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Free flexural vibration of a simply supported sandwich beam on an elastic foundation is the main purpose of the presented investigation. An analytical model of multi-layered beam on elastic foundation has been prepared. The authors submitted an original beam-foundation interaction model which based on variable parameters of the foundation and their influence on the beam response. This explanation leads to the possibility of continuous characterization of the beam-foundation interplay. A nonlinear mathematical function for symmetrical properties of the foundation has been adopted. The frequency equation as a function of geometric and mechanical properties of the beam and the parameters of the elastic foundation was derived using the Galerkin method. The analytical investigation has been divided into two parts: the analysis of elastic foundation with constant and variable properties. The unconventional shape function and the function of deflection have been introduced and employed. Moreover, the finite element analysis has been performed. Sample analytical and numerical calculations have been performed, demonstrating a good concurrence between both models. The difference between analytical and numerical values of the fundamental natural frequency did not exceed 0:5%. [ABSTRACT FROM AUTHOR]

The paper is devoted to a sandwich cylindrical pressure vessel closed with a dished head at both ends and loaded with external uniformly distributed pressure. Non-standard construction of the vessel is presented characterised by an asymmetric cross-section and superellipsoidal dished heads. The strength and buckling of such structure is numerically studied with the use of the finite element method limited to the linear range. The calculations are carried out for models with aluminium faces and aluminium foam core. The obtained results revealed the advantage of the superellipsoidal dished head compared to the hemispherical one in terms of stress distribution — the edge effect being a typical problem in such structures is diminished. This opens potential applications of such solution in actual structures. It is pointed out that the application of a superellipsoidal head assure a more favourable shear stress distribution in the core. • Alternative closure of the cylindrical tank is proposed. • The edge effect can be diminished by application of superellipsoidal dished head. • The edge effect influence the most the light core of a sandwich shell. • Symmetrical sandwich shell is characterised with the highest buckling load. [ABSTRACT FROM AUTHOR]

The paper is devoted to a thin-walled rectangular frame. The frame is simply supported in the planes of symmetry and in-plane compression forces are applied in the corners. The longitudinal and transverse thin-walled beams of the frame are rigidly joint at the corners. Two buckling forms of the frame are studied. The analytical and numerical-FEM (SolidWorks) models are formulated. The results of the studies are presented in Tables and Figures. [ABSTRACT FROM AUTHOR]

The paper is devoted to the static stress analysis of a cylindrical tank closed with two non-classical dished heads. The description of the geometry of the dished head in the form of super-ellipsoid is provided containing two dimensionless parameters to control the depth and curvature of the ellipsoid. The equivalent stress distribution along the meridian of the head is calculated analytically and numerically with the use of the finite element method. Based on the analysis of the stress in the whole tank it can be concluded that the replacement of the classical ellipsoidal head with the super-ellipsoidal one may decrease the edge effect at the junction of the two shells. This positive effect increases with the increase of the depth of the head. • Geometrical description of the super-ellipsoidal shell is provided. • Application of the super-ellipsoidal shell as a dished head of the cylindrical tank is discussed. • Super-ellipsoidal head allows to control the stress distribution in the cylindrical tank. • The use of super-ellipsoidal head diminishes the edge effect in cylindrical tank. [ABSTRACT FROM AUTHOR]

Abstract: The work is devoted to the strength and elastic stability analysis of a barrelled shell loaded with uniform radial pressure. The shell is assumed to be isotropic, homogeneous and of constant thickness. The geometry of the shell is described as well as the field of displacement for which Kirchhoff–Love hypothesis is applied. On the basis of the linear equilibrium equations the relations describing the membrane state of stress in the pre-buckling state are derived. The buckling problem of the barrelled shell is described analytically and solved approximately with the use of Bubnov–Galerkin method. As a result the formula for the critical pressure is obtained. The numerical examples are presented which were solved analytically and with the use of finite element method. The comparison of the results obtained in both ways shows very good agreement as to the values of membrane forces, buckling load and buckling shape. The formulae presented in the paper may help in the design of shell structures in the shape of barrel. [Copyright &y& Elsevier]

The subject of the study are open circular cylindrical thin shells with two edges supported and two edges free. The elastic buckling and limit load of these shells in pure bending state are investigated. The study includes simple analytical description, numerical analysis with the use of the Finite Element Method (FEM), and laboratory tests for shells. The results of these three investigation methods are compared and presented in figures. The critical load and limit load for these shells are described in detail. Moreover, an analytical formula of critical stresses for open circular cylindrical thin shells in pure bending state is proposed. The main goal of the paper is comparison of the results of critical load values obtained by analytical, numerical (FEM), and experimental methods. [ABSTRACT FROM AUTHOR]

The subject of the paper is cold-formed thin-walled channel beams with open or closed profile of drop flanges. The geometric properties of two C-sections are described including warping functions and warping inertia moments. The analytical solutions of problems of global and local stability of thin-walled beams are presented. The theoretical solutions of elastic buckling problems of these beams are numerically found using FEM and are experimentally verified. The results of analytical and numerical investigations are compared and presented in the tables and figures. [ABSTRACT FROM AUTHOR]

Abstract: The paper is devoted to a thin-walled beam with a flat web and cosinusoidally corrugated flanges. Considered beam has an open cross section and is mono-symmetric. Two different types of load are taken into account, i.e. pure bending and uniformly distributed load. The authors are searching for an optimal cross section shape of the beam. The beam cross section is characterized by dimensionless parameters, which are design variables. The dimensionless objective function is so defined as to comprise both a cross section area and a maximal allowable bending moment. The constraints follow from the local buckling condition for corrugated flange and geometric restrictions. The beams with different length to height ratio are analyzed. Results of the numerical calculations are presented graphically. [Copyright &y& Elsevier]

The subject of this study is a simple thin-walled beam carrying a uniformly distributed transverse load. Strength and stability problems of the beam are resolved on the ground of Vlasov’s theory. Local stability is described according to the theory of thin plates and shells. The results of analytical solution are verified with the use of finite element method. Discrete model of the beam is built on the bases of shell elements SHELL4 of the COSMOS/M system. The results of both methods are compared using diagrams. [Copyright &y& Elsevier]

The subject of this paper is the supporting saddle of a horizontal cylindrical pressure vessel filled with liquid. A parametric model of the saddle support has been developed; the effect of the geometrical parameters on the stress values arising in the structure has been examined by means of the Finite Element Method. The shape and location of the supporting saddle have been determined with a view to minimizing the concentration of stresses. Results of numerical analysis allow determination of the effective proportions of the geometrical parameters of the vessel. [Copyright &y& Elsevier]