bluuebunny/crossref_metadata_2025 huggingface dataset:
Sliding Mode Control of Gas Turbines Using Multirate-Output Feedback
Authors: Panda Subrat , Bandyopadhyay Bijnan
Published: April 2008

The advent of electronic controllers in the field of gas turbine control has allowed the implementation of sophisticated control algorithms. The design of a control system requires accurate models of the plant to be controlled. A real-time program for the dynamic simulation of a gas turbine engine has been developed. Most of the control design techniques need the linear representation of a plant at various operating points. In this regard, the linear analysis tool box of MATLAB-SIMULINK (Anon., 2004, SIMULINK: User’s Guide, The Math Works, Inc.) has been used to obtain linear models at various operating points. The linear models are discretized at various sampling times. The algorithm for discrete sliding mode control using the output samples has been reviewed and the same has been used to develop a controller for the gas turbine engine. A fast output sampling sliding mode controller is synthesized using a linear model of the engine. The controller developed is implemented in the nonlinear model and simulation with external disturbance is carried out. The responses with and without the controller are compared. It is shown that discrete sliding mode control law can be directly obtained in terms of the output samples and immediate past control function. The control law thus obtained is of practical importance. The algorithm needs the states of the system neither for feedback purpose nor for switching function evaluation. Thus, it is easily implemented in practice. The algorithm is computationally simple and easy to implement on a gas turbine.
In-Cylinder Pressure Measurement: Requirements for On-Board Engine Control
Authors: Ponti Fabrizio
Published: April 2008

During these last years, passenger vehicles have been equipped with an increasing number of sensors, in an effort to monitor and control their behavior in terms of global performance and emissions. This, together with constantly increasing electronic control unit computing power and data storage capabilities, allowed the development of more efficient engine-vehicle control strategies. In this perspective, new sensors will be employed as soon as their use will be shown to be necessary to design new engine control and diagnostic strategies, and their cost and expected life will be compatible with on-board application. A sensor that has been largely studied in recent years is the in-cylinder pressure one: advanced engine control strategies that make use of the signal coming from such a sensor have been investigated, while reliable and low-cost sensors are being developed to survive for the vehicle life the harsh on-board environment. The signal coming from the in-cylinder pressure is, in fact, very rich in information and could be used, for example, to improve engine torque management (by directly computing the instantaneous indicated torque), to improve air∕fuel ratio control, misfire and knock detection capabilities, engine emission estimation (to be used for DeNOx catalysts purging management as an example), residual gas fraction estimation, etc. Many sensor concepts have been developed, although none seems to actually fully meet both the precision and low-cost requirements necessary for on-board application. This work deals with defining the sensor precision characteristics necessary to effectively implement the aforementioned engine control and diagnostic capabilities improvements. In particular, it will be shown that only the low-frequency signal content has to be precisely measured and is critical for certain application. In addition, the importance of a correct reference of the in-cylinder pressure signal is discussed, and a novel methodology to quickly obtain this information once the engine has been setup with a proper in-cylinder pressure sensor is discussed.
The Application of System CFD to the Design and Optimization of High-Temperature Gas-Cooled Nuclear Power Plants
Authors: Greyvenstein Gideon P.
Published: April 2008

The objective of this paper is to model the steady-state and dynamic operation of a pebble-bed-type high temperature gas-cooled reactor power plant using a system computational fluid dynamics (CFD) approach. System CFD codes are 1D network codes with embedded 2D or even 3D discretized component models that provide a good balance between accuracy and speed. In the method presented in this paper, valves, orifices, compressors, and turbines are modeled as lumped or 0D components, whereas pipes and heat exchangers are modeled as 1D discretized components. The reactor is modeled as 2D discretized system. A point kinetics neutronic model will predict the heat release in the reactor. Firstly, the layout of the power conversion system is discussed together with the major plant parameters. This is followed by a high level description of the system CFD approach together with a description of the various component models. The code is used to model the steady-state operation of the system. The results are verified by comparing them with detailed cycle analysis calculations performed with another code. The model is then used to predict the net power delivered to the shaft over a wide range of speeds from zero to full speed. This information is used to specify parameters for a proportional-integral-derivative controller that senses the speed of the power turbine and adjusts the generator power during the startup of the plant. The generator initially acts as a motor that drives the shaft and then changes over to a generator load that approaches the design point value as the speed of the shaft approaches the design speed. A full startup simulation is done to demonstrate the behavior of the plant during startup. This example demonstrates the application of a system CFD code to test control strategies. A load rejection example is considered where the generator load is suddenly dropped to zero from a full load condition. A controller senses the speed of the low pressure compressor/low pressure turbine shaft and then adjusts the opening of a bypass valve to keep the speed of the shaft constant at 60rps. The example demonstrates how detailed information on critical parameters such as turbine and reactor inlet temperatures, maximum fuel temperature, and compressor surge margin can be obtained during operating transients. System CFD codes is a powerful design tool that is indispensable in the design of complex power systems such as gas-cooled nuclear power plants.
Flame Extinction Limits of H2‐CO Fuel Blends
Authors: Choudhuri Ahsan R. , Subramanya Mahesh , Gollahalli Subramanyam R.
Published: April 2008

