of the supported shell on the critical values of combined loading and its stability region has been evaluated. Development of the Finite Element Model for the Supported Shell Considering Geometric Imperfection. The shell is a cylinder with two openings, which are reinforced with stiffening ribs. The shell walls are reinforced with vertical stiffening ribs at the top and with lower and upper rings. The shell has the following geometry: diameter D 56 1 . m, height H 53 . m, and wall thickness t 10 mm. The rings take the shape of a plate with width of 200