bluuebunny/crossref_metadata_2025 huggingface dataset:
Unified Second-Order Stochastic Averaging Approach
Authors: Hijawi M. , Moschuk N. , Ibrahim R. A.
Published: February 2008

First-order stochastic averaging has proven very useful in predicting the response statistics and stability of dynamic systems with nonlinear damping forces. However, the influence of system stiffness or inertia nonlinearities is lost during the averaging process. These nonlinearities can be recaptured only if one extends the stochastic averaging to second-order analysis. This paper presents a systematic and unified approach of second-order stochastic averaging based on the Stratonovich-Khasminskii limit theorem. Response statistics, stochastic stability, phase transition (known as noise-induced transition), and stabilization by multiplicative noise are examined in one treatment. A MACSYMA symbolic manipulation subroutine has been developed to perform the averaging processes for any type of nonlinearity. The method is implemented to analyze the response statistics of a second-order oscillator with three different types of nonlinearities, excited by both additive and multiplicative random processes. The second averaging results are in good agreement with those estimated by Monte Carlo simulation. For a special nonlinear oscillator, whose exact stationary solution is known, the second-order averaging results are identical to the exact solution up to first-order approximation.
Dynamic Substructuring of Damped Structures Using Singular Value Decomposition
Authors: Ohayon R. , Sampaio R. , Soize C.
Published: February 2008

This paper deals with the theoretical aspects concerning linear elastodynamic of damped continuum medium in the frequency domain. Eigenvalue analysis and frequency response function are studied. The methods discussed here use a dynamic substructuring approach. The first method is based on a mixed variational formulation in which Lagrange multipliers are introduced to impose the linear constraints on the coupling interfaces. A modal reduction of each substructure is obtained using its free-interface modes. A practical construction of a unique solution is carried out using the Singular Value Decomposition (SVD) related only to the frequency-independent Lagrange multiplier terms. The second method is similar to the first one replacing the free-interface modes by the fixed-interface modes and elastostatic operator on the interface of each substructure.
Exact Solutions for Simply Supported Laminated Piezoelectric Plates
Authors: Heyliger P.
Published: February 2008

Exact solutions are presented for the static behavior of laminated piezoelectric plates with simple support. The upper and lower surfaces of the laminate can be subjected to a number of applied loadings, confined in this study to an applied transverse load or a specified surface potential. Each layer of the laminate can be piezoelectric, elastic/dielectric, or conducting, with perfect bonding assumed between each interface. Expressions are obtained for the components of displacement, stress, electric displacement, and potential through the thickness of the laminate. Representative examples are shown to demonstrate the fundamental behavior, and the influence of the piezoelectric coefficients and internal electrodes are discussed.
Generalized Cross-Correlation Functions for Engineering Applications, Part I: Basic Theory
Authors: Belmont M. R. , Hotchkiss A. J.
Published: February 2008

Traditional cross-correlation considers situations where two functions or data sets are linked by a constant shift either in time or space. Correlation provides estimates of such shifts even in the presence of considerable noise corruption. This makes the technique valuable in applications like sonar, displacement or velocity determination and pattern recognition. When regions are decomposed into patches in applications such as Particle Image Velocimerty it also allows estimates to be made of whole displacement/flow fields. The fundamental problem with traditional correlation is that patch size and hence statistical reliability must be compromised with resolution. This article develops a natural generalization of cross-correlation which removes the need for such compromises by replacing the constant shift with a function of time or space. This permits correlation to be applied globally to a whole domain retaining any long-range coherences present and dramatically improves statistical reliability by using all the data present in the domain for each estimate.
Generalized Cross-Correlation, Part II: Discretization of Generalized Cross-Correlation and Progress to Date in Its Implementation
Authors: Belmont M. R. , Hotchkiss A. J. , Maskell S. J. , Morris E. L.
Published: February 2008

The companion article, “Generalised Cross-Correlation Functions, Part I,” introduced a generalization of cross-correlation in which the constant shift used in traditional cross-correlation is replaced by a function of time or space. This allows correlation to be applied globally to the whole domain of interest avoiding the need to compromise spatial resolution with statistical reliability. The development in Part I was entirely in terms of continuous variables. This article examines the issues that arise when Generalized Cross-Correlation is applied to discrete variable situations. Topics discussed include sampling rate requirements, noise rejection, and efficient approximate algorithms, with special attention being paid to the condition number for the system.
Energy Release Rates for an Interface Crack Embedded in a Laminated Beam Subjected to Three-Point Bending
Authors: Toya M. , Aritomi M. , Chosa A.
Published: February 2008