The flame extinction limits of syngas (H2‐CO) flames were measured using a twin-flame counterflow burner. Plots of extinction limits (%f: volumetric percent of fuel in air) versus global stretch rates were generated at different fuel blend compositions and were extrapolated to determine the flame extinction limit corresponding to an experimentally unattainable zero-stretch condition. The zero-stretch extinction limit of H2‐CO mixtures decreases with the increase in H2 concentration in the mixture. The average difference between the measured flame extinction limit and the Le Chatelier’s calculation is around 7% of the mean value. The measured OH chemiluminescence data indicates that regardless of blend composition the OH radical concentration reduces to a critical value prior to the flame extinction. The measured laminar flame velocity close to the extinction indicates that regardless of fuel composition, the premixed flame of hydrogen fuel blends extinguishes when the mixture laminar flame velocity falls below a critical value.
Nonlinear Dynamic Characterization of Oil-Free Wire Mesh Dampers
Authors: Ertas Bugra H. , Luo Huageng
Published: April 2008

The present work focuses on the dynamic characterization of oil-free wire mesh dampers. The research was aimed at determining nonlinear stiffness and damping coefficients while varying the excitation amplitude, excitation frequency, and static eccentricity. Force coefficients were extracted using a forced response method and also a transient vibration method. Due to the nonlinearity of the dampers, controlled amplitude single frequency excitation tests were required for the forced excitation method, whereas the transient response was analyzed using a Hilbert transform procedure. The experimental results showed that eccentricity has minimal influence on force coefficients, whereas increasing excitation amplitude and frequency yields decreasing stiffness and damping trends. In addition to the parameter identification tests, a rotating test was performed demonstrating high-speed damping capability of the oil-free wire mesh dampers to 40,000 rpm, which was also simulated using a nonlinear rotordynamic response to imbalance analysis.
Low NOx Advanced Vortex Combustor
Authors: Edmonds Ryan G. , Williams Joseph T. , Steele Robert C. , Straub Douglas L. , Casleton Kent H. , Bining Avtar
Published: April 2008

A lean-premixed advanced vortex combustor (AVC) has been developed and tested. The natural gas fueled AVC was tested at the U.S. Department of Energy’s National Energy Technology Laboratory in Morgantown, WV. All testing was performed at elevated pressures and inlet temperatures and at lean fuel-air ratios representative of industrial gas turbines. The improved AVC design exhibited simultaneous NOx∕CO∕unburned hydrocarbon (UHC) emissions of 4∕4∕0ppmv (all emissions corrected to 15% O2 dry). The design also achieved less than 3ppmvNOx with combustion efficiencies in excess of 99.5%. The design demonstrated marked acoustic dynamic stability over a wide range of operating conditions, which potentially makes this approach significantly more attractive than other lean-premixed combustion approaches. In addition, the measured 1.75% pressure drop is significantly lower than conventional gas turbine combustors, which could translate into an overall gas turbine cycle efficiency improvement. The relatively high velocities and low pressure drop achievable with this technology make the AVC approach an attractive alternative for syngas fuel applications.
Dynamic Mixed Mode I-II Crack Kinking Under Oblique Stress Wave Loading in Brittle Solids
Authors: Ma Chien-Ching
Published: April 2008

The dynamic stress intensity factors of an initially stationary semi-infinite crack in an unbounded linear elastic solid which kinks at some time tf after the arrival of a stress wave is obtained as a function of kinking crack tip velocity v, kinking angle δ, incident stress wave angle α, time t, and the delay time tf. A perturbation method, using the kinking angle δ as the perturbation parameter, is used. The method relies on solving simple problems which can be used with linear superposition to solve the problem of a kinked crack. The solutions can be compared with numerical results and other approximate results for the case of tf = 0 and give excellent agreement for a large range of kinking angles. The elastodynamic stress intensity factors of the kinking crack tip are used to compute the corresponding fluxes of energy into the propagating crack-tip, and these results are discussed in terms of an assumed fracture criterion.
Residual Stress Determination Using Acoustoelasticity
Authors: Dike J. J. , Johnson G. C.
Published: April 2008

