Krzysztof Magnucki

Stress state and elastic buckling of a thin-walled beam with monosymmetrical open cross-section

Abstract 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.

Minimization of stress concentration factor in cylindrical pressure vessels with ellipsoidal heads

The paper presents the problem of stress concentration in a cylindrical pressure vessel with ellipsoidal heads subject to internal pressure. At the line, where the ellipsoidal head is adjacent to the circular cylindrical shell, a shear force and bending moment occur, disturbing the membrane stress state in the vessel. The degree of stress concentration depends on the ratio of thicknesses of both the adjacent parts of the shells and on the relative convexity of the ellipsoidal head, with the range for radius-to-thickness ratio between 75 and 125. The stress concentration was analytically described and, afterwards, the effect of these values on the stress concentration ratio was numerically examined. Results of the analysis are shown on charts.

Global buckling of a sandwich column with metal foam core

The subject of the paper is about sandwich beam-column with a metal foam core. The global buckling phenomenon of an axially loaded member is investigated. Two analytical models of the beam-column are presented. In the first model, a classical one, the mechanical properties of the core are assumed to be linear. In the second model, the non-linear behaviour of the core is taken into account. Solutions of these two models are presented and the formulae for the critical loads are determined. The numerical finite element models of the beam-column are also elaborated and the linear buckling and the non-linear analyses are performed. The results of experimental tests on the aluminium sandwich beam-columns with aluminium foam core are described. Analytical, numerical finite element model and experimental values of the critical loads are compared.

Dynamic Stability of an Isotropic Metal Foam Cylindrical Shell Subjected to External Pressure and Axial Compression

This paper presents a nonlinear approach with regard to the dynamic stability of an isotropic metal foam circular cylindrical shell subjected to combined loads. The mechanical properties of metal foam vary in the thickness direction. Combinations of external pressure and axial load are taken into account. A nonlinear hypothesis of deformation of a plane cross section is formulated. The system of partial differential equations of motion for a shell is derived on the basis of Hamilton’s principle. The system of equations is analytically solved by Galerkin’s method. Numerical investigations of dynamic stability for the family of cylindrical shells with regard to analytical solution are carried out. Moreover, finite element model analysis is presented, and the results of the numerical calculations are shown in figures.

Flexible saddle support of a horizontal cylindrical pressure vessel

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.

Critical sizes of ground and underground horizontal cylindrical tanks

The paper deals with ground and underground horizontal cylindrical tanks supported at both ends. The ground tanks are loaded with internal hydrostatic pressure and small negative pressure. On the other hand, the underground tanks are located in water containing soil and loaded with external hydrostatic pressure. Critical states of both structures are determined based on solving the equation of stability of cylindrical shell. The problem so defined has been converted to calculation of critical thicknesses of walls for the family of circular cylindrical tanks of different capacities. Critical sizes of the structures have been determined as functions of dimensionless critical thickness and dimensionless tank length.

Optimal Design of an Isotropic Porous-Cellular Cylindrical Shell

The paper outlines the effects on an isotropic porous-cellular cylindrical shell when subjected to a combined load: of axial force and external pressure. Metal porosity varies across the thickness of the shell wall. A dimensionless porosity parameter is introduced to compensate for this. Nonlinear hypothesis of deformation of the flat cross section of the shell wall is formulated. A system of five differential equations is defined on the basis of the theorem of the minimum of total potential energy. This system of equations is then analytically solved with Galerkin’s method. Critical loads for a family of porous shells are numerically determined based on the analytical solution. The optimization problem considers two criteria: minimum of mass and maximum of critical load on the shell. Optimal porosity variability for the cylindrical shell is determined numerically. An optimal dimensionless porosity parameter is then defined. Moreover, a comparative analysis for selected cylindrical shells with the use of FEM is performed. Results of the calculation are shown in respective figures. Finally, the results of the investigation for porous cylindrical shells are compared to the corresponding results for isotropic homogeneous shells.Copyright

Bending and free vibrations of beams with symmetrically varying mechanical properties—Shear effect

ABSTRACT The subject of the paper is a beam with symmetrically varying mechanical properties in the depth direction. The proposed formulation of the functions of the properties makes a certain generalization in the research of functionally graded materials and allows to describe homogeneous, nonlinearly variable and sandwich structures with the use of only one, consistent analytical model. The individual nonlinear hypothesis for planar cross section is assumed. Basing on the Hamiltons principle two differential equations of motion are obtained. The system of equations is analytically solved. The results are compared with numerical solutions obtained with FEM.

Stability of an ellipsoidal head with a central nozzle under axial load

Abstract The subject of the numerical investigation is an ellipsoidal head with a central (axis-symmetrical) nozzle. The nozzle is loaded by axial load force. The ellipsoidal head is under axial-symmetrical compression load. The numerical FEM model is elaborated. The calculation will provide the critical loads and equilibrium paths for the sample head.. The investigation will measure the influence of the diameter of the nozzle on the critical state of the ellipsoidal head.

Stability of Elastic Orthotropic Circular Cylindrical Vessels

This paper is devoted to stability investigation of orthotropic circular cylindrical vessels subjected to external pressure. An untypical orthotropic structure that consist of two layers: smooth-external and corrugated-internal is proposed. The investigation is divided into two steps. In first one analytical formulas describing buckling behaviour are derived. In second step numerical analysis is performed by using FEM to obtain the correlation between analytical and numerical results. Authors also considered linear and nonlinear buckling analysis. During the linear analysis the influence of vessel geometry on critical pressure is determined. Nonlinear analysis is carried out to create equilibrium paths which show the behaviour of vessels in post-buckling state. The results of the analysis are presented in figures.Copyright