Asymmetric three-point bending of a layered beam with an interface crack is analyzed on the basis of the classical beam theory. Axial forces induced by bending in the parts of the beam above and below the delamination are determined by regarding the cracked part as two lapped beams hinged at both ends. The compliance and the energy release rate are then derived. Numerical analyses based on the finite element method are carried out, which show that delamination growth occurs in mixed mode, i.e., both the normal separation (mode I) and mutual sliding (mode II) of the crack surfaces contribute to the fracturing process. Finally the decomposition of the energy release rate into mode I and mode II components is made by combining the analysis of the energy release rates by Toya (1992) and the two-dimensional linear beam solutions by Suo and Hutchinson (1990).
Dynamic Analysis of the Axially Moving String Based on Wave Propagation
Authors: Tan C. A. , Ying S.
Published: February 2008

In this paper, we present an exact solution for the linear, transverse response of an axially moving string with general boundary conditions. The solution is derived in the frequency domain and interpreted in terms of wave propagation functions. The boundary effects are included by the use of compliance functions at the boundaries. The response in the time domain involves only several convolution integrals which can easily be obtained for many physical boundary conditions. A comparison of this method with an existing solution method shows that this method requires much less computation time. The transient response of the translating string with a spring or a dashpot at a boundary is presented. It is shown that complete wave absorption occurs at a boundary when that boundary has a dashpot with damping coefficient equal to the propagation speed of the reflected wave.
Nondimensional Parameters for Geometric Nonlinear Effects in Pressurized Cylinders With Axial Cracks
Authors: Budiman H. T. , Lagace P. A.
Published: February 2008

The effects of geometric nonlinearity on the response of axially cracked cylindrical shells under internal pressure are investigated in a general way. Using the Donnell-Mushtari-Vlasov nonlinear shell equations, the nonlinear response is shown to depend on two nondimensional parameters: the geometrical parameter λ, which is a function of the cylinder geometries and crack length, and the loading parameter η, which depends on the applied pressure, material properties, and cylinder geometries. To assess the applicability of such parameters, nonlinear analyses of different cylindrical configurations were performed using the STAGS finite element code. The results show that the two parameters are able to characterize the nonlinear response of such cylinders. Effects of nonlinearity are then presented in the form of an iso-nonlinear plot showing the percentage difference between the linear and nonlinear stress intensification factors. Using the iso-nonlinear plot, the importance of geometric nonlinearity can thus be assessed once the cylinder geometries, loading parameters, and material properties are known.
Shakedown Analysis for Trusses and Frames
Authors: Chinh Pham Duc
Published: February 2008

The kinematic method is applied to study the shakedown behavior of certain bar structures subjected to variable loads. For trusses, the possible elastic instability of a thin bar in compression is taken into account. In the case of frames, the possibility of formulating the problem in generalized variables is explored. The result implies that the methods available in plastic limit analysis, such as the method of hinge mechanisms, can be developed for use in shakedown analysis of the structures.
On the Problem of Equilibrium Length of a Bridged Crack
Authors: Morozov N. , Paukshto M. , Ponikarov N.
Published: February 2008

A solution is given for a partially bridged straight crack in orthotropic elastic material in particular unidirectionally fiber-reinforced brittle composite. The problem of crack with constant bridging forces is solved by use the complex potentials. By use of Novogilov’s fracture criterion the estimation of the bridged part of crack and full length of equilibrium crack is obtained.
Finite Strain Elastostatics With Stiffening Materials: A Constrained Minimization Model
Authors: Hollister S. J. , Taylor J. E. , Washabaugh P. D.
Published: February 2008

Finite strain elastostatics is expressed for general anisotropic, piecewise linear stiffening materials, in the form of a constrained minimization problem. The corresponding boundary value problem statement is identified with the associated necessary conditions. Total strain is represented as a superposition of variationally independent constituent fields. Net stress-strain properties in the model are implicit in terms of the parameters that define the constituents. The model accommodates specification of load fields as functions of a process parameter.
The Rebound of an Elastic Sphere Against a Rigid Wall
Authors: Villaggio P.
Published: February 2008