A technique for the complete nondestructive evaluation of plane states of residual stress is presented. This technique is based on the acoustoelastic effect in which the presence of the residual stress causes a shift in the speed at which a wave propagates through the material. The particular acoustoelastic technique considered here employs longitudinal waves propagating normal to the plane of the stress. Such waves experience a shift in propagation speed which, for an isotropic material, is proportional to the sum of the principal stresses. A Poisson’s equation for the in-plane shear stress is obtained from the two-dimensional equilibrium equations in which the forcing function is obtained directly from the measured velocity variations. Once this equation is integrated for the shear stress, the normal stresses may be evaluated directly from the equilibrium equations. In this paper, the basic equations are derived for the case of an anisotropic material. The experimental and numerical procedures are reviewed, and results of residual stresses in an aluminum ring are presented.
Elementary, Static Beam Theory is as Accurate as You Please
Authors: Duva J. M. , Simmonds J. G.
Published: April 2008

Starting with a solution of elementary beam theory and integrating polynomials in the thickness coordinate, we generate kinematically-admissible strain fields and statically-admissible strain fields whose average approximates the actual two-dimensional strain field in an orthotropic beam to within a relative mean square error of the order of magnitude of an arbitrary power of the ratio of the thickness of the beam to a characteristic wavelength of the elementary beam solution.
A Mechanical Model for Elastic Fiber Microbuckling
Authors: Waas A. M. , Babcock C. D. , Knauss W. G.
Published: April 2008

A two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite half-plane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the interior of the half-plane. It is demonstrated that for composites of low volume fraction (<0.3), this decay mode furnishes values of buckling strain that are below the values predicted by the Rosen (1965) model. At a higher volume fraction the buckling mode corresponds to a half wavelength that is in violation of the usual assumptions of beam theory. Causes for deviations of the model prediction from existing experimental results are discussed.
Polynomial Chaos in Stochastic Finite Elements
Authors: Ghanem Roger , Spanos P. D.
Published: April 2008

A new method for the solution of problems involving material variability is proposed. The material property is modeled as a stochastic process. The method makes use of a convergent orthogonal expansion of the process. The solution process is viewed as an element in the Hilbert space of random functions, in which a sequence of projection operators is identified as the polynomial chaos of consecutive orders. Thus, the solution process is represented by its projections onto the spaces spanned by these polynomials. The proposed method involves a mathematical formulation which is a natural extension of the deterministic finite element concept to the space of random functions. A beam problem and a plate problem are investigated using the new method. The corresponding results are found in good agreement with those obtained through a Monte-Carlo simulation solution of the problems.
Dynamics of the Elastica With End Mass and Follower Loading
Authors: Snyder J. M. , Wilson J. F.
Published: April 2008

Orthotropic, polymeric tubes subjected to internal pressure may undergo large deformations while maintaining linear moment-curvature behavior. Such tubes are modeled herein as inertialess, elastic cantilever beams (the elastica) with a payload mass at the tip and with internal pressure as the eccentric tip follower loading that drives the configurations through large deformations. From the nonlinear equations of motion, dynamic beam trajectories are calculated over a range of system parameters for the special case of a point mass at the tip and a terminated ramp pressure loading. The dynamic responses, which are unique because the loading history and the range of motion are fully defined, are presented in nondimensional form and are compared to static responses presented in a companion study. These results are applicable to the dynamic design of high flexure, tube-type, robotic manipulator arms.
The Self-Noise From Ordered Structures in a Low Mach Number Jet
Authors: Mankbadi R. R.
Published: April 2008

This article is concerned with examining the self-noise produced by instability waves in a round jet. The self-noise is defined here as the noise attributed to the nonlinear sources in Lighthill’s stress tensor. The calculated self-noise is found to be proportional to the fourth order of the velocity amplitude saturation. The self-interaction of the instability waves results in a “super-directivity.” The dependency of the sound intensity on the Strauhal number and on the Mach number is in accordance with observations.
Stress Distribution in Plane Scarf and Butt Joints
Authors: Chen Du , Cheng Shun
Published: April 2008

The stress distribution in a plane scarf joint, which may have an arbitrary angle of scarf as well as arbitrary elastic parameters for its adherends and adhesive, is analyzed. The analysis is based on the two-dimensional elasticity theory in conjunction with the variational principle of complementary energy. Minimizing the energy functional leads to a specific optimization problem with two variables for the determination of the stresses. Some typical features of the stress distribution are shown by numerical examples. Criteria for uniformly distributed adhesive stresses which are of importance in practice are deduced. The butt joint is treated as a special case of scarf joints.
Viscoplastic Constitutive Modeling of High Strain-Rate Deformation, Material Damage, and Spall Fracture
Authors: Nemes J. A. , Eftis J. , Randles P. W.
Published: April 2008

