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Results for “SHELL THEORY”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1968

Notes on nonlinear shell theory.

Nonlinear membrane shell theory and small perturbations of pressurized membrane shells, noting bending, buckling and vibration of stressed shells

Budiansky, B.↗
NASA NTRS1983

Vibrations of cantilevered circular cylindrical shells Shallow versus deep shell theory

Free vibrations of cantilevered circular cylindrical shells having rectangular planforms are studied in this paper by means of the Ritz method. The deep shell theory of Novozhilov and Goldenveizer is used and compared with the usual shallow shell theory for a wide range of shell parameters. A thorough convergence study is presented along with comparisons to previously published finite element solutions and experimental results. Accurately computed frequency parameters and mode shapes for various shell configurations are presented. The present paper appears to be the first comprehensive study presenting rigorous comparisons between the two shell theories in dealing with free vibrations of cantilevered cylindrical shells.

Lee, J. K.↗
NASA NTRS2013

A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

Nemeth, Michael P.↗
NASA NTRS1976

Recent advances in shell theory

The results reviewed are divided into two categories: those that relate two-dimensional shell theory to three-dimensional elasticity theory and those concerned with shell theory per se. In the second category results for general elastic systems that carry over, by specialization or analogy, to shells and results that are unique to shell theory itself are considered.

Simmonds, J. G.↗
NASA NTRS1967

Notes on non-linear shell theory

Tensor equations of equilibrium for nonlinear membrane shell theory and small perturbations of pressurized membrane shells

TENSOR ANALYSIS↗
NASA NTRS2002

Applicability of the Continuum-Shell Theories to the Mechanics of Carbon Nanotubes

Validity of the assumptions relating the applicability of continuum shell theories to the global mechanical behavior of carbon nanotubes is examined. The present study focuses on providing a basis that can be used to qualitatively assess the appropriateness of continuum-shell models for nanotubes. To address the effect of nanotube structure on their deformation, all nanotube geometries are divided into four major classes that require distinct models. Criteria for the applicability of continuum models are presented. The key parameters that control the buckling strains and deformation modes of these classes of nanotubes are determined. In an analogy with continuum mechanics, mechanical laws of geometric similitude are presented. A parametric map is constructed for a variety of nanotube geometries as a guide for the applicability of different models. The continuum assumptions made in representing a nanotube as a homogeneous thin shell are analyzed to identify possible limitations of applying shell theories and using their bifurcation-buckling equations at the nano-scale.

Harik, V. M.↗
NASA NTRS1998

Some Comments on the Status of Shell Theory at the End of the 20th Century: Complaints and Correctives

This review is divided into complaints and correctives. Complaints are directed at: sloppy refereeing and editing; authors who fail to read or acknowledge what others have done; the mis-naming or mis-crediting of results; the misunderstanding and misuse of the Kirchhoff hypothesis; inflated claims of accuracy based on overly-simplified benchmark problems; the failure to appreciate the inherent errors in various shell models; the failure to appreciate that the physical response and mathematical structure of shell theory are fundamentally different from 3-dimensional elasticity; and the irrelevance of Cosserat-type theories. Correctives include a simple, straight-forward derivation of a general nonlinear dynamic shell theory with the following features: (1) the equations of motion and kinematics (and those of thermodynamics, if desired) are exact consequences of their 3-dimensional counterparts; (2) there are no asymptotic or series expansions through the thickness; (3) all approximations (including the Kirchhoff Hypothesis) occur in the constitutive relations; (4) in static problems, there is a mixed form of the governing equations involving a mixed-energy density and exhibiting remnants of the well-known static-geometric duality of linear theory which is numerically robust because the limiting cases of nonlinear membrane theory and inextensional bending theory fall out naturally. (These latter two special cases are known to produce numerical nightmares unless treated with great care); and (5) all equations may be expressed in coordinate-free form (although, sometimes, a hybrid form is shown to be superior).

Simmonds, James G.↗
NASA NTRS1973

Numerical analysis of stiffened shells of revolution. Volume 2: Users' manual for STAR-02S - shell theory automated for rotational structures - 2 (statics), digital computer program

A procedure for the structural analysis of stiffened shells of revolution is presented. A digital computer program based on the Love-Reissner first order shell theory was developed. The computer program can analyze orthotropic thin shells of revolution, subjected to unsymmetric distributed loading or concentrated line loads, as well as thermal strains. The geometrical shapes of the shells which may be analyzed are described. The shell wall cross section can be a sheet, sandwich, or reinforced sheet or sandwich. General stiffness input options are also available.

Svalbonas, V.↗
NASA NTRS1973

Numerical analysis of stiffened shells of revolution. Volume 3: Users' manual for STARS-2B, 2V, shell theory automated for rotational structures, 2 (buckling, vibrations), digital computer programs

The User's manual for the shell theory automated for rotational structures (STARS) 2B and 2V (buckling, vibrations) is presented. Several features of the program are: (1) arbitrary branching of the shell meridians, (2) arbitrary boundary conditions, (3) minimum input requirements to describe a complex, practical shell of revolution structure, and (4) accurate analysis capability using a minimum number of degrees of freedom.

Svalbonas, V.↗
NASA NTRS2014

Buckling Analysis for Stiffened Anisotropic Circular Cylinders Based on Sanders Nonlinear Shell Theory

Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.

Nemeth, Michael P.↗
NASA NTRS1983

Vibrations of blades with variable thickness and curvature by shell theory

A procedure for analyzing the vibrations of rotating turbomachinery blades has been previously developed. This procedure is based upon shallow shell theory, and utilizes the Ritz method to determine frequencies and mode shapes. However, it has been limited heretofore to blades of uniform thickness, uniform curvature, and/or twist and rectangular planform. The present work shows how the procedure may be generalized to eliminate the aforementioned restrictions. Nonrectangular planforms are dealt with by a suitable coordinate transformation. This, as well as variable thickness, curvature and twist, require using numerical integration. The procedure is demonstrated on four examples of cantilevered blades for which theoretical and experimental data have been previously published: (1) flat plate with spanwise taper, (2) flat plate with chordwise taper, (3) twisted plate with chordwise taper, and (4) cylindrical shell with chordwise taper.

Lee, J. K.↗
NASA NTRS1972

Application of various elastic thin shell theories to blood flow problems

Some existing theories, on elastic thin shells, are reviewed to ascertain their influence on the computation of phase velocities in fluid filled cylinders representing certain aspects of the behavior of arteries and veins in vivo. For physiologically meaningful parameters, including moderately large in plane prestrain that occurs in mammals, the results suggest that with one exception, the small differences in the formulations exercise little influence on the phase velocities. However, it is demonstrated that inclusion of the forces induced by the rotation of the hydrostatic pressure is essential or significantly erroneous torsional wave speeds result. Also the introduction of moderate implane prestrains that are present in living mammals is shown to lead to nonselfadjoint differential equations of motion, whose biorthogonal eigenvectors differ slightly from each other.

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