Three directions of nonlinear analysis: limit, elastoplastic, and structurally nonlinear, are discussed. Works reporting theoretical and experimental data are reviewed. The current state of this subject is critically analyzed.Structural objects in the form of intersecting shells are used widely in various engineering fields (pressure vessels and apparatuses with branch pipes and sleeves, structural joints of piping system, etc.). Serious attention is being paid to intersecting shells in scientific and engineering sphere by conducting special experimental and theoretical research. Linear analysis is enough in certain practical cases. At the same time, considering the lack of adequate data on various parameters of the structure, precise prediction of its behavior in all stages of operation is possible only when methods of nonlinear analysis are used.In the recent decade, many standards, both foreign, for instance [1-3], and domestic [4], in the field of design and calculation of pressure vessels were updated. Also, in foreign standards, procedures are provided for determination of limit load using methods of nonlinear analysis. In view of the urgency of this matter, this work is devoted to a brief review of the information sources on the determination of limit load for intersecting shells published over the period 1999-2009. For clarity of terminology, standard joints of intersecting shells, namely, radial, nonradial, and tangential, have been used in the review [5]. As applies to vessels and apparatuses, such joints are union assemblies (connection pipes, sleeves, couplings, adapters, etc.) in the housing or the end plate (bottom). Elasticity analysis shows [5] that for structures in the form of intersecting shells, appearance of local stressed state characterized by significant unevenness and a relatively high degree of stress concentration in the vicinity of the point of intersection of the shells is typical. Because of this, loading of the shells may give rise to a local area of plastic deformation (strain), which influences the assessment of limit and permissible loads.In experimental or computational analysis of elastic-plastic behavior of structural joints of intersecting shells, in foreign information sources, including in strength standards, use is made of various methods of determination of the static plastic limit load (hereafter, limit load). For any of these methods, a load parameter q − deformation parameter δ curve that characterizes the process of loading and deformation (straining) of structural joints from plastic material is constructed. The choice of the load parameter is obvious if one load (internal pressure, force, moment, etc.) is applied. In the case of combined loading, generally simple loading is considered and a specific parameter in proportion to which each of the loads increases is chosen. Linear deformation (equivalent, most prominent, or components of deformation) or typical displacement of a certain point (section) is generally chosen as the deformation parameter. There is, howeve...
The problem of the elasto-plastic analysis of a vessel with a branch pipe reinforced by a overlay ring is examined. An applied procedure developed for analysis of intersecting shells with use of the finite-element method, theory of shells, and theory of plastic flow is employed to solve the problem. Results are presented for comparison of computed and experimental data on the model of a vessel with a radial branch pipe under internal pressure. Various means are examined for approximation of the actual deformation diagram of the material, and their effect on maximum stresses in shells subject to elasto-plastic deformation. Results are presented for the limiting plastic pressure in a vessel with a branch pipe calculated using the criterion of a double elastic gradient.Structural connections in the form of intersecting cylindrical shells have come into widespread use in various technical entities. Branch or connecting pipes on the cylindrical housings of vessels operating under an excess internal pressure are typical examples of these connections. Internal excess pressure is the basic load for which the geometric parameters of vessels are determined.It is well known [1] that a local induced stress state, which is characterized by high stress concentration, especially for thin-wall shells, develops in the region of shell intersection. Different methods of local reinforcement of vessels at the point of connection with a branch pipe are used to reduce the level of maximum stresses. Here, selection of the means of reinforcement should be substantiated with consideration of both its effect on maximum stresses in the shells, and also structuralprocedural limitations. Reinforcement by an overlay ring is one of the simplest and most effective means of local attachment of vessels to branch pipes, proceeding from structural design and production realization. This paper presents results of an investigation of the elasto-plastic strains and stresses that develop when the housing of a vessel is attached to a branch pipe in the connection zone, as determined by the finite-element method (FEM).The connection has two planes of symmetry: a principal plane passing through the axis of both shells -the basic shell and the shell of the branch pipe; and a transverse plane passing through the axis of the of the branch pipe and perpendicular to the principal plane. The stress state of the reinforced connection between the intersecting shells under consideration will depend on the following set of basic relative geometric parameters:where d/D is the ratio of the diameters of the median surfaces of the branch pipe and basic shell, D/H is a parameter of the thinness of the wall of the basic shell, h/H is the ratio of the thickness of the branch pipe to that of the basic shell, and H o /H is the relative thickness of the overlay ring.
High-pressure units (vessels) are used in the chemical and petrochemical industry, and also in related branches. Various designs of these units are employed, depending on the purpose, operating conditions, and other requirements [1]. The internal excess pr~e, which may reach 100 MPa, is the determining load in the structural standards and computational methods developed for these units.The connection subassemblies on the housing or bottom of a high-pressure unit are some of its most critical structural components. The pipe connector is considered the reinforcing element of the hole; in that ease, the adapter between the pipe connector and the housing or bottom of the unit is a complex structural connection between shells that are usually thick-walled. An appreciably nonuniform stress state, frequently with a high level of stress concentration, which must be rather accurately determined to ensure the unit's required reliability, develops in the connection zone.The design of connection subassemblies, especially for a eylinclrieal housing, is classed among complex problems of the meehanies of a deformable body. Complete computational analysis of connection subassemblies is possible only with the use of numerical methods, the most general of which is a three-dimensional analysis of these connections; this analysis does, however, require use of an adequate applied procedure.Let us examine applied developments in the field of stress analysis in intersecting shells [2]. Three-dimeusional analysis of connection subassemblies can be performed using the finite-element method (FEM) in a mixed variational formulation [3]. This approach makes it possible to develop a highly economical and effective computational procedure for computational investigation of elastic stresses in connection subassemblies. General positions of the computational investigation of connections between intersecan~ shells are based on the following applied procedure of three-dimensional analysis [2]:--use of curvilinear coordinate systems linked to the surfaces of the shells; -use of a modified mixed variational formulation of the FEM with independent approximation of the displacement and strain fields to build effective finite-element models; and, -use of a rational computational algorithm that takes into account characteristic features of the geometry of the computed entity.The solving system of FEM equations for three-dimeusioual analysis assumes the form Ks = e, K= F= F', <1)where K, F, and 8 are the stiffness matrix, load vector, and vector of nodal displacements of the finite-element model of the connection, and ICe and F r are the stiffness matrix and vector of the equivalent nodal loading of the element. The characteristics of an element (K e, b "e) can be determined in the eurvilinear coordinate system of the corresponding shell (for example, in cylindrical coordinate systems for a connection subassembly on the housing of the unit). As compared with the traditional approach (use of a Cartesian coordinate system), this offers the following advan...
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