Search NASA⌕ Search

SEARCH · Search NASA

Results for “Shells”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

A triangular thin shell finite element: Nonlinear analysis

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

Thomas, G. R.↗
NASA NTRS1974

A note on the interference of two collinear cracks in a cylindrical shell

A simple interference problem in shells is evaluated and the results are compared with the obtained data for flat plates. A pressurized shallow cylindrical shell containing two collinear axial through cracks of equal lengths is investigated. It is found that as the size of the net ligament between the two cracks approaches zero, the stress intensity factors at the inner crack tips go to infinity, and the factors at the outer tips approach values that correspond to a single crack except that they are twice as long.

Erdogan, F.↗
NASA NTRS1975

A search for H/-/ in the shell surrounding chi Ophiuchi

Assuming that chi Oph is an extreme Be star, some consequences are investigated for the interpretation that the IR excesses in such stars are produced by H(-) free-bound emission. The column density of H(-) in the shell surrounding chi Oph is estimated from the observed IR excess, and Copernicus UV spectrophotometric data are used to search for a predicted absorption feature at 1129.54 A due to H(-) and to derive an upper limit to the H(-) column density. No feature resembling the predicted H(-) line is seen in the spectrum of chi Oph, and a marked discrepancy is noted between the estimated column density and the derived upper limit. Possible causes of these discrepancies are discussed, including incorrect interpretation of the IR excess in extreme Be stars, incorrect theoretical calculations describing the predicted H(-) UV absorption line, and the possibility that the line of sight through the shell does not intersect the regions where the IR excess originates.

Snow, T. P., Jr.↗
NASA NTRS1975

A computerized symbolic integration technique for development of triangular and quadrilateral composite shallow-shell finite elements

Computerized symbolic integration was used in conjunction with group-theoretic techniques to obtain analytic expressions for the stiffness, geometric stiffness, consistent mass, and consistent load matrices of composite shallow shell structural elements. The elements are shear flexible and have variable curvature. A stiffness (displacement) formulation was used with the fundamental unknowns consisting of both the displacement and rotation components of the reference surface of the shell. The triangular elements have six and ten nodes; the quadrilateral elements have four and eight nodes and can have internal degrees of freedom associated with displacement modes which vanish along the edges of the element (bubble modes). The stiffness, geometric stiffness, consistent mass, and consistent load coefficients are expressed as linear combinations of integrals (over the element domain) whose integrands are products of shape functions and their derivatives. The evaluation of the elemental matrices is divided into two separate problems - determination of the coefficients in the linear combination and evaluation of the integrals. The integrals are performed symbolically by using the symbolic-and-algebraic-manipulation language MACSYMA. The efficiency of using symbolic integration in the element development is demonstrated by comparing the number of floating-point arithmetic operations required in this approach with those required by a commonly used numerical quadrature technique.

Anderson, C. M.↗
NASA NTRS1975

Shear-flexible finite-element models of laminated composite plates and shells

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

Noor, A. K.↗
NASA NTRS1976

A computer program for anisotropic shallow-shell finite elements using symbolic integration

A FORTRAN computer program for anisotropic shallow-shell finite elements with variable curvature is described. A listing of the program is presented together with printed output for a sample case. Computation times and central memory requirements are given for several different elements. The program is based on a stiffness (displacement) finite-element model in which the fundamental unknowns consist of both the displacement and the rotation components of the reference surface of the shell. Two triangular and four quadrilateral elements are implemented in the program. The triangular elements have 6 or 10 nodes, and the quadrilateral elements have 4 or 8 nodes. Two of the quadrilateral elements have internal degrees of freedom associated with displacement modes which vanish along the edges of the elements (bubble modes). The triangular elements and the remaining two quadrilateral elements do not have bubble modes. The output from the program consists of arrays corresponding to the stiffness, the geometric stiffness, the consistent mass, and the consistent load matrices for individual elements. The integrals required for the generation of these arrays are evaluated by using symbolic (or analytic) integration in conjunction with certain group-theoretic techniques. The analytic expressions for the integrals are exact and were developed using the symbolic and algebraic manipulation language.

Andersen, C. M.↗
NASA NTRS1976

On the elastic stability of shells

A synopsis of a series of investigations into the instability of axially compressed cylindrical shells is given. The objective of the research, which was made with models, was to devise a technique of nondestructive evaluation. The results show that, with models at any rate, success was achieved. Probing methods which can be used to determine the locations of weakness and the pertinent instability load levels were devised. The research on large scale shells was undertaken to determine the critical loads under as uniform a circumferential distribution of axial compressive force as possible. It is clear from the results presented that this objective was met.

Horton, W. H.↗
NASA NTRS1975

The computer in shell stability analysis

Some examples in which the high-speed computer has been used to improve the static stability analysis capability for general shells are examined. The fundamental concepts of static stability are reviewed with emphasis on the differences between linear bifurcation buckling and nonlinear collapse. The analysis is limited to the stability of conservative systems. Three examples are considered. The problem of cylinders subjected to bending loads is used as an example to illustrate that a simple structure can have a sufficiently complicated nonlinear behavior to require a computer analysis for accurate results. An analysis of the problems involved in the modeling of stiffening elements in plate and shell structures illustrates the necessity that the analyst recognizes all important deformation modes. The stability analysis of the Skylab structure indicates the size of problems that can be solved with current state-of-the-art capability.