The Perzyna viscoplastic constitutive theory, which contains a scalar variable for description of material damage, is used to study material behavior at high strain rates. The damage parameter for materials which undergo ductile fracture by nucleation, growth, and coalescence of microvoids, is taken to be the void volume fraction. The linear hardening law in both the constitutive equation and the derivation of the void growth rate equation has been replaced by a nonlinear hardening law that allows for the saturation of the hardening with increase of strain. The modified constitutive equations are then specialized to uniaxial deformation with multiaxial stress, which is typical of that occurring in flyer plate impact experiments. Calculations are performed showing the rate dependence of the material response and the effects of the growth of the void volume (damage). The change in the predicted response due to the modification of the hardening law is illustrated. Ductile spall fracture is modeled by considering the response to a simulated compressive-tensile wave using a critical value of the void volume as the local criteria for fracture.
A Rudimentary Analysis of Improving Fatigue Life of Metals by Shot-Peening
Authors: Al-Obaid Y. F.
Published: April 2008

In this paper, a rudimentary analysis of improving fatigue life of metals is presented. The process is viewed as one of repeated impact of a stream of hard shots on to a target. The model considers first a single shot impinging upon a target and, on bouncing, it leaves a residual stress below the surface of the target. The problem is then generalized to consider the effect of a stream of shots by assuming their effect to be uniformly distributed over the entire surface. The analysis is highly simplified and it mainly aims at understanding the mechanics of this complicated process. Although rudimentary, the theoretical analysis is seen to be in reasonable agreement with experimental results performed with shots on targets of various materials.
A Method for Identifying Parameters of Mechanical Joints
Authors: Wang J. , Sas P.
Published: April 2008

A method for identifying the physical parameters of joints in mechanical systems is presented. In the method, a multi-d.o.f. (degree-of-freedom) system is transformed into several single d.o.f. systems using selected eigenvectors. With the result from modal testing, each single d.o.f. system is used to solve for a pair of unknown physical parameters. For complicated cases where the exact eigenvector cannot be obtained, it will be proven that a particular physical parameter has a stationary value in the neighborhood of an eigenvector. Therefore, a good approximation for a joint physical parameter can be obtained by using an approximate eigenvector and the exact value for the joint parameters can be reached by carrying out this process in an iterative way.
Cross-Approximation Method for Solving Dynamics Problems of Arbitrarily Shaped Plates
Authors: Poltorak K.
Published: April 2008

This paper deals with a new method for solving dynamics problems of arbitrarily shaped plates. The method consists in cross approximation of functions satisfying solely an equation of motion and functions satisfying solely boundary conditions on irregular plate edges. This approach is applied in the paper to the case of free and forced vibration of homogeneous and sandwich plates with edges of various shapes. Functions satisfying boundary conditions are determined by the Rvachev’s R-function method. The validity of the method is discussed.
Hypersingular Boundary Integral Equations: Some Applications in Acoustic and Elastic Wave Scattering
Authors: Krishnasamy G. , Schmerr L. W. , Rudolphi T. J. , Rizzo F. J.
Published: April 2008

The properties of hypersingular integrals, which arise when the gradient of conventional boundary integrals is taken, are discussed. Interpretation in terms of Hadamard finite-part integrals, even for integrals in three dimensions, is given, and this concept is compared with the Cauchy Principal Value, which, by itself, is insufficient to render meaning to the hypersingular integrals. It is shown that the finite-part integrals may be avoided, if desired, by conversion to regular line and surface integrals through a novel use of Stokes’ theorem. Motivation for this work is given in the context of scattering of time-harmonic waves by cracks. Static crack analysis of linear elastic fracture mechanics is included as an important special case in the zero-frequency limit. A numerical example is given for the problem of acoustic scattering by a rigid screen in three spatial dimensions.
Analysis of Surface Wave Generation by Laser Interference
Authors: Faran K. J. , Miller R. J. Dwayne , Gracewski S. M.
Published: April 2008

An analytical solution for thermal excitation of elastic waves in an homogeneous, isotropic, elastic half-space resulting from a pulsed laser interference pattern incident on the solid surface is presented. The spacially-periodic laser field absorbed by the surface causes rapid heating within the optical penetration depth. Thus, a temperature field is generated which can be modeled as being spacially harmonic along the free edge, decaying exponentially with depth, and having a Heaviside dependence on time. Transform techniques yield expressions for the resulting transverse and normal displacements within the laser interference region in terms of infinite integrals over frequency. The integrands contain poles indicating the expected Rayleigh waves propagating along the surface, as well as branch points corresponding to the bulk longitudinal and transverse wave speeds. The solution is obtained by integrating numerically in the complex frequency plane with an appropriate contour around the poles and branch cuts. Normal and transverse displacements are plotted as functions of time and depth for various materials and temperature fields.
Nonlinear Finite Deformation Response of Open Cell Polyurethane Sponge to Fluid Filtration
Authors: Lanir Y. , Sauob S. , Maretsky P.
Published: April 2008

