VTechWorks Repository :: Browsing by Author "Smith, C.W."

Browsing by Author "Smith, C.W."

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Acoustic scattering by discontinuities in waveguides
Sen, Rahul (Virginia Polytechnic Institute and State University, 1988)
The scattering of acoustic waves by boundary discontinuities in waveguides is analyzed using the Method of Matched Asymptotic Expansions (MAE). Existing theories are accurate only for very low frequencies. In contrast, the theory developed in this thesis is valid over the entire range of frequencies up to the first cutoff frequency. The key to this improvement lies in recognizing the important physical role of the cutoff cross-modes of the waveguide, which are usually overlooked. Although these modes are evanescent, they contain information about the interaction between the local field near the discontinuity and the far-field. This interaction has a profound effect on the far-field amplitudes and becomes increasingly important with frequency. The cutoff modes also present novel mathematical problems in that current asymptotic techniques do not offer a rational means of incorporating them into a mathematical description. This difficulty arises from the non-Poincare form of the cross-modes, and its resolution constitutes the second new result of this thesis. We develop a matching scheme based on block matching intermediate expansions in a transform domain. The new technique permits the matching of expansions of a more general nature than previously possible, and may well have useful applications in other physical situations where evanescent terms are important. We show that the resulting theory leads to significant improvements with just a few cross-mode terms included, and also that there is an intimate connection with classical integral methods. Finally, the theory is extended to waveguides with slowly varying shape. We show that the usual regular perturbation analysis of the wave regions must be completely abandoned. This is due to the evanescent nature of the cross-modes, which must be described by a WKB approximation. The pressure field we so obtain includes older results. The new terms account for the cutoff cross-modes of the variable waveguide, which play a central role in extending the dynamic range of the theory.
Analysis for Taylor vortex flow
Li, Rihua (Virginia Polytechnic Institute and State University, 1986)
Taylor vortex flow is one of the basic problems of nonlinear hydrodynamic stability. In contrast with the wide region of wavenumber predicted by the linear theory, experiments show that Taylor vortex flow only appears in a small region containing the critical wavenumber ß_er This phenomenon is called wave selection. In this work, several high-order perturbation methods and a numerical method are established. Both evolution and steady state of the How caused by single or several disturbances are studied. The existence of multiple steady states for disturbances with small wavenumber is discovered and proved. The stable and unstable steady state solutions and some associated phenomena such as jump phenomenon and hysteresis phenomenon are found. and explained. In the small region, the wavenumbers and initial amplitudes of disturbances determine the wavenumber of the flow. But outside this region, only the wavenumbers of the disturbances have effect on the wave selection. These results indicate that unstable solutions play a key role in wave selection. The side-band stability curve produced by the high-order perturbation methods is accurate at low Taylor numbers but incorrect at relatively high Taylor numbers. The relation of the unstable solutions and side-band stability is discussed. Besides, the overshoot and the oscillation phenomena during evolution are studied in detail. Connections between this work and experiments are discussed.
Analytical solutions for the statics and dynamics of rectangular laminated composite plates using shearing deformation theories
Khdeir, Ahmed Adel (Virginia Polytechnic Institute and State University, 1986)
The Levy-type analytical solutions in conjunction with the state-space concept are developed for symmetric laminated composite rectangular plates. Combinations of simply-supported, free and clamped boundary conditions are considered. The solutions are obtained for the first-order and higher-order theories in predicting the transverse deflections and stresses. Numerical results are presented for various boundary conditions, aspect ratios, lamination schemes and different loadings. The developments of these theories accomplished in general coordinates allow one to fulfill both the invariance requirements and to derive the relevant equations in any convenient planar systems of coordinates. The dynamic response problems are analyzed in the framework of higher order theories where the effects of transverse normal stress and rotary inertia forces are evaluated. The comparison between the theories as well as previously reported results is reported.
