Prismatic Shells Research Articles

Stability of thin-walled prismatic and cylindrical shells of average length stressed by longitudinal forces

Stability of thin-walled prismatic and cylindrical shells of average length stressed by longitudinal forces

Torsional behaviour of prismatic shell of variable cross-section through finite-difference approach

This paper presents a finite-difference approach for analysing prismatic shells of varible cross-section. Such shells have wide application in machine tools and mechanical handing. The construction of the design model allows for warping and distortion. The problem is formulated by use of Vlasv's variational method and solved by means of a finite-difference technique for various boundary conditions. The results are compared with those obtained by use of the cylindrical-shell theory developed by Krishanamurthy and the theoretical and experimental results obtained by Kristek. A study of the influence of various geometric parameters such as thickness of shell, length of shell, taper angle, and number of diaphragms is also made.

Torsional vibrations of prismatic shells

Prismatic shells find wide application in mechanical, civil and aeronautical engineering. The object of this paper is to propose a method of analysing such shells having different internal ribbing for their torsional vibrations. The governing equations of motion are derived by using a finite difference method and solved by the simultaneous iteration technique. The accuracy of the method is ascertained by comparing the results for some wellknown boundary conditions with the results obtained by classical methods. Shells of square cross-section and rectangular shells of variable and constant cross-section have been analysed. The effects of introduction of diaphragms on the eignefrequencies have been analysed. The effects of variations in shell thickness and length on the dynamic behaviour also have been studied.

Prismatic shells with hexagonal cross-section

A new discrete-continuous analytical model for prismatic shells with hexagonal cross-section is developed on the basis of the semimembrane shell theory. Final results for stresses are derived in form of simple expressions. The proposed analytical model is checked against test and finite element results. The accuracy is judged to be exceptionally good in all cases examined. Therefore, it appears that the method provides a simple but powerful tool in design of nuclear reactor subassembly ducts.

Stress, stability and vibration of complex, branched shells of revolution

A comprehensive computer program, designated BOSOR4, for analysis of the stress, stability and vibration of segmented, ring-stiffened, branched shells of revolution and prismatic shells and panels is described. The program performs large-deflection axisymmetric stress analysis, small-deflection nonsymmetric stress analysis, modal vibration analysis with axisymmetric nonlinear prestress included, and buckling analysis with axisymmetric or nonsymmetric prestress. One of the main advantages of the code is the provision for realistic engineering details such as eccentric load paths, internal supports, arbitrary branching conditions, and a ‘library’ of wall constructions. The program is based on the finite-difference energy method which is very rapidly convergent with increasing numbers of mesh points. The organization of the program is briefly described with flow of calculations charted for each of the types of analysis. Overlay charts and core storage requirements are given for the CDC 6600, IBM 370/165, and UNTVAC 1108 versions of BOSOR4. A large number of cases is included to demonstrate the scope and practicality of the program period.

多重有向連続体理論序説 : 一般化された連続体力学理論における director frame の多重化について

This paper tries to construct the theory of multi-directed continuum mechanics, by multiplying the director frame based on the thought of generalized continua. The multi-directed continuum corresponds to the medium which has many degrees of freedom for the deformation of every material particle. Mathematically it is considered as an assemblage of material points which have a macro director polyad (i.e. frame) and n micro director polyads. And actually, one of such continua will be the continuous model of discrete or heterogeneous media (e.g. reticulated framestructures, prismatic shells, layered media, and composit materials). Independently of dimension the basic equations are formulated by Hamilton's principle (§4), after defining the geometrical relations (§2) and the strain measures (§3). In section 5 some different expressions of them are concidered for comparison. Therefore by varying values of indices, they can form the theories of one, two and three dimension respectively, and fundamentally imply the concepts in many published works of the generalized continuum mechanics. Section 6 is a review of the concept of directors and gives the outline of an ideal multi-directed continuum model for actual media by analogy. Then it is noted that the deformation of a macro polyad space which includes micro polyads, is constrained homogeneously.

Evaluation of various analytical models for buckling and vibration of stiffened shells.

An investigation is made of the magnitude of errors introduced by various widely accepted modeling techniques. Numerical studies are made of ring-stiffened cylinders under external pressure and semisandwich corrugated panels under axial compression. The investigation is performed with use of BOSOR4, a computer code for the stress, buckling, and vibration analysis of branched shells of revolution and prismatic shells with complex wall construction. It is shown that predicted buckling loads and vibration frequencies can be unexpectedly sensitive to modeling details such as fastener dimensions, prestress deformations, out-of-piane stiffness of rings, and differing locations of ring shear center and centroid. A procedure is demonstrated for the inclusion of effects of local wall distortion on the instability failure of shells with complex wall construction.