The nonlinear finite deformation response of open cell polyurethane sponge to fluid filtration was studied, both experimentally and theoretically. The equilibrium uniaxial strain distribution along a sponge cylinder was optically measured while it was supported on its downstream surface by a rigid filter and loaded by fluid pressure of various levels. The strain along the cylinder was found to be highly nonuniform and of sigmoidal pattern—flat near both ends and steep in the middle. The theoretical investigation considers the fluid-filled sponge as an incompressible solid-fluid mixture. The response of the sponge to uniaxial filtration was analyzed in terms of its constitutive properties which were determined experimentally. The model’s predictions show good agreement to the measured strain distribution.
Axisymmetric Upheaval Buckling of a Heavy Sheet
Authors: Hobbs R. E.
Published: April 2008

A large elastic sheet with a significant self-weight subject to biaxial in-plane compression while lying on a rigid horizontal plane may buckle. The buckles, circular areas which lift away from the rigid subgrade, are essentially a plate phenomenon, an axisymmetric analogue to the widely discussed upheaval buckling of beams. It is found that plate upheaval is relatively insensitive to subgrade friction, a fact which may simplify design against such buckling.
Equilibrium Configurations of Cantilever Beams Subjected to Inclined End Loads
Authors: Navaee S. , Elling R. E.
Published: April 2008

In this study, equilibrium configurations of a cantilever beam subjected to an end load with constant angle of inclination is investigated. It is shown analytically that if the beam is sufficiently flexible, there are multiple equilibrium solutions for a specific beam and loading condition. A method is also presented for the determination of these deflected configurations. The cantilever beam studied in this research is considered to be initially straight and prismatic in addition to being homogeneous, elastic, and isotropic. The procedure outlined in this paper is utilized to show that for each combination of load and beam parameters, there are certain number of equilibrium configurations for a cantilever beam. The ranges of these combinations, along with some examples of the deflected shapes of the beams, are provided for several load inclination angles.
Initial Development of Microdamage Under Impact Loading
Authors: Bai Yilong , Ling Zhong , Luo Limin , Ke Fujiu
Published: April 2008

In this paper, the initial development of microdamage in material subjected to impulsive loading was investigated experimentally and analytically with controllable short-load duration. Based on a general solution to the statistical evolution of a one-dimensional system of ideal microcracks, a prerequisite to experimental investigation of nucleation of microcracks was derived. By counting the number of microcracks, the distribution of nucleation of microcracks was studied. The law of the nucleation rate of microcracks can be expressed as a separable function of stress and cracksize. It is roughly linear dependence on loading stress. The normalized number density of microcracks is in agreement with that of a second-phase particle.
Auto and Cross-Bispectral Analysis of a System of Two Coupled Oscillators With Quadratic Nonlinearities Possessing Chaotic Motion
Authors: Pezeshki Charles , Elgar Steve , Krishna R. , Burton T. D.
Published: April 2008

Auto and cross-bispectral analyses of a two-degree-of-freedom system with quadratic nonlinearities having two-to-one internal (autoparametric) resonance are presented. Following the work of Nayfeh (1987), the method of multiple scales is used to obtain a first-order uniform expansion yielding four first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases of the two modes. The particular case of parametric resonance of the first mode considered in this paper admits Hopf bifurcations and a pure period doubling route to chaos. Auto bicoherence spectra isolate the phase coupling between increasing numbers of triads of Fourier components for a pure period doubling route to chaos for the individual degrees-of freedom. Cross-bicoherence spectra, on the other hand, yield information about the phase coupling between the two degrees-of-freedom. The results presented here confirm the capacity of bispectral techniques to identify a quadratically nonlinear mechanical system that possesses chaotic motions. For the chaotic case, cross-bicoherence spectra indicate that most of the nonlinear energy transfer between the modes is owing to cross-coupling between phase modulations rather than between amplitude modulations.
Nonuniqueness in Elastoplastic Frames
Authors: Alwis W. A. M.
Published: April 2008

Lack of uniqueness of the kinematic solution of elastoplastic flexural frames is studied by deriving a general solution for nonholonomic behavior. A singular hinge set is defined as a collection of plastic hinges that would form a mechanism if they were replaced by mechanical hinges. It is shown that whenever singular subsets can be found among active plastic hinges, the kinematic solution may become nonunique. The rate of work done by the load rates on the contributing mechanisms must be zero if a prevailing nonuniqueness is to sustain.
Viscoelastic Damping Calculations Using a p-Type Finite Element Code
Authors: Wilson C. J. , Carnevali P. , Morris R. B. , Tsuji Y.
Published: April 2008