Calculation of skin-stiffener interface stresses in stiffened composite panels
Cohen, David (Virginia Polytechnic Institute and State University, 1987)
A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. In the first part of the investigation the accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. It is found that the finite-element/local elasticity solution scheme produce a very accurate interface stress representation in the local flange termination region. The use of 10 to 15 eigenvalues, in the eigenvalue expansion series, and 100 collocation points results in a converged local elasticity solution. In the second part of the investigation, the local elasticity solution is extended to include geometric nonlinearities. Using this analysis procedure, the influence of geometric nonlinearities on skin-stiffener interface stresses is evaluated. It is found that in flexible stiffened skin structures, which exhibit out-of-plane deformation on the order of 2 to 4 times the skin thickness, inclusion of geometrically nonlinear effects in the calculation of interface stresses is very important. Thus, the use of a geometrically linear analysis, rather than a nonlinear analysis, can lead to considerable error in the computation of the interface stresses. Finally, using the analytical tool developed in this investigation, it is possible to study the influence of stiffener parameters on the state of interface stresses.
Crack growth in unidirectional composites using singular finite elements and interactive computer graphics
Choksi, Gaurang Nalin (Virginia Polytechnic Institute and State University, 1988)
Graphical simulation of crack growth using singular finite elements and interactive computer graphics is presented. The study consists of two main parts : (i) the formulation and application of an anisotropic singular element (ASE) for analyzing homogeneous anisotropic materials with cracks and, (ii) graphical simulation of crack growth in unidirectional composites. Lekhnitskii’s stress function method is used to formulate the traction-free crack boundary value problem with the stress function expressed in a Laurent series. The geometry of the element is arbitrary. The development of the stiffness matrix for general anisotropic materials is presented and it is shown how the singular element can be incorporated into a conventional displacement based finite element program. The anisotropic singular element (ASE) developed is implemented to analyze cracked anisotropic materials subjected to inplane loading. A 2-D, displacement based linite element code is used and center cracked on- and off-axis coupons under tensile loading are analyzed using the element developed. A general, interactive menu driven program is developed to track crack growth in composite materials. PHIGS (Programmers Hierarchical Interactive Graphics System) is used as the application program interface to integrate the finite element program with interactive graphics. Simulation studies are performed for center cracked on- and off-axis Iaminae using the normal stress ratio theory as the crack propagation criterion. The direction of crack propagation and values of the crack initiation stresses predicted are in reasonable agreement with the experimental values for the cases analyzed.
The effects of rubber modification on friction and wear of epoxy networks
Chitsaz-Zadeh, Majid R. (Virginia Polytechnic Institute and State University, 1987)
An epoxy resin (Epon 828) was chemically modified with two different elastomers, poly(dimethyl-co-diphenyl) siloxane (PSX) and carboxyl-terminated butadiene-acrylonitrile (CTBN), to enhance its fracture toughness. The friction and wear of specimens modified with different amounts of elastomer were investigated in a pin-on-disk wear machine. An attempt was made to correlate the fracture toughness of the epoxy material to its fatigue wear rate for experiments in which a steel ball was sliding on a modified epoxy disk. A different type of experiment, modified epoxy pin sliding on an abrasive disk, was performed to detect whether abrasive wear of modified epoxies responds differently than fatigue wear to the fracture toughness. Other experiments were performed in which the wear debris produced during sliding was blown out of the interface to study its influence on friction and wear behavior. The effect of surface morphology on friction and wear was also studied. The results indicated that a marked improvement in fracture toughness was achieved for samples with higher elastomer content. Regardless of the type of the experiment, epoxy pin-on-abrasive disk or steel ball-on-epoxy disk, wear rates correlated positively with inverse of fracture toughness. Both friction coefficient and wear rate were found to be influenced by the removal of the wear debris, especially for samples with higher elastomer content. The friction coefficient was reduced for samples with higher elastomer content and this was attributed to the low surface energy of the elastomer. CTBN-modified epoxies exhibited lower friction coefficients than epoxies modified with polysiloxane. It was found that sample morphology had a significant effect on both friction coefficient and wear rate; the sample with approximately the same domain size but the least number of elastomeric domains exhibited the highest friction coefficient and the highest wear rate.
