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28 records · Page 2

Ranges of applicability for the continuum beam model in the mechanics of carbon nanotubes and nanorods

Limitations in the validity of the continuum beam model for carbon nanotubes (NTs) and nanorods are examined. Applicability of all assumptions used in the model is restricted by the two criteria for geometric parameters that characterize the structure of NTs. The key non-dimensional parameters that control the NT buckling behavior are derived via dimensional analysis of the nanomechanical problem. A mechanical law of geometric similitude for NT buckling is extended from continuum mechanics for different molecular structures. A model applicability map, where two classes of beam-like NTs are identified, is constructed for distinct ranges of non-dimensional parameters. Expressions for the critical buckling loads and strains are tailored for two classes of NTs and compared with the data provided by the molecular dynamics simulations. copyright 2001 Elsevier Science Ltd. All rights reserved.

Continuum beam model↗

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.↗

Structural similitude and design of scaled down laminated models

The excellent mechanical properties of laminated composite structures make them prime candidates for wide variety of applications in aerospace, mechanical and other branches of engineering. The enormous design flexibility of advanced composites is obtained at the cost of large number of design parameters. Due to complexity of the systems and lack of complete design based informations, designers tend to be conservative in their design. Furthermore, any new design is extensively evaluated experimentally until it achieves the necessary reliability, performance and safety. However, the experimental evaluation of composite structures are costly and time consuming. Consequently, it is extremely useful if a full-scale structure can be replaced by a similar scaled-down model which is much easier to work with. Furthermore, a dramatic reduction in cost and time can be achieved, if available experimental data of a specific structure can be used to predict the behavior of a group of similar systems. This study investigates problems associated with the design of scaled models. Such study is important since it provides the necessary scaling laws, and the factors which affect the accuracy of the scale models. Similitude theory is employed to develop the necessary similarity conditions (scaling laws). Scaling laws provide relationship between a full-scale structure and its scale model, and can be used to extrapolate the experimental data of a small, inexpensive, and testable model into design information for a large prototype. Due to large number of design parameters, the identification of the principal scaling laws by conventional method (dimensional analysis) is tedious. Similitude theory based on governing equations of the structural system is more direct and simpler in execution. The difficulty of making completely similar scale models often leads to accept certain type of distortion from exact duplication of the prototype (partial similarity). Both complete and partial similarity are discussed. The procedure consists of systematically observing the effect of each parameter and corresponding scaling laws. Then acceptable intervals and limitations for these parameters and scaling laws are discussed. In each case, a set of valid scaling factors and corresponding response scaling laws that accurately predict the response of prototypes from experimental models is introduced. The examples used include rectangular laminated plates under destabilizing loads, applied individually, vibrational characteristics of same plates, as well as cylindrical bending of beam-plates.

Simitses, G. J.↗

Effects of scale in predicting global structural response

In the course of previous composite structures test programs, the need for and the feasibility of developing analyses for scale-up effects has been demonstrated. The analysis techniques for scale-up effects fall into two categories. The first category pertains to developing analysis methods independently for a single, unique failure mode in composites, and using this compendium of analysis methods together with a global structural model to identify and predict the response and failure mode of full-scale built-up structures. The second category of scale-up effects pertains to similitude in structural validation testing. In this latter category, dimensional analysis is used to develop scale-up laws that enable extrapolation of sub-scale component test data to full-scale structures. This viewgraph presentation describes the approach taken and some developments accomplished in the first category of analysis for scale-up effects. Layup dependence of composite material properties severely limits the use of the dimensional analysis approach and these limitations are illustrated by examples.

Kan, Han-Pin↗

Investigations on wings with and without sweepback at high subsonic speeds

Drag tests at zero lift have been made at Mach numbers from 0.7 to approximately 0.95 in the high speed wind tunnel of the Institute of Aerodynamics, ETH, Zurich, on a group of untapered wings of aspect ratio 3.25, having sweep angles of 0 degree and 35 degrees. For each sweep angle, a series of geometrically similar models was tested at a constant Reynolds number to provide a verification of computed tunnel blocking corrections. Tests were also made for wings having thickness ratios of 0.09 and 0.12 and the results compared with results predicted by von Karman's similarity law.

RESEARCH TECHNIQUE - CORRECTIONS↗

Nonlinear Analysis and Scaling Laws for Noncircular Composite Structures Subjected to Combined Loads

Results from an analytical study of the response of a built-up, multi-cell noncircular composite structure subjected to combined internal pressure and mechanical loads are presented. Nondimensional parameters and scaling laws based on a first-order shear-deformation plate theory are derived for this noncircular composite structure. The scaling laws are used to design sub-scale structural models for predicting the structural response of a full-scale structure representative of a portion of a blended-wing-body transport aircraft. Because of the complexity of the full-scale structure, some of the similitude conditions are relaxed for the sub-scale structural models. Results from a systematic parametric study are used to determine the effects of relaxing selected similitude conditions on the sensitivity of the effectiveness of using the sub-scale structural model response characteristics for predicting the full-scale structure response characteristics.

Hilburger, Mark W.↗

Mechanical similitude and turbulence

This report deals with the theory of the vortex street which enables the reproduction of the mechanism of the form resistance with suitable approximation under stated conditions, although such a resistance is precluded in a fluid which is perfectly inviscid. Disregarding for the present the origination of the vortex, the stream attitude in the wake of the body may be described approximately correct by the representation of individual vortices, without transgressing the law governing the motion of such vortices in an ideal fluid. Another striking example is the theory of the induced drag of wings, which likewise shows the extent of applying the vortex equations without overstepping the bounds of the dynamics of ideal fluids.

Von Karman, TH↗

An Analysis of the Applicability of the Hypersonic Similarity Law to the Study of Flow About Bodies of Revolution at Zero Angle of Attack

The hypersonic similarity law as derived by Tsien has been investigated by comparing the pressure distributions along bodies of revolution at zero angle of attack. In making these comparisons, particular attention was given to determining the limits of Mach number and fineness ratio for which the similarity law applies. For the purpose of this investigation, pressure distributions determined by the method of characteristics for ogive cylinders for values of Mach numbers and fineness ratios varying from 1.5 to 12 were compared. Pressures on various cones and on cone cylinders were also compared in this study. The pressure distributions presented demonstrate that the hypersonic similarity law is applicable over a wider range of values of Mach numbers and fineness ratios than might be expected from the assumptions made in the derivation. This is significant since within the range of applicability of the law a single pressure distribution exists for all similarly shaped bodies for which the ratio of free-stream Mach number to fineness ratio is constant. Charts are presented for rapid determination of pressure distributions over ogive cylinders for any combination of Mach number and fineness ratio within defined limits.

PRESSURE DISTRIBUTION - BODIES OF REVOLUTION↗