Transmission of concentrated forces into prismatic shells—II

The paper treats the remaining two cases of an unbounded prismatic shell subjected to concentrated forces at the ridge. When the load is perpendicular to the plane of symmetry of the shell, the membrane forces remain bounded, while the moments and transverse shearing forces are singular at the load point. In contrast, the membrane forces dominate the far field. When the concentrated force is applied in the direction of the ridge, the membrane and transverse shearing forces are singular and both are of the same order at the point of loading. The far field for this case again is dominated by the membrane forces.

Vibrations of prismatic shells with hexagonal cross section

Presented is an approximate method for the vibration analysis of nuclear reactor subassembly ducts in form of slender thin-walled polygonal shells with hexagonal cross section. The method is based on the semimembrane shell theory. Inadequacies of this approximate theory are not expected to play a significant role in the determination of fundamental natural frequencies. According to the simplified theory employed, three basic types of motion appear as independent: purely longitudinal vibrations, flexural vibrations and distortional vibrations.

Transmission of concentrated forces into prismatic shells—I

The work deals with the membrane and bending fields induced in prismatic shells by concentrated forces that are applied at the joints or ridges between two plates. Since many of the basic questions have little to do with supports or finite boundaries, an unbounded prismatic shell consisting of two semi-infinite plates is considered. This geometry lends itself to a straightforward analysis by Fourier transforms, and the results can be expressed in terms of exponential integrals of complex arguments for which tables are available. When the concentrated force lies in the plane of symmetry and is perpendicular to the ridge, an unexpected result is that the membrane forces remain bounded at the load point. In contrast, the moments and transverse shearing forces are singular at the point of loading. The asymptotic forms of the far fields show that the membrane forces decay more slowly than the moments and shearing forces. Thus the orders of the near and far fields reveal that the symmetri cally applied perpendicular force is transferred into the prismatic shell principally through bending, and diffused far away through membrane action.

Stress, Buckling, and Vibration of Prismatic Shells

A computer code for the general treatment of complex shells of revolution is applied to the analysis of prismatic shells such as oval cylinders, corrugated sheets, and longitudinally stiffened cylinders with stringer discreteness retained in the model. Cylinders of circular and noncircular cross section are treated as portions of very slender toroids. Corrugated and beaded panels are treated as portions of cylinders with very large radii. Longitudinally stiffened cylinders are treated as portions of very slender toroids with discrete ring stiffeners. The technique also permits analysis of buckling of cylinders with nonsymmetric pressure or thermal loading. The analysis is based on the finite-difference method which is used in conjunction with energy minimization. Included are convergence studies proving the validity of the technique and buckling calculations for nonuniformly loaded cylinders, externally pressurized and axially compressed elliptic cylinders, and axially compressed corrugated and beaded panels. Vibration modes and frequencies are calculated for an eccentrically stiffened cylinder in which the stringers are treated as discrete. Several numerical examples are given.

Stress analysis of hexagonal shells

A convenient method for the stress analysis of long prismatic shells with hexagonal cross sections, subjected to static loading, is developed. By employing the semi-membrane method in conjunction with a variational principle a closed form solution is obtained. It is. therefore, easy to perform a parametric study of the influence of various geometries and boundary conditions on the state of stress. Among other things, it is shown that stiffening the shell with cross-sectional diaphragms is not always advisable.

Torsion of prismatic shells

The paper presents a matrix method of analysis of prismatic shells with a box-type cross-section with two axes of symmetry. Such a prismatic shell is approximated by a suitable design model allowing for the warping and distortion of the cross section. The problem is solved using Vlasov's variational method in conjunction with the transfer matrices. The procedure is illustrated by two examples, one of which indicates that the diaphragms stiffening the cross-section may not be beneficial in a global sense.

The exact theory of bending of prismatic shells ? an application of transfer matrices

In this paper a new application of transfer matrices has been made in connection with the exact theory of bending of prismatic shells. It is shown that use of transfer matrices reduces the number of unknowns from 8 n to four, where n is the total number of walls, for a given integer m. This simplification is specially applicable to structures with open or simply connected closed sections.

Design of Prismatic Shells

Design of Prismatic Shells