An examination of flow characteristics in collapsing elastic tubes
Davis, Roy Benjamin (Virginia Polytechnic Institute and State University, 1983)
A hydraulic collapse mechanism was incorporated into a recirculating pulsatile flow system to simulate the physiologic problem cf coronary artery vasospasm. A dimensional analysis of the hemodynamic problem provided the basis for i) the specifications for elastic test sections (both straight and branching), ii) the determination of the flow modelling parameters, Reynolds number and unsteady Reynolds number, and iii) the determination of the dimensionless collapse parameters. The models were collapsed in a controlled manner while changes in volumetric flow rate into and out of the models as well as axial pressure drop were monitored. It was found that the driven collapse of the vessel acts as a pump, the effectiveness of which is dependent on upstream and downstream resistance. There was noted a difference in the volumetric flow curves representing fluid leaving the pre- and the post-collapse models under the same inflow conditions. This was due to both the elastic properties of the models and to the post-collapse shape of the models (curved walls and non-circular cross-section). Time-exposed photographs of tracer particle displacements within the model indicate increased volumetric flow in each branch during the initial phase of the collapse process. Moreover, it was seen that the radial gradient of the axial velocity at each wall surface varied in magnitude (and possibly in sign) during the collapse. The in vitro results do not substantiate the coronary spasm/myocardial ischemia connection, but do further implicate vasospasm as a factor in atherogenesis.
Failure processes in unidirectional composite materials
Sundaresan, Mannur J. (Virginia Polytechnic Institute and State University, 1988)
Failure processes in unidirectional composite materials subjected to quasi-static tensile load along the fiber direction are investigated. The emphasis in this investigation is to identify the physical processes taking place during the evolution of failure in these materials. An extensive literature review is conducted and the information relevant to the present topic is summarized. The nature of damage growth in five different commercially available composite systems are studied. In-situ scanning electron microscopy is employed for identifying the failure events taking place at the microscopic level. Acoustic emission monitoring is used for estimating the rate of damage growth on a global scale and determining the size of individual failure events. The results of this study have shown the important roles of the matrix material and the interphase in determining the tensile strength of unidirectional composite materials. Several failure modes occurring at the microscopic scale are revealed for the first time. Further, the results indicate that dynamic fracture participates to a significant extent in determining the failure process in these materials. Based on the results of this study the influence of various parameters in determining the composite strength is described.
Fatigue growth and closure of short cracks
Iyyer, Nagaraja S. (Virginia Polytechnic Institute and State University, 1988)
A study has been carried out to investigate the growth and closure behavior of short cracks in 2024-T351 aluminum alloy and four different conditions of 4340 steel using through thickness cracks of straight fronts. The experiments were carried out to study the influence of stress level, stress ratio, yield strength and prior austenitic grain A sizes in notched and unnotched specimens. The stereoimaging technique was developed and adapted to obtain crack closing and opening points, and also near tip displacement fields. Experimental results are presented with a general discussion. It was found that long cracks showed good correlation when analyzed in terms of effective stress intensity range. However,correlations were poor for short cracks. lt was found that short cracks show less closure behavior than long cracks. The estimates of initial crack lengths based on linear elastic data were made. These estimates differed significantly from the actual initial crack lengths for completely reversed cycling tests. Suggestions have been made to the equivalent initial flaw size approach and conclusions have been drawn.
A finite element analysis of adhesively bonded composite joints including geometric nonlinearity, nonlinear viscoelasticity, moisture diffusion and delayed failure
Roy, Samit (Virginia Polytechnic Institute and State University, 1987)
A two-dimensional finite-element computational procedure is developed for the accurate analysis of the strains and stresses in adhesively bonded joints. The large displacements and rotations experienced by the adherends and the adhesive are taken into account by invoking the updated Lagrangian description of motion. The adhesive layer is modeled using Schapery's nonlinear single integral constitutive law for uniaxial and multiaxial states of stress. Effect of temperature and stress level on the viscoelastic response is taken into account by a nonlinear shift factor definition. Penetrant sorption is accounted for by a nonlinear Fickean diffusion model in which the diffusion coefficient is dependent on the penetrant concentration and the dilatational strain. A delayed failure criterion based on the Reiner-Weisenberg failure theory has also been implemented in the finite element code. The applicability of the proposed models is demonstrated by several numerical examples.
