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Sobel, L. H.

Publications and source records attributed to Sobel, L. H..

Novel composites for wing and fuselage applications

Probabilistic predictions based on the IPACS code are presented for the material and structural response of unnotched and notched, IM6/3501-6 Gr/Ep laminates. Comparisons of predicted and measured modulus and strength distributions are given for unnotched unidirectional, cross-ply and quasi-isotropic laminates. The predicted modulus distributions were found to correlate well with the test results for all three unnotched laminates. Correlations of strength distributions for the unnotched laminates are judged good for the unidirectional laminate and fair for the cross-ply laminate, whereas the strength correlation for the quasi-isotropic laminate is judged poor because IPACS did not have a progressive failure capability at the time this work was performed. The report also presents probabilistic and structural reliability analysis predictions for the strain concentration factor (SCF) for an open-hole, quasi-isotropic laminate subjected to longitudinal tension. A special procedure was developed to adapt IPACS for the structural reliability analysis. The reliability results show the importance of identifying the most significant random variables upon which the SCF depends, and of having accurate scatter values for these variables.

Sobel, L. H.↗

Buckling of prismatic structures under biaxial loading

A one term analysis is presented for the elastic buckling of prismatic structures with either classical simple support or completely clamped boundary conditions on the transverse ends. Results suggest that a one term solution based on an appropriate choice of coordinate functions may lead to satisfactory buckling loads for other prismatic structures with completely clamped and other end conditions.

Ashour, H. A.↗

Buckling of eccentrically stringer-stiffened cylindrical panels under axial compression

The paper presents numerical results, based on Donnell shell theory, for the axial compressive buckling loads for eccentrically stringer-stiffened circular cylindrical panels, in a study of the effect of boundary conditions and panel width on the buckling load. The two cases of inside and outside stiffeners were considered. The complete cylinder buckling load was reached only for panels under classical simply supported boundary conditions. The prevention of circumferential displacement is found to be the most important in-plane boundary condition from the point of view of increasing the buckling load. Clamping is found more effective in increasing the buckling loads of panels with free circumferential edge displacement than of panels with zero edge displacement. When panel width is equal to or greater than 180 deg, the panel buckling loads are within 10% of the complete cylinder load for all cases except one simply supported panel with outside stringers. Buckling loads were higher for outside stringers, except for very narrow panels that are restrained against circumferential edge displacement. Eccentricity effects are generally similar for clamped and simply supported panels with the same in-plane boundary conditions.

Sobel, L. H.↗

Buckling of Cylindrical Panels Under Axial Compression

This paper investigates the effects of boundary conditions and panel width on the axially compressive buckling behavior of unstiffened, isotropic, circular cylindrical panels. Numerical results are presented for eight different sets of boundary conditions along the straight edges of the panels. For all sets of boundary conditions except one (SSI), the results show that the panel buckling loads monotonically approach the complete cylinder buckling load from above as the panel width is increased. Low buckling loads, sometimes less than half the complete cylinder buckling load, are found for simply supported panels with free in-plane edge displacements (SSI). The SSI buckling loads are below the complete cylinder load even for '360deg panels'. It is also observed that the prevention of circumferential edge displacement is the most important in-plane boundary condition from the point of view of increasing the buckling load, and that the prevention of edge rotation (i.e. clamping) in the circumferential direction also significantly increases the buckling load. Parametric studies are also performed to determine the effects of variations in panel length and thickness on the buckling loads.

Sobel, L. H.↗

Weight comparisons of optimized stiffened, unstiffened, and sandwich cylindrical shells made from composite or aluminum materials

This work presents optimum designs for unstiffened, hat stringer-stiffened and honeycomb sandwich cylinders under axial compression. Optimization results for graphite-epoxy cylinders show about a 50 percent weight savings over corresponding optimized aluminum cylinders for a wide loading range. The inclusion of minimum gage considerations results in a significant weight penalty, especially for a lightly loaded cylinder. Effects of employing a smeared stiffener buckling theory in the optimization program are investigated through comparison of results obtained from a more accurate branched shell buckling computer code. It was found that the stiffener cross-sectional deformations, which are usually ignored in smeared stiffener theory, result in about a 30 percent lower buckling load for the graphite-epoxy hat stiffened cylinder.

Agarwal, B. L.↗

Stress tests on cylinders and aluminum panels

An optimization study of composite stiffened cylinders is discussed. The mathematical model for the buckling has been coupled successfully with the optimization program AESOP. The buckling analysis is based on the use of the smeared theory for the buckling of stiffened orthotropic cylindrical shells. The loading, radius, and length of the cylinder are assumed to be known parameters. An optimum solution gives the value of cross-sectional dimensions and laminate orientations. The different types of buckling modes are identified. Mathematical models are developed to show the relationships of the parameters.

Sobel, L. H.↗

Convergence of finite difference transient response computations for thin shells.

Numerical studies pertaining to the limits of applicability of the finite difference method in the solution of linear transient shell response problems are performed, and a computational procedure for the use of the method is recommended. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. This is not a serious limitation in view of natural constraints imposed by the extension of Saint Venant's principle to transient response problems. It is also found that the short wavelength limitations of thin shell (Bernoulli-Euler) theory create significant convergence difficulties in computed response to certain types of transverse excitations. These difficulties may be overcome, however, through proper selection of finite difference mesh dimensions and temporal smoothing of the excitation.

Sobel, L. H.↗

Optimization of a corrugated stiffened composite panel under uniaxial compression

An approach of structural optimization has been used to optimize the weight of a simply supported, corrugated hat stiffened composite panel under uniaxial compression. The approach consists of the employment of nonlinear mathematical programming techniques to reach an optimum solution. Some simplifying assumptions are made in the stress analysis to obtain faster convergence to an optimum solution. With these simplifying assumptions the number of unknown design parameters is reduced to twelve.

Agarwal, B. L.↗

Analysis of the transient response of shell structures by numerical methods.

This paper examines some basic considerations underlying dynamic shell response analysis and the impact of these considerations upon the practical aspects of solution by numerical methods. Emphasis is placed on the solution of linear problems. The present states of development of the finite difference and finite element methods are reviewed, and techniques for the treatment of temporal variation are discussed. An examination is made of the frequency parameters characteristic of thin shell theory, applied excitations, and spatial mesh geometries, and the significance of these parameters with respect to computational convergence is illustrated.

Geers, T. L.↗

Analysis of transient, linear wave propagation in shells by the finite difference method

The applicability of the finite difference method to propagation problems in shells, and the response of a cylindrical shell with cutouts to both longitudinal and radial transient excitations are investigated. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. The short wave length limitations of thin shell theory create significant convergence difficulties may often be overcome through proper selection of finite difference mesh dimensions and temporal or spatial smoothing of the excitation. Cutouts produce moderate changes in early and intermediate time response of a cylindrical shell to axisymmetric pulse loads applied at one end. The cutouts may facilitate the undesirable late-time transfer of load-injected extensional energy into nonaxisymmetric flexural response.

Geers, T. L.↗