Damping factors of viscoelastically damped structures can be calculated using the modal strain energy method, implemented with a sequence of undamped modal analysis computations. There are significant advantages in performing these calculations using p-type finite element codes. These include ease of mesh design, an indicator of degree of solution convergence, modest computation time, and an insensitivity to element aspect ratio. Capitalizing on these advantages an algorithm is defined, which is effective in solving for the natural frequencies and modal loss factors of damped structures. The algorithm is demonstrated using a sandwiched cantilevered beam as an example.
Alternative Formulation of Elastic Fields due to Inhomogeneous Isotropic Spherical Inclusions Undergoing Shape-Conserving Volume Change
Authors: Schmauder S. , Mader W.
Published: April 2008

In this Note alternative formulae are derived for the elastic fields due to homogeneous initial strains in an isotropic spherical inclusion embedded in an isotropic infinite medium, assuming a shape conserving volume change of the inclusion. The bulk modulus of the inclusion and the shear modulus of the matrix are the only physically relevant elastic constants necessary to describe analytically displacements, strains, and stresses in the inclusion and the matrix.
Finite Element Analysis of Multiphase Viscoelastic Solids
Authors: Brinson L. C. , Knauss W. G.
Published: April 2008

The properties of composite solids containing multiple, viscoelastic phases are studied numerically. The dynamic correspondence principle of viscoelasticity is utilized in a finite element model to solve boundary value problems for obtaining global complex moduli of the composite. This numerical procedure accounts for the coupled interactive deformation of the phases and thus the resultant accuracy is limited only by that of finite element analyses in general. The example composite considered in this study contains cylindrical viscoelastic inclusions embedded in a viscoelastic matrix. This investigation focuses on the global composite moduli and their relationship to the individual phase properties as a function of volume fraction. A given phase material is shown to have differing effects on the composite properties, depending on whether it is the continuous or the included phase: In general, the composite moduli are dominated by the matrix material. Comparison is made with two simple analytical models for global effective moduli of composites. “Upper Bounds” reproduce the behavior over the whole frequency range when the matrix is the “stiffer” of the two solids while the “lower bond” associates with the converse arrangement, also over the whole frequency range. The nature of time-temperature behavior of multiphase composite materials is examined in a companion paper.
Axial Decay of Self-Equilibrating End Loads in Compressible Solids
Authors: Durban David , Karp Boris
Published: April 2008

The axial diffusion rate of self-equilibrating surface loads is investigated for axially prestretched solids under plane-strain conditions. The perturbed field within the body, induced by an instantaneous end disturbance, is examined by using the eigenfunction spectral analysis. A general solution is given for a wide range of compressible materials. Particular examples are presented for a few hyperelastic solids. Very slow rate of decay, of the first antisymmetric eigencomponent, has been found near the stress-free configuration. Also, there is almost no decay of the first symmetric eigencomponent near the ultimate tension load. The diffusion length is greater for less compressible solids. Axial decay is exponential and depends quite strongly on material moduli and prestrain.
Spectral Decomposition of the Elasticity Tensor
Authors: Sutcliffe S.
Published: April 2008

The elasticity tensor in anisotropic elasticity can be regarded as a symmetric linear transformation on the nine-dimensional space of second-order tensors. This allows the elasticity tensor to be expressed in terms of its spectral decomposition. The structures of the spectral decompositions are determined by the sets of invariant subspaces that are consistent with material symmetry. Eigenvalues always depend on the values of the elastic constants, but the eigenvectors are, in part, independent of these values. The structures of the spectral decompositions are presented for the classical symmetry groups of crystallography, and numerical results are presented for representative materials in each group. Spectral forms for the equilibrium equations, the acoustic tensor, and the stored energy function are also derived.
Interface Blunting of Matrix Cracks in Fiber-Reinforced Ceramics
Authors: Dollar Anna , Steif Paul S.
Published: April 2008

A crack impinging upon an interface that can debond and then offer frictional resistance is studied theoretically. The central question at issue is the level of the remote load at which the crack penetrates the interface, whether or not some debonding of the interface occurs first. To answer this question, we compute the stress enhancement experienced by the impinged material—averaged over a microstructural length such as the fiber diameter—as a function of interface parameters. The solution to this elasticity problem is arrived at by means of distributed dislocations to represent relative motion at the interface. Special care needs to be taken to account properly for the contact problem at the interface. Not unexpectedly, it is found that higher debond energies and greater frictional resistances lead to higher stress concentrations and, hence, to lower remote failure loads.
Transient Analysis of a Semi-infinite Crack Subjected to Dynamic Concentrated Forces
Authors: Tsai Chwan-Huei , Ma Chien-Ching
Published: April 2008