Geometric and material nonlinear analysis of laminated composite plates and shells
Chandrashekhara, K. (Virginia Polytechnic Institute and State University, 1985)
An inelastic material model for laminated composite plates and shells is formulated and incorporated into a finite element model that accounts for both geometric nonlinearity and transverse shear stresses. The elasto-plastic material behavior is incorporated using the flow theory of plasticity. In particular, the modified version of Hill's initial yield criterion is used in which anisotropic parameters of plasticity are introduced with isotropic strain hardening. The shear deformation is accounted for using an extension of the Sanders shell theory and the geometric nonlinearity is considered in the sense of the von Karman strains. A doubly curved isoparametric rectangular element is used to model the shell equations. The layered element approach is adopted for the treatment of plastic behavior through the thickness. A wide range of numerical examples is presented for both static and dynamic analysis to demonstrate the validity and efficiency of the present approach. The results for combined nonlinearity are also presented. The results for isotropic results are in good agreement with those available in the literature. The variety of results presented here based on realistic material properties of more commonly used advanced laminated composite plates and shells should serve as references for future investigations.
Lamb wave propagation in laminated composite plates
Tang, Bruce S. (Virginia Polytechnic Institute and State University, 1988)
Low frequency Lamb waves in composite laminates were investigated theoretically and experimentally. To have a general solution for Lamb wave propagation in multilayered composite laminates is not practical due to a large number of boundary conditions needed to be satisfied at the interlaminar interfaces. Various approximate theories have been proposed to model low frequency Lamb wave propagation in composite laminates. In the present study, an approximate solution was derived from an elementary shear deformation plate theory and was shown to work well in the low frequency, long wavelength region. A simple method, similar in configuration to the acousto-ultrasonic technique, was used to measure Lamb wave phase velocities. Low frequency Lamb waves, usually in the range of 10 kHz to 1 MHz, were generated. Dispersion curves of the lowest symmetric Lamb mode and the lowest antisymmetric Lamb mode were obtained. The experimental data were compared with the results obtained from the approximate solution for the lowest Lamb modes in the low frequency, long wavelength region for a unidirectional laminate, a symmetric cross-ply laminate, a symmetric quasi-isotropic laminate and an aluminum plate. There is good correlation between the data and the results obtained from the approximate solution, which suggests that the lowest Lamb modes are modeled adequately by the present theory in these cases. This experimental procedure of measuring phase velocities can be used to characterize laminated composite plates with and without damage since each material and stacking sequence gives distinct lowest symmetric and antisymmetric curves. Stiffness reduction of composite laminates caused by damage can be related to the change in Lamb wave propagation speed. Damage in the form of transverse cracks in the 90° plies of a [90/90/90/0], graphite/epoxy laminate reduced the phase velocities of the Lamb modes. The lowest antisymmetric mode is sensitive to stiffness reduction in composite plates. Consequently, axial stiffness reduction in [0/45/0/45/0/45], and [0]₁₂ woven graphite/polyimide composite laminates was monitored by the lowest antisymmetric Lamb mode.
Nonlinear optimal control and near-optimal guidance strategies in spacecraft general attitude maneuvers
Lin, Yiing-Yuh (Virginia Polytechnic Institute and State University, 1988)
Solving the optimal open-loop control problems for spacecraft large-angle attitude maneuvers generally requires the use of numerical techniques whose reliability is strongly case dependent. The primary goal of this dissertation is to increase the solution reliability of the associated nonlinear two-point boundary-value problems as derived from Pontryagin’s Principle. Major emphasis is placed upon the formulation of the best possible starting or nominal solution. Constraint relationships among the state and costate variables are utilized. A hybrid approach which begins with the direct gradient method and ends with the indirect method of particular solutions is proposed. Test case results which indicate improved reliability are presented. The nonlinear optimal control law derived from iterative procedures cannot adjust itself in accordance with state deviations measured during the control period. A real-time near-optimal guidance scheme which takes the perturbed states to the desired manifold by tracking a given optimal trajectory is also proposed. Numerical simulations are presented which show that highly accurate tracking results can be achieved.
