Elastic Constants for Corrugated-core Sandwich Plates
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PLATES - ELASTICITY↗
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Sinusoidal response of composite-material plates with material damping.
A general forced-vibration analysis is presented for laminated anisotropic rectangular plates including material damping. The theory used is the laminated version of the Mindlin plate theory and includes thickness-shear flexibility and rotatory and coupling inertia. A solution is obtained by the Rayleigh-Ritz method, extended to include the energy dissipated and the work done by the excitation. The analysis is applied to prediction of the resonant frequencies and associated nodal patterns and damping ratios of the first five modes for a series of rectangular plates with free edges. The plates considered consist of unidirectional boron-fiber/epoxy composite material with respective fiber orientations of 0, 10, 30, 45, 60, and 90 deg.
Siu, C. C.↗
A unified theory of plastic buckling of columns and plates
On the basis of modern plasticity considerations, a unified theory of plastic buckling applicable to both columns and plates has been developed. For uniform compression, the theory shows that long columns which bend without appreciable twisting require the tangent modulus and that long flanges which twist without appreciable bending require the secant modulus. Structures that both bend and twist when they buckle require a modulus which is a combination of the secant modulus and the tangent modulus. (author)
PLATES - PLASTICITY↗
A unified theory of plastic buckling of columns and plates
On the basis of modern plasticity considerations, a unified theory of plastic buckling applicable to both columns and plates has been developed. For uniform compression, the theory shows that long columns which bend without appreciable twisting require the tangent modulus and that long flanges which twist without appreciable bending require the secant modulus. Structures that both bend and twist when they buckle require a modulus which is a combination of the secant modulus and the tangent modulus.
Stowell, Elbridge Z↗
Stationary and nonstationary random vibrations of laminated composite plates via a higher order theory
Higher order shear deformation theory is utilized to study he weakly stationary and nonstationary random vibrations of cross-ply laminated plates. Normal mode method, in conjunction with the biorthogonality condition, for the nonsymmetric differential equations is applied. Detailed derivation is given for the governing equations, biorthogonality condition, the generalized mass and the generalized forces. Results are listed for a plate which is simply supported at all the edges, and subjected to a point load which is either timewise stationary or nonstationary random process.
Elishakoff, Isaac↗
Postbuckling of long thick plates in compression including higher order transverse shearing effects
Aluminum plates of various length/width ratios loaded in compression are examined analytically in terms of buckling and postbuckling for comparison with classical theory. The plates are considered to be subjected to longitudinal compressive displacement with no edge stress and are assumed to be simply supported at the side edges. The average longitudinal direct stresses are computed to plot characteristic curves by means of the following theories: 3D flexibility, higher-order shear deformation, first-order shear deformation, and classical von Karman. The 3D flexibility approach yields the lowest results with more unknowns than the higher-order shear-deformation method. The 3D flexibility approach is considered to be the most accurate, and it is shown that the calculated resultants and displacements tend to vary when consideration is given to the effects of transverse shear.
Stein, Manuel↗
Nonlinear theory for laminated and thick plates and shells including the effects of transverse shearing
Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensional theory, the displacements are expressed by trigonometric series representation through-the-thickness. The nonlinear strain-displacement relations are expanded into series which contain all first and second degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin.
Stein, M.↗
General theory of conical flows and its application to supersonic aerodynamics
Points treated in this report are: homogeneous flows, the general study of conical flows with infinitesimal cone angles, the numerical or analogous methods for the study of flows flattened in one direction, and a certain number of results. A thorough consideration of the applications on conical flows and demonstration of how one may solve within the scope of linear theory, by combinations of conical flows, the general problems of the supersonic wing, taking into account dihedral and sweepback, and also fuselage and control surface effects.
THEORIES - FLOW - LINEAR↗
Vibration characteristics of 1/8-scale dynamic models of the space-shuttle solid-rocket boosters
Vibration tests and analyses of six 1/8 scale models of the space shuttle solid rocket boosters are reported. Natural vibration frequencies and mode shapes were obtained for these aluminum shell models having internal solid fuel configurations corresponding to launch, midburn (maximum dynamic pressure), and near endburn (burnout) flight conditions. Test results for longitudinal, torsional, bending, and shell vibration frequencies are compared with analytical predictions derived from thin shell theory and from finite element plate and beam theory. The lowest analytical longitudinal, torsional, bending, and shell vibration frequencies were within + or - 10 percent of experimental values. The effects of damping and asymmetric end skirts on natural vibration frequency were also considered. The analytical frequencies of an idealized full scale space shuttle solid rocket boosted structure are computed with and without internal pressure and are compared with the 1/8 scale model results.