Almroth, B. O.↗
NASA NTRS1975

On sound transmission into a thin cylindrical shell under 'flight conditions'

A mathematical model for sound transmission into a thin cylindrical shell is used to study sound transmission under flight conditions, i.e., under conditions of external air flow past a pressurized cylinder at flight altitude. Numerical results for different incidence angles are presented for a typical narrow-bodied jet in cruising flight at 10,660 m with interior pressure at 2440 m. A comparison is made between no-flow sound transmission at standard conditions on the ground to sound transmission under flight conditions. It is shown that at M = 0, the cylinder transmission loss (TL) has dips at the cylinder ring frequency (fR) and the critical frequency (fc) for a flat panel of same material and thickness as shell. Between fR and fc, cylinder TL follows a mass-law behavior. Flow provides a modest increase in TL in the mass-law region, and strongly interacts with the cylinder resonances below fR.

Koval, L. R.↗
NASA NTRS1977

X-ray spectra of Hercules X-1. 1: Iron line fluorescence from a subrelativistic shell

The X-ray spectrum of Hercules X-1 was observed in the energy range 2-24 keV from August 29 to September 3, 1975. A broad iron line feature is observed in the normal high state spectrum. The line equivalent width is given along with its full-width-half-maximum energy. Iron line fluorescence from an opaque, cool shell of material at the Alfven surface provides the necessary luminosity in this feature. The line energy width can be due to Doppler broadening if the shell is forced to corotate with the pulsar at a radius 800 million cm. Implications of this model regarding physical conditions near Her X-1 are discussed.

Pravdo, S. H.↗
NASA NTRS1976

K I 7699 A emission from the Betelgeuse shell

A map of the circumstellar gas shell around Betelgeuse is presented from observations of the fluorescent emission in the K I 7699 A resonance line. The observations obtained at 3 sec and 5 sec from the star indicate approximate spherical symmetry in the 10 km/s expanding shell responsible for the blueshifted sharp cores seen in strong resonance and low excitation lines. Calculations show that the density of neutral K atoms is approximately constant between 3 sec and 5 sec from the star. The emission profiles in the west show a second, higher velocity, component at 5 sec from the star.

Bernat, A. P.↗
NASA NTRS1977

What quenches the helium shell flashes

An analysis is conducted of a typical stellar helium shell flash cycle. A sequence of 12 flashes for a population I star is considered. The changes taking place at a constant mass layer in the helium-burning shell are studied as the flash develops. A highly simplified mathematical description is presented, taking into account the three necessary conditions for the occurrence of the flash and the pressure-density and temperature-density relationships. Quantities which are helpful in explaining what triggers the flash are found to be useful in explaining what quenches the flash.

Sackmann, I.-J.↗
NASA NTRS1977

X-ray spectra of Hercules X-1. I - Iron line fluorescence from a subrelativistic shell

The X-ray spectrum of Her X-1 was observed in the energy range from 2 to 24 keV from August 29 to September 3, 1975. Emission features are observed near the K-alpha iron-line energy which exhibit both broadening and a double line structure. The total luminosity in these features is about 4 by 10 to the 35th power ergs/s. Iron line fluorescence from an opaque cool (not exceeding 1 million K) shell of material at the Alfven surface provides the necessary luminosity in this feature. The double line structure and the line energy width can be due to Doppler shifts if the shell is forced to corotate with the pulsar at a radius of at least 800 million cm. Implications of this model regarding physical conditions near Her X-1 are discussed.

Pravdo, S. H.↗
NASA NTRS1977

Design, fabrication and test of a lightweight shell structure, phase 3

Progress is reported in the construction of lightweight orthogrid shells. Graphite/epoxy panels are being used in the fabrication. The shell structure is diagramed in detail. Panel laminates, and panel stiffener flanges are described while illustrations delineate panel assembly procedures.

Source record↗
NASA NTRS1977

Transverse shear effects on the stress-intensity factor for a circumferentially cracked, specially orthotropic cylindrical shell

The problem of a cylindrical shell containing a circumferential through crack is considered by taking into account the effect of transverse shear deformations. The formulation is given for a specially orthotropic material within the confines of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions regarding moment and stress resultants on the crack surface. Consequently, aside from multiplicative constants representing the stress intensity factors, the membrane and bending components of the asymptotic stress fields near the crack tip are found to be identical. The stress intensity factors are calculated separately for a cylinder under a uniform membrane load, and that under a uniform bending moment. Sample results showing the nature of the out-of-plane crack surface displacement and the effect of the Poisson's ratio are presented.

Delale, F.↗
NASA NTRS1978

Transverse shear stiffness of laminated anisotropic shells

Equations are derived for the transverse shear stiffness of laminated anisotropic shells. Without making assumptions for thickness distribution for either transverse shear stresses or strains, constitutive equations for the transverse shear deformation theory of anisotropic heterogeneous shells are found. The equations are based on Taylor series expansions about a generic point for stress resultants and couples, identically satisfying plate equilibrium equations. These equations are used to find statically correct expressions for in-surface stresses, transverse shear stresses, and the area density of transverse shear strain energy, in terms of transverse shear stress resultants and redundants. The application of Castigliano's theorem of least work minimizes shear strain energy with respect to the redundants. Examples are presented for several laminated walls. Good agreement is found between the results and those of exact three-dimensional elasticity solutions for the cylindrical bending of a plate.

Cohen, G. A.↗