Prediction model for the onset of edge-effect delamination at holes in composite laminates
Shalev, Doron (Virginia Polytechnic Institute and State University, 1988)
Composite laminates are prone to delamination at free edges, straight edges or at holes, due to the mismatch at interfaces where two adjacent plies have different fiber orientations and/or different material properties. The linear analysis of the mismatch at the edge results in a mathematical singularity. That phenomenon occurs in a boundary layer and has to be treated mathematically and physically as such. In the literature it is called the "Boundary Layer Effect" or simply the "Edge Effect". It is of great importance to recognize and be able to predict delamination locations at edges prone to such events. The goal of this research was to create a model capable of providing such a prediction. In an effort to generalize the model, the more complicated case of a free edge at holes in the composite laminate was chosen rather than the case of a straight free edge. A sequel of three major efforts was completed: 1) Development of the analysis of the free-edge effect at a hole in a composite laminate, 2) Performance of an extensive experimental program to provide data for the creation of the prediction model, and 3) On the basis of the analysis, establishment of the model, and comparison with the experimental results. The prediction model consists of two major products of the analysis, the order of the singularity and the strain energy release rate. Both are useful in locating the interface most prone to delaminate and the point along the hole circumference where it initiates. Two material systems (AS4/3501-6 and AS4/1808) and two stacking sequences [(0/45/0/-45)_s)₄] and [ (0/45/90/-45)_s)₄]s , quasi-orthotropic and quasi-isotropic respectively, were quasi-statically tested under tension and compression. The specimens were X-rayed after each loading stage in order to locate the initiation of delaminations. The fact that both materials consisted of the same type of fibers, was an excellent opportunity to examine the performance of the matrix and its influence on the process of delamination. Matrix dependent behavior was successfully examined and studied through the experiments and the prediction model. Results showed good correlation and high sensitivity to the type of matrix material involved.
Probabilistic service life prediction of composite viscoelastic cylindrical structure under random outdoor environment
Thangjitham, Surot (Virginia Polytechnic Institute and State University, 1984)
This study developed a general methodology for probabilistic service life prediction of a composite viscoelastic cylindrical structure under random outdoor environment. The analysis emphasized both the statistical variations of environmental thermal loads and of material properties. The daily probability of failure was calculated considering failures due to both the excessive stress and strain. The probabilistic service life was then obtained via the evaluation of cumulative hazard function. Models for the deterministic and random variations of environmental thermal loads- ambient temperature, sky radiation, wind convection, and solar radiation, were developed and were considered in obtaining the structure's surface temperature. The statistical characteristics such as the mean and variance of the induced stresses and-strains were calculated via the uses of complex frequency response functions. Methods for statistical characterization of time and temperature dependent viscoelastic material properties were presented. Five statistical distributions- Normal, Log-Normal, Beta, Gamma, and Weibull, were considered for the goodness of fit. Two forms of material deterioration- time and temperature dependent aging and cumulative damage due to loading were also recognized. Three statistical distributions- Normal, Log-Normal, and Weibull, were used to represent the variations of induced daily maximum stress and strain. The daily probabilities of failure due to the maximum stress and strain were calculated based on the concept of load and resistance interference. The effects of these failure modes were then combined to define daily probability of failure of the structure.
The residual strength determination due to fatigue loading by fracture mechanics in notched composite materials
Jen, Ming-Hwa Robert (Virginia Polytechnic Institute and State University, 1985)
The objective of this investigation is to predict the residual strength of notched composite Iaminates with various layups, subjected to low frequency fatigue loading with constant amplitude at room temperature, by using a material modeling approach, fracture and fatigue mechanics and the finite element method (FEM). For simplicity, after thousands of cycles, the geometry of a circular hole of the deformed laminate was categorized as (1) uniformly expanded hole into elliptic shape, (2) crack propagation around the hole transversely. Both types were studied for 12 cases of layups with various proportions of 0, 45, -45 and 90 degree plies. The effect of geometry change during fatigue on residual strength was attributed to the elliptical hole, longitudinal splitting, matrix cracking (reduction moduli of plies), crack propagation and local delamination. Due to the thin through-the-thickness notched laminate, two-dimensional FEM was used and interlaminar stresses were not considered. Reduction of stress concentration is a reason for the increase of the residual strength of the notched laminate. The stress concentration factor decreases while the elliptic hole becomes more slender; that was examined by the FEM. The residual strength and stiffness were determined by the material modeling with moduli reduction and damaged zone, and the numerical result was obtained by FEM. Laminate theory, point stress criterion, polynomial failure criterion, ply discount method, and fatigue and fracture mechanics (Paris' Power Law) were also included in this research. Geometry change and moduli reduction are two major effects that are considered to predict the notched strength. The WN point stress fracture model is adopted for simplicity, instead of the average stress criterion. K_tg that corresponds to the unnotched strength in the normalized stress base curve is used to obtain the characteristic length (d_o). We find that K_tg decreases when the elliptic hole becomes more slender and more moduli are reduced (more plies crack). At the time d_o that is determined from K_tg in the base curve is not necessarily a fixed material constant. The correlation between the fatigue life and the residual strength as predicted by the model and those determined numerically is found within acceptable errors in comparison with the experimental data.