Leadbetter, S. A.↗
Handbook of structural stability part III : buckling of curved plates and shells
Available theories and test data on buckling of curved plates and shells are reviewed. For torsion and external-pressure loadings, the test data are correlated in terms of linear buckling theories for both the elastic and inelastic ranges. The cases which exhibit a marked disagreement between linear theory and test data include those of curved plates and cylinders under axial compression, cylinders under bending, and spherical plates under external pressure. These cases have been analyzed by a unified semiempirical approach for both the elastic and inelastic ranges which is satisfactory for analysis and design purposes. The effects of internal pressure on buckling of elements under uniaxial loads are discussed and data on various combined loadings are presented in interaction form. (author)
Gerard, George↗
Studies of von Karman's similarity theory and its extension to compressible flow : investigation of turbulent boundary layer over a flat plate in compressible flow by the similarity theory
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Shen, S F↗
Refined Zigzag Theory for Homogeneous, Laminated Composite, and Sandwich Plates: A Homogeneous Limit Methodology for Zigzag Function Selection
The Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is presented from a multi-scale formalism starting with the inplane displacement field expressed as a superposition of coarse and fine contributions. The coarse kinematic field is that of first-order shear-deformation theory, whereas the fine kinematic field has a piecewise-linear zigzag distribution through the thickness. The condition of limiting homogeneity of transverse-shear properties is proposed and yields four distinct sets of zigzag functions. By examining elastostatic solutions for highly heterogeneous sandwich plates, the best-performing zigzag functions are identified. The RZT predictive capabilities to model homogeneous and highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy ; and a wide range of applicability. The present theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient CO-continuous finite elements, and is thus appropriate for the analysis and design of high-performance load-bearing aerospace structures.
Tessler, Alexander↗
A geometrically nonlinear theory of shear deformable laminated composite plates and its use in the postbuckling analysis
This paper is devoted to the formulation of a higher-order, geometrically nonlinear theory of anisotropic symmetrically-laminated composite plates and to the analysis, in this context, of their postbuckling behavior. Special attention is given to the postbuckling analysis of plates made of transversely isotropic layers for which case, the influence played by the degree of transversal-isotropy of the layers as well as by the goemetrical parameters of the panel is investigated. Finally, the results obtained within the present higher-order theory are compared with their first order transverse shear deformation as well as with their classical (Kirchhoff) counterparts and a number of conclusions concerning their range of applicability and the influence of various parameters are presented.
Librescu, L.↗
Lubricant evaluation of the alpha and beta joints, phase 2
A research study was conducted to evaluate dry film lubrication of long life space components such as the alpha and beta joints of the Space Station. The problem addressed in the report pertains to the longevity of sputtered MoS2 or ion plated lead films in a rolling contact environment. A special technique was devised for the experiments, which incorporated a coated ball cyclically loaded against a flat plate. At fixed intervals the surface of the coating was photographed at 100X magnification. By computer scanning the photographs, the rate of coating loss was determined. Experimental variables include load and surface finish of the plate. A theory was developed to analyze the state of stress between ball and flat. The stress condition in the ball apparatus was related to the state of stress under rolling contact conditions. Based on the experiments life appeared to decrease with increasing load and increasing surface roughness. An ion plated lead film gave better life than a sputtered MoS2 film. However, by keeping the interfacial shear stress at a low level, adequate coating life was achieved for either coating. For the lead film, the critical stress was about 0.19 GPa (28 ksi). The study dealt only with mechanical wear. Before a coating is selected for a critical space application, other factors such as reaction with atomic oxygen must also be considered.
Kannel, J. W.↗
Surface and through crack problems in orthotropic plates
The present treatment of the general mode I crack problem in bending- and membrane-loaded orthotropic plates proceeds by formulating the bending problem for a series of planar and through-cracks; by independently varying the six independent constants, the effect of material orthotropy on the stress intensity factor is determined. The surface-crack problem is then formulated by means of the line-spring model, using a transverse-shear theory of plate bending. Attention is given to composite laminates with through-cracks or semielliptic surface cracks. A significant effect is noted for material orthotropy.
Erdogan, F.↗
Seismicity as a guide to global tectonics and earthquake prediction.
From seismicity studies, evidence is presented for several aspects of plate-tectonic theory, including ideas of sea-floor spreading, transform faulting and underthrusting of the lithosphere in island arcs. Recent advances in seismic instrumentation, the use of computers in earthquake location, and the installation of local networks of instruments are shown to have vastly increased the data available for seismicity studies. It is pointed out that most of the world's earthquakes are located in very narrow zones along active plate margins and are intimately related to global processes in an extremely coherent manner. Important areas of uncertainty calling for further studies are also pointed out.
Sykes, L. R.↗
On the breakup of tectonic plates by polar wandering
The observed boundary system of the major tectonic plates on the surface of the earth lends fresh support to the hypothesis of polar wandering. A dynamic model of the outer shell of the earth under the influence of polar shift is developed. The analysis falls into two parts: (1) deriving equations for stresses caused by polar shifting; and (2) deducing the pattern according to which the fracture of the shell can be expected. For stress analysis, the theory of plates and shells is the dominant feature of this model. In order to determine the fracture pattern, the existence of a mathematical theorem of plasticity is recalled: it says that the plastic flow begins to occur when a function in terms of the differences of the three principal stresses surpasses a certain critical value. By introducing the figures for the geophysical constants, this model generates stresses which could produce an initial break in the lithosphere.
Liu, H. S.↗
Modeling of composite beams and plates for static and dynamic analysis
A rigorous theory and the corresponding computational algorithms were developed for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants of a plate. Additionally, the analysis is used to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. It was decided that the variational-asymptotical method (VAM) would serve as a suitable framework in which to solve these types of problems. Work during this reporting period has progressed along two lines: (1) further evaluation of neo-classical plate theory (NCPT) as applied to shear-coupled laminates; and (2) continued modeling of plates with nonuniform thickness.
Hodges, Dewey H.↗