The normal impact of an elastic sphere against a rigid plane is described using an elastic solution for a heavy sphere on a rigid plane found by Bondareva (1970). The solution is valid only in the case of equilibrium, but may be extended also to the dynamical case, provided that the time of duration of the impact is much larger that the time employed by the elastic waves in traversing the whole sphere after the first impact. The fundamental result is that, according to the new solution, the time of adherence between the first contact and the detachment is slightly higher than the same time evaluated according to the classical Hertz’s theory.
Interface Cracks in a Layered Solid Subjected to Contact Stresses
Authors: Liu C. H. , Chen I-Feng
Published: February 2008

A boundary element technique has been developed to analyze interface cracks in a layered solid. The loading applied on the solid may be tension, compression, shear, or an arbitrary combination of these. Crack surfaces may be open, closed, or partially open and partially closed. In all these cases, energy release rates can always be determined by using this technique. Crack-tip conditions are determined by an iterative procedure so that they themselves are parts of the solutions of a problem. The numerical technique is utilized to analyze subsurface interface cracks in a layered solid. Results are shown for various materials and under various loading conditions.
Three-Dimensional Analysis of Surface Cracks in an Elastic Half-Space
Authors: Guo Quanxin , Wang Jian-Juei , Clifton R. J.
Published: February 2008

A numerical method is presented for analyzing arbitrary planar cracks in a half-space. The method is based on the fundamental solution for a dislocation loop in a half-space, which is derived from the Mindlin solution (Mindlin, Physics, Vol. 7, 1936) for a point force in a half-space. By appropriate replacement of the Burgers vectors of the dislocation by the differential crack-opening displacement, a singular integral equation is obtained in terms of the gradient of the crack opening. A numerical method is developed by covering the crack with triangular elements and by minimizing the total potential energy. The singularity of the kernel, when the integral equation is expressed in terms of the gradient of the crack opening, is sufficiently weak that all integrals exist in the regular sense and no special numerical procedures are required to evaluate the contributions to the stiffness matrix. The integrals over the source elements are converted into line integrals along the perimeter of the element and evaluated analytically. Numerical results are presented and compared with known results for both surface breaking cracks and near surface cracks.
Stress Distributions During Fiber Pull-Out
Authors: Kumar R. Krishna , Reddy J. N.
Published: February 2008

Fiber pull-out resistance is an important mechanism of energy absorption during the failure of fiber-reinforced composite materials. This paper deals with axial stress distribution in the fiber during a pull-out. The frictional constraint between the fiber and the matrix is modeled with a perturbed Lagrangian approach and Coulomb’s law of friction. Stress distribution has been determined for three cases, using the finite element method. The first case deals with the pull out of a fully embedded fiber. The second determines the stress distribution during fiber pull-out in the presence of a broken-embedded fiber. The third model attempts to solve the pull out of a coated fiber. The results for the first case compares favorably with those in existing literature. A local “pinching” effect, due to the matrix collapse behind the pulled fiber, is brought out clearly by this model. The second study indicates that the “plug” effect may not be significant in affecting the stress distribution. Lastly, the effects of coating stiffness and thickness are investigated.
A Critical Study of the Applicability of Rigid-Body Collision Theory
Authors: Stoianovici D. , Hurmuzlu Y.
Published: February 2008

This article deals with the collision of steel bars with external surfaces. The central issue of the article is the investigation of the fundamental concepts that are used to solve collision problems by using rigid-body theory. We particularly focus on low-velocity impacts of relatively rigid steel bars to test the applicability of these concepts. An experimental analysis was conducted to study the rebound velocities of freely dropped bars on a large external surface. A high-speed video system was used to capture the kinematic data. The number of contacts and the contact time were determined by using an electrical circuit and an oscilloscope. Tests were performed by using six bar lengths and varying the pre-impact inclinations and the velocities of the bars. The experimental results were used to verify the applicability of Coulomb’s law of friction and the invariance of the coefficient of restitution in the class of impacts considered in this study. Then, given the unusual variation the coefficient of restitution as a result of changing pre-impact inclinations, a theoretical model was developed to explain this variation. A discrete model of the bar was used to obtain the equations of motion during impact. Computed and experimental results were compared to establish the accuracy of numerical model. The internal vibrations of the bar and multi impacts between the bar and the surface were found to be two main factors that cause the variation of the coefficient of restitution. Furthermore, a slenderness factor was proposed to identify the subset of collision problems where the coefficient of restitution was invariant to the inclination angle.
Bifurcation of Orthotropic Solids
Authors: deBotton G. , Schulgasser K.
Published: February 2008