Scaling effect in cone penetration testing in sand
Eid, Walid Khaled (Virginia Polytechnic Institute and State University, 1987)
The Cone Penetration Test (CPT) was developed originally in Holland in the 1930’s as a device which provides a small scale model of a pile foundation. Early versions were simple cone points for which the only measurement was the thrust required to push the point through the ground. Over the past 20 years, the cone was standardized to a tip area of 10 cm², and an electrical version was produced, which allows for continuous measurement of the cone tip resistance and sleeve friction along with a computer-based data acquisition system. The electrical cone represents a significant step forward for the CPT, since it provides a continuous profile of information that can be used to identify soil type and define important engineering parameters. More recently, the CPT has shown considerable potential for calculation of settlements of footings on sand, determination of pile capacity, assessment of ground pressures, and evaluation of liquefaction potential for cohesionless soils. Along with the widening application of the CPT, new varieties of cone penetrometers have appeared, with different sizes than the standard. Smaller cones are used for instances where relatively small depths of soil need to be penetrated, and larger cones have been developed for penetrating dense and gravelly soils. With the introduction of the new cones, there has been a tendency to assume that the methods for reducing CPT data for the standard sized cone can be extrapolated to the other sizes of cones. That is, it is assumed that there are no scale effects in cones of different sizes. While this may be true, to date, little direct evidence has been produced to support this view, and the issue is an important one from two points of view: 1. The present data analysis technology is based on that primarily from testing with a standard cone. lt is important to know if any changes are needed in this approach, or if the existing methods can be used with confidence for any size cone. 2. If it can be shown that no scale factor exists, then this will allow the use of new, smaller cones in experimentation in modem calibration chambers with the knowledge that the test results are applicable for the cones that a.re more widely used in practice. The smaller cones offer several advantages in this type of work in that they facilitate the research considerably by reducing the effort involved in sample preparation, and they are less likely to produce results influenced by boundary conditions in the chamber. One of the major objectives of this research is to develop an insight into the issue of the scale factor caused by the use of different sizes of cones. This is accomplished through an experimental program conducted in a new large scale calibration chamber recently constructed at Virginia Tech. Many of the latest developments in cone penetration testing have been forthcoming from testing done in calibration chambers where a soil mass can be placed to a controlled density under known stress conditions. To conduct the experimentation of this work, it was necessary to design, fabricate, and bring to an operational stage a calibration chamber. The Virginia Tech chamber is one of the largest in the world. A significant portion of the effort involved in this thesis research was devoted to this task. In particular, attention was devoted to the development of a system for placement of a homogeneous soil mass in the chamber, and the implementation of a microcomputer-based data acquisition unit to record and process the test results. The scale effects investigation was performed using three different sizes of cone penetrometers in a test program conducted in the calibration chamber. Of the three cones, one is smaller than the standard with a tip area of 4.23 cm², one was a standard cone with a tip area of 10 cm², and one was larger than the standard cone with a tip area of 15 cm². A total of 47 tests were carried in the chamber using two different levels of confining stress and two different sand densities. The test results show that while a scale factor might exist, the degree of its influence on interpreted soil parameters for a practical problem does not appear significant.

Browsing by Author "Smith, C.W."

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