Jerzy Lewiński

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.

Fully stressed head of a pressure vessel

This work is devoted to a head of a vessel charged with internal uniform pressure. The analysis is aimed at finding a shape of the head that ensures its full charge with stresses. In a classical torispherical or ellipsoidal head the region of its joint with the cylindrical shell is loaded with shear force and bending moment as a result of the forced consistency of displacements of both parts of a vessel. The load causes high bending stresses in the area of the joint. Therefore, a shape of a head meridian is sought for which the shear force and the bending moment approach zero. Only membrane state stresses should occur in such a structure. The mathematical description is based on the theory of shells, taking account of boundary disturbances. The numerical solution determines the sought-after shape of the head and its minimal relative convexity.

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.

Bending of I-beam with the transvers shear effect included – FEM calculated

The paper is devoted to three-point bending of an I-beam with include of transvers shear effect. Numerical calculations were conducted independently with the use of the SolidWorks system and the multi-purpose software package ANSYS The results of FEM study conducted with the use of two systems were compared and presented in tables and figures.