We consider a large deformation plane-strain problem involving a compressible orthotropic solid subjected to uniaxial compressive loading along one of the principle directions which is aligned with the boundary of a half-space. An exact solution for the displacement field is obtained and a condition for the smallest compressive load corresponding to the onset of a surface instability is determined. It is shown that when the compression occurs along the stiffest direction this condition is expressible in terms of a cubic polynomial, and that the corresponding critical load is lower than the well-known estimate which determines the critical load to be equal to the inplane shear modulus.
Conservation Laws for Thermo or Poroelasticity
Authors: Chien N. , Herrmann G.
Published: February 2008

It is the purpose of the present paper to establish conservation laws for time-independent and time-dependent thermoelasticity in two dimensions via the NA method. Due to the analogy between the mechanics of a thermoelastic and a poroelastic medium, the results obtained can be applied to studies of poroelasticity. The conservation laws derived here should prove useful in studies of fracture and defects in a linear elastic body under the influence of nonuniform temperature fields and in a porous elastic solid whose pores are filled with a compressible viscous fluid. In particular, a path-independent integral was derived which represents the energy release rate accompanying crack growth.
Transient Elastic Waves in a Transversely Isotropic Plate
Authors: Weaver R. L. , Sachse W. , Kim Kwang Yul
Published: February 2008

The elastodynamic response of a thick plate, with the axis of transverse isotropy normal to the plate surface, is calculated by double numerical inverse transforms, a method particularly well-suited for calculations of responses in the near field of layered structures. Applications of these calculations include point-source/point-receiver ultrasonics, quantitative acoustic emission measurements, and seismology. The singularities of the integrand are eliminated by the introduction of a small, but nonzero, imaginary part to the frequency. We discuss issues of numerical efficiency and accuracy in the evaluation of the resulting integrals. The method can be generalized to calculate the responses in materials of more general symmetry, in viscoelastic materials and to include the effects of finite aperture sources and receivers. The calculated responses are compared to those measured in a single crystal specimen of zinc.
The Effective Dilatational Response of Fiber-Reinforced Composites With Nonlinear Interface
Authors: Levy A. J.
Published: February 2008

This paper presents a model of the dilatational response of fiber-reinforced composites for situations where the fibers interact with the matrix through a nonlinear interfacial separation mechanism. The solution to a planar solitary fiber-interface-matrix problem is employed together with the geometrically consistent composite cylinders model to obtain an exact solution for the bulk response of an elastic matrix reinforced with unidirectional elastic fibers. In the solitary fiber problem interface characterization assumes the form of a nonlinear force-separation law which couples the normal component of displacement jump to the normal component of interface traction and which requires a characteristic length for its prescription. Under decreasing values of characteristic length to inclusion radius ratio ductile or brittle decohesion or closure can occur provided the applied load, interface strength and elastic moduli of fiber and matrix are within the required bounds. Interaction effects due to finite fiber volume concentration, along with the phenomenon of brittle decohesion arising in the solitary fiber problem from the bifurcation of equilibrium separation at the fiber matrix interface, are shown to precipitate instability in the composite. An inequality relating the elastic moduli and interface properties is provided which governs the smooth or abrupt transition in composite response from rigid interface behavior to void behavior. The results are shown to apply equally well for composite geometry based on the three-phase model.
Three-Dimensional Finite Element Analysis of Surface Deformation and Stresses in an Elastic-Plastic Layered Medium Subjected to Indentation and Sliding Contact Loading
Authors: Kral E. R. , Komvopoulos K.
Published: February 2008

Three-dimensional finite element simulations of the indentation and sliding of a rigid sphere on a half-space with a harder and stiffer layer are presented. The sphere is modeled by contact elements, thereby avoiding a priori assumptions for the pressure profile. Indentations are performed to normal loads of 100 and 200 times the initial yield load of the substrate material and subsequent sliding is performed at a constant normal load to distances of approximately twice the indentation contact radius. Two complete load cycles are performed in selected cases to assess the effect of repeated sliding on the surface displacements and contact stresses. The effects of layer material properties, interface friction, and normal load on the sliding and residual contact stresses and forward plastic flow are examined. Emphasis is given to the sliding and residual tensile stresses at the surface in order to assess the consequences for crack initiation and subsequent failure as a function of the layer material properties, the coefficient of friction, and normal load. The finite element results are shown to be in good agreement with the results of analytical and experimental studies.
Dynamics of Plane Motion of an Elastic Rod
Authors: Atanackovic T. M. , Cveticanin L. J.
Published: February 2008