An exact transient closed-form solution for a semi-infinite crack subjected to a timedependent concentrated force is obtained in this study. The total wave field is due to the effect of this point source and the scattering of the incident waves by the crack tip. An alternative methodology for constructing the reflected and diffracted field is proposed, which proves both powerful and efficient in solving complicated dynamic crack problems. An exponentially distributed loading at the crack surfaces in the Laplace transform domain is used as the fundamental problem. The waves reflected by the traction-free crack surface and diffracted from the crack tip can be constructed by superimposing this fundamental solution. The superposition is performed in the Laplace transform domain. Numerical results for the time history of stresses and stress intensity factors during the transient process are obtained and compared with the corresponding static values. It is shown that the field solution will approach the static value after the last diffracted wave has passed.
Variational Principles for Hydraulic Fracturing
Authors: Advani S. H. , Lee T. S. , Dean R. H.
Published: April 2008

A new application of an energy rate variational principle for hydraulic fracturing processes is introduced. The formation structural, fracture mechanics, and fracture fluid flow responses are integrally coupled in this treatment. This unified principle, with various specialized forms, provides a formal framework for the study of continuum as well as discrete models. The applicability of the developed formulations is demonstrated by deriving time-explicit solutions for a penny-shaped model and comparing numerical results with corresponding responses from Lagrangian and finite element methods.
An Inverse Formulation With Boundary Elements
Authors: Zeng Xiaogang , Saigal Sunil
Published: April 2008

A mathematical formulation for the solution of inverse problems pertaining to the identification of flaw shapes and the reconstruction of boundary conditions in a continua is described. Integral relationships are derived for the variation of field variables with respect to variation in flaw shape using Taylor series expansions. Similar relationships for the variation of boundary conditions with variation inflow shape are also obtained. These variations allow the development of an iterative framework to advance an initially assumed flaw shape towards its actual configuration. The iterations are based upon and are driven by the difference in the values of computed response for the assumed flaw shape from their experimentally measured values at specified locations. The resulting equations are cast into the matrix form for solution using the boundary element method.
Three-Dimensional Solutions for the Thermal Buckling and Sensitivity Derivatives of Temperature-Sensitive Multilayered Angle-Ply Plates
Authors: Noor A. K. , Burton W. Scott
Published: April 2008

Analytic three-dimensional thermoelasticity solutions are presented for the thermal buckling of muitilayered angle-ply composite plates with temperature-dependent thermoelastic properties. Both the critical temperatures and the sensitivity derivatives are computed. The sensitivity derivatives measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the plate. The plates are assumed to have rectangular geometry and an antisymmetric lamination with respect to the middle plane. The temperature is assumed to be independent of the surface coordinates, but has an arbitrary symmetric variation through the thickness of the plate. The prebuckling deformations are accounted for. Numerical results are presented, for plates subjected to uniform temperature increase, showing the effects of temperature-dependent material properties on the prebuckling stresses, critical temperatures, and their sensitivity derivatives.
Damping and Resonance Characteristics of Thermal Waves
Authors: Tzou Da Yu
Published: April 2008

Amplification of thermal waves in response to high-frequency excitations is studied in this work. The resonance behavior is explored along with the underdamped behavior in thermal wave oscillations. In transition from an overdamped to an underdamped wave behavior, the relaxation distance is found to dominate the process. A relationship between the resonance frequency and the thermal wave speed is derived. The emphasis is placed on the frequency approach determining the thermal wave speed in engineering materials.
Convex Models for Uncertain Imperfection Control in Multimode Dynamic Buckling
Authors: Lindberg H. E.
Published: April 2008

Control of uncertain imperfections by means of convex bounds on finite Fourier transforms is shown to be more direct and not as overly conservative as control based on uniform bounds, i.e., bounding maximum and minimum imperfections. With either method, conservatism in bounds on buckling response is reduced by filtering the imperfection measurements. Extraction of the needed filtered information by operating directly on the Fourier coefficients is straightforward and allows use of additional information on the variation of the coefficients with mode number. Use of this information in example multimode buckling problems gives a bound on maximum possible buckling response that is a factor of1.6 larger than the response at a reliability of 99.5 percent for hypothetical (but reasonably representative) probabilistic imperfections. The bounding response itself, of course, does not depend on any assumptions concerning the probabilistic distribution of imperfections. Two additional combined uniform and Fourier ellipsoid bound models further reduce this factor to 1.1 and 0.5, and require only a simple, unfiltered imperfection bound measurement during quality control inspection.
A Boundary Element Method for Plane Anisotropic Elastic Media
Authors: Lee Kyu J. , Mal A. K.
Published: April 2008

The general problem of plane anisotropic elastostatics is formulated in terms of a system of singular integral equations with Cauchy kernels by means of the classical stress function approach. The integral equations are represented over the image of the boundary in the complex plane and a numerical scheme is developed for their solution. The boundary curve is discretized and suitable polynomial approximations of the unknown functions in terms of the complex variable are introduced. This reduces the equations to a set of complex linear algebraic equations which can be inverted to yield the stresses in a straightforward manner. The major difference between the present technique and the previous ones is in the numerical formulation. The integral equations are discretized in the complex plane and not in terms of real variables which depend on arc length, resulting in improved accuracy in presence of strong boundary curvature.
Three-Dimensional Effects Near a Crack Tip in a Ductile Three-Point Bend Specimen: Part II—An Experimental Investigation Using Interferometry and Caustics
Authors: Zehnder Alan T. , Rosakis Ares J.
Published: April 2008

