Eccentric Stiffeners Research Articles

Buckling of elastic-plastic discretely stiffened cylinders in axial compression

Bifurcation under axial compression of discretely stringer-stiffened cylinders in the elastic and plastic ranges is studied. The stiffeners are treated as long plates. Small-strain J2 flow and deformation theories of plasticity are used. The effect of stiffener size on the critical stress is investigated; this is discussed with reference to the critical stresses of an equivalent simply-supported panel, and of a long plate simply-supported on three edges and free along one longitudinal edge. The effects of stiffener eccentricity, and of the number of stiffeners, is also discussed.

Buckling of waffle cylinders

There is a growing interest in the analysis and design of waffle cylinders because of the advantages of integrally stiffened shell wall construction. The usual approach to the stability analysis of a stiffened shell has been to replace it by an equivalent orthotropic shell. The eccentricity of the stiffener has a large effect on the critical load in cylindrical shells, and outside stiffening has been found to be stronger than inside stiffening. Inversion of the stiffener eccentricity effect has been observed in cylinders under hydrostatic pressure loading. Naturally, regardless of whether the stiffened cylinder is considered as an orthotropic continuum or a composite of discrete elements, the treatment cannot be complete if it fails to include the coupling between bending and extensional forces and deformations resulting from one-sidedness of the stiffeners.

Snap-through buckling of eccentrically stiffened shallow spherical caps

The problem of snap-through buckling of a clamped, eccentrically stiffened shallow spherical cap is considered under quasi-statically applied uniform pressure and a special case of dynamically applied uniform pressure. This dynamic case is the constant load infinite duration case (step time-function) and it represents an extreme case of blast loading-large decay time, small decay rate.The analysis is based on the nonlinear shallow shell equations under the assumption of axisymmetric deformations and linear stress-strain laws. The eccentric stiff eners are disposed orthogonally along directions of principal curvature in such a way that the smeared mass, and extensional and flexural stiffnesses are constant. The stiffeners are also taken to be one-sided with constant eccentricity, and the stiffener-shell connection is assumed to be monolithic.The method developed in an earlier paper is employed. In this method, critical pressures are associated with characteristics of the total potential surface in the configuration space of the generalized coordinates.In addition, buckling of the complete thin eccentrically stiffened spherical shell under uniform quasi-statically applied pressure is considered, and these results are used to check the numerical answers. The complete spherical shell is stiffened in the same manner as the shallow cap.The results are presented in graphical form as load parameter vs initial rise parameter. Geometric configurations corresponding to isotropic, lightly stiffened, moderately stiffened and heavily stiffened geometries are considered. By lightly stiffened geometry one means that most of the extensional stiffness is provided by the thin shell. A computer program was written to solve for critical pressures. The Georgia Tech Univac 1108 high speed digital computer was used for this purpose.

Axisymmetric Vibrations of Ring Stiffened Circular Plates

The free-flexural vibrations of elastic circular plates with an attached axisymmetric ring stiffener are considered on the basis of both classical as well as improved theories of plates. Effects of symmetric as well as eccentric stiffeners on the frequencies in the first four modes of axisymmetric vibration are investigated for various plate and stiffener dimensions.

Natural vibrations of thin, flat-walled structures with different boundary conditions

The natural frequencies of thin, flat-walled structures with different boundary conditions are analyzed by the finite strip method. This class of structures includes plates with eccentric stiffeners, thin multi-celled box girder bridges, and folded plate roofs, etc. The method is simple and at the same time very powerful and versatile, and can treat problems with variably-spaced stiffeners, and with orthotropic and variable thickness plates without any difficulty. The finite strip method is an extension of the now well-known finite element method. This method is, however, semi-analytical in nature, since the displacement functions chosen are always of the form φ( x) ψ( y), in which φ( x) is a polynomial with undetermined parameters, and ψ( y) a function series satisfying a priori the two end conditions. Thus a two-dimensional strip is reduced to a one-dimensional problem, with a corresponding reduction in computational efforts.