Plane motion of an elastic rod, subjected to a compressive force is analyzed. Equations of motions are derived for the case when deformations are not small. It is assumed that the compressive force has a periodic component, so that parametric instability is possible. Stability boundary is estimated analytically and determined numerically. In the special case of static loading a new formula for the slenderness ratio, below which there is no buckling, is obtained. In deriving the differential equations of motion a generalized constitutive equations taking in to account compressibility and shear stresses are used.
Nonstandard Models for Thin-Walled Beams With a View to Applications
Authors: Rizzi N. , Tatone A.
Published: February 2008

A direct theory of a one-dimensional structured continuum is introduced in order to study the postbuckling behavior of thin-walled beams. A simply supported beam bent by end couples is analyzed showing that, in the case of nonsymmetric cross sections, lateral buckling gives rise to imperfection sensitivity. Then an axially loaded beam is studied taking also into account the interaction between torsional and flexural buckling. The results obtained prove that in this case imperfection sensitivity, though slighter than in the previous case, arises also for symmetric cross sections.
Dynamics of a Gas Permeable Contact Lens During Blinking
Authors: Raad P. E. , Sabau A. S.
Published: February 2008

The dynamics of a gas permeable contact lens during blinking are analyzed. The contact lens is considered to be a planar, circular, porous disk of specified permeability. On one side, the lens is in solid contact with the eyelids, while on the other, it is separated from the corneal surface by a thin tear film. The rigid-body dynamics of the lens are coupled with the fluid dynamics of the tear film, and a velocity slip condition is imposed at their interface. The coupled system of ordinary and partial differential equations is solved by a combination of analytical and numerical techniques subject to boundary conditions and physical constraints limiting the duration and extent of the motion of the lens. In addition to the contact lens aspect ratio, this work investigates the effects of those variables that characterize the porous nature of the lens such as the Darcy number and the effective slip coefficient. The motion of a permeable contact lens can be controlled by a proper choice of the lens material microstructure. In fact, analysis of the results indicates that the motion of the lens is enhanced by lower values of the slip coefficient and higher values of the Darcy number, independent of the lens thickness. In addition, it is found that thicker lenses as well as thicker tear films cause the lens to move faster.
The Strain Energy Density of Compressible, Rubber-Like Shells of Revolution
Authors: Yu¨kseler R. F.
Published: February 2008

An approach for the derivation of two-dimensional strain energy density functions of compressible, rubber-like shells of revolution which undergo axisymmetric, arbitrarily large rotations and strains including transverse normal and transverse shear strains is proposed. The proposed method is applied to polyurethane rubber, circular plates and numerical results for the flexural buckling of polyurethane circular plates are obtained for an illustrative comparison with a method presented previously.
The Flow Near a Rotating Disk: An Approximate Solution
Authors: Ariel P. D.
Published: February 2008

An approximate solution to the problem of steady laminar flow near a rotating disk is presented. It is based upon the idea of stretching of the independent variable and the minimization of the residual in a differential equation using the least squares method. The solution is simple and gives results which compare favorably with those obtained by other approximate methods.
Vibration and Stability of a Spinning Disk Under Stationary Distributed Edge Loads
Authors: Chen Jen-San
Published: February 2008

The vibration and stability of a spinning disk under conservative distributed edge tractions are studied both numerically and analytically. The edge traction is circumferentially stationary in the space. When the compressive traction is uniform, it is found that no modal interaction occurs and the natural frequencies of all nonreflected waves decrease, while the natural frequencies of the reflected waves increase. When the spinning disk is under distributed traction in the form of cos kθ, where k is a nonzero integer, it is found that the eigenvalue only changes slightly under the edge traction if the natural frequency of interest is well separated from others. When two modes are almost degenerate, however, modal interaction may or may not occur. It is observed that when the difference between the number of nodal diameters of these two modes is equal to ±k, frequency veering occurs when both modes are nonreflected, and merging occurs when one of these two modes is a reflected wave. In applying this rule, the number of nodal diameters of the forward and the reflected wave is considered as negative.
Stress and Strain Analysis in Molecular Dynamics