An experimental investigation is undertaken to assess three-dimensional effects near a crack front in a ductile three-point bend specimen. The possibility of using the optical method of caustics for the measurement of the J-integral in the presence of large-scale yielding and three-dimensional fields is also investigated. Experiments using the optical methods of caustics by reflection and Twyman-Green interferometry are performed simultaneously on either side of the test specimen. The load and load-point displacement are also measured. The experimental results are compared with very good agreement to the results of a finite element simulation of the experiment. The caustics experiments are used to obtain a calibration relation between the value of the J-integral and the caustic diameter for load levels up to fracture initiation. It is proposed that such a calibration be used in dynamic fracture initiation experiments for the measurement of the time history of the dynamic J-integral.
Crack Extension Force in a Piezoelectric Material
Authors: Pak Y. Eugene
Published: April 2008

A conservation law that leads to a path-independent integral of fracture mechanics is derived along with the governing equations and boundary conditions for linear piezoelectric materials. A closed-form solution to the antiplane fracture problem is obtained for an unbounded piezoelectric medium. The path-independent integral is evaluated at the crack tip to obtain the energy release rate for a mode III fracture problem. For a fixed value of the mechanical load, it is shown that the crack growth can be either enhanced or retarded depending on the magnitude, the direction, and the type of the applied electrical load. It is also shown that, for certain ratios of the applied electrical load to mechanical load, crack arrestment can be observed.
An Experimental Study of the Unloading Waves in a Plucked Hyperelastic String
Authors: Wegner J. L. , Haddow J. B.
Published: April 2008

This paper is concerned with the unloading response of symmetrically plucked hyperelastic strings and presents some results of an experimental study. The validity of certain similarity solutions due to Wegner et al. (1989) is investigated and the experimental results are in acceptable agreement with the predictions of these solutions. A small extension of the similarity solutions to consider the response of a string after the first reflection is presented along with some experimental verification.
Elastodynamic Scattering From Inclusions Surrounded by Thin Interface Layers
Authors: Olsson P. , Datta S. K. , Bostrom A.
Published: April 2008

The scattering of elastic waves by elastic inclusions surrounded by interface layers is a problem of interest for nondestructive evaluation of interfaces in composites. In the present paper the scattering by a single elastic inclusion is studied. The scattering problem is solved by means of the null field approach and the properties of the interface layer enters through the boundary conditions on the inclusion. Various ways of doing this have been tried, from the simpler approach of just keeping the inertia of the layer, to using a membrane type of approximation or a more sophisticated method that includes all effects to first order in the layer thickness. The results obtained by using these different methods are compared numerically and with the exact solution for a layered sphere and with some recent results for a spheroid obtained using a hybrid finite element and wave function expansion technique. The numerical results show significant dependence on parameters containing the thickness and stiffness of the interface layer.
Inflation of an Axisymmetric Membrane: Stress Analysis
Authors: Sagiv A.
Published: April 2008

An analysis of the stresses and deformations of an inflated axisymmetric membrane was obtained. Large deformations of Mooney material were assumed. The development of the governing differential equations is an extension of the Adkins-Rivlin equations. The extension is for a general form of undeformed profiles with symmetry of revolution. The equations obtained, when reduced identically to the special cases treated in the literature of flat, spherical, and half-ellipsoid undeformed shapes, are fully compatible. A family of axisymmetric ellipsoid curves were used as an example of undeformed shapes for numerical demonstration. A fourth-order Runge-Kutta method was applied to integrate the equations. The results show relations between the nondimensional parameters governing the deformed membrane, such as pressure, membrane height, undeformed profiles, stresses, and deformations. An analysis of a very large deformation was carried out. It was found that in this case the membrane surface approaches a spherical shape except near the support, regardless of its undeformed profile.
Complementarity Problem Formulation of Three-Dimensional Frictional Contact
Authors: Kwak B. M.
Published: April 2008

A general three-dimensional frictional contact problem has been formulated in the form of a complementarity problem in an incremental analysis setting. The derivation is straight forward and very natural. It is shown that the complementarity problem for a three-dimensional case is inherently nonlinear, not like the two-dimensional problem where a linear complementarity problem formulation is possible. The two-dimensional case is a special case of the three-dimensional formulation. Approximate linear complementarity problems of the nonlinear complementarity problem by a Newton approach, or by introducing polyhedral law of friction, have been proposed for efficient numerical implementations.