Errata: "Buckling of Circular Cylindrical Shells with Multiple Orthotropic Layers and Eccentric Stiffeners"

An exact solution is derived for the buckling of a circular cylindrical shell with multiple orthotropic layers and eccentric stiffeners under axial compression, lateral pressure, or any combination thereof. Classical stability theory (membrane prebuckled shape) is used for simply supported edge boundary conditions. The present theory enables the study of coupling between bending and extension due to the presence of different layers in the shell and the presence of eccentric stiffeners. Previous approaches to stiffened multilayered shells are shown to be erratic in the prediction of buckling results because of neglect of coupling between bending and extension.

Buckling of circular cylindrical shells with multiple orthotropic layers and eccentric stiffeners.

Buckling of circular cylindrical shells with multiple orthotropic layers and eccentric stiffeners.

Optimum stiffened cylinders for combined axial compression and internal or external pressure.

A nondimensional ized structural optimization analysis that recognizes several design restraints is described for cylinders stiffened with stringers and/or rings of rectangular cross section and subjected to uniform axial compression in combination with either internal or external pressure. The lateral (pressure)-to-axial load ratio Ny/Nx is positive for external pressure and negative for internal pressure. Results are presented for Ny/Nx = 0.2, 0.5, 2.0, and —0.2, —0.5, —1.0 in Parts I and II of this paper, respectively, for L/R ratios of 0.25 and 1.5. Designs stiffened with both rings and stringers are lightest when Ny/Nx « 0, except for short cylinders where rings may not be required. With increasing positive Nv/Nx9s9 designs stiffened with stringers only are very inefficient, but designs stiffened with rings only become almost as light as those with both rings and stringers. The differences in the weights of the latter two configurations often are small at the higher Ny/Nx's. On the other hand, with increasing negative Ny/Nx's, designs stiffened only with rings are relatively inefficient, whereas those stiffened only with stringers rapidly become more efficient than ring and stringer designs. The effect of ring/stringer eccentricity upon weight is most important when Ny/Nx = 0; for large Ny/Nx values, either positive or negative, it has an insignificant effect. Inversions in stiffener eccentricity effects occur at Ny/Nx = +2 and —1.

On the stability of eccentrically stiffened cylindrical shells under axial compression

The effect of stiffener eccentricity on the critical load is studied for cylindrical shells under axial compression. Classical simple support and classical clamped end conditions are considered. A detailed physical explanation of the causes of the eccentricity effect is proposed and verified by computations for 350 typical shells.As in the case of buckling under hydrostatic pressure and torsion, the behavior of the eccentricity effect in the case of axial compression also depends very strongly on the geometry of the shell, represented by the Batdorf parameter. On the other hand the geometry of the stiffeners influences only its magnitude. At very low Z, inversion of the eccentricity effect occurs, but for practical dimensions outside stringers always stiffen the shell more than inside ones. The eccentricity effect has a pronounced maximum at practical values of Z. The behavior of the eccentricity effect is very similar for clamped and for simply supported shells. The effects of eccentricity of ring stiffeners are also considered.

Plastic buckling of eccentrically stiffened circular cylindrical shells.

A solution for the plastic buckling of eccentrically stiffened cylinders is derived by use of the J2 deformation theory of plasticity for a set of simply supported edge boundary conditions. The uniaxial character of the stiffeners and the stiffener eccentricity (asymmetry about the cylinder middle surface) are explicitly accounted for as is a variable Poisson's ratio in the plastic region. A closed-form stability criterion is obtained for axial compression, lateral pressure, and hydrostatic pressure loadings. The present results are more realistic for most practical stiffened cylinders than an existing solution in which an orthotropic shell model is used. A numerical example is given to illustrate the effect of plastic action on the buckling load of a typical aerospace structure.

Influence of stiffener eccentricity and end moment on stability of cylinders in compression.

Stiffener eccentricity and end moment effect on stability of cylindrical panel in axial compression

Static and dynamic effects of eccentric stiffening of plates and cylindrical shells.

Buckling characteristics of eccentrically stiffened cylindrical shells under hydrostatic pressure loading and vibration, buckling and flutter characteristics of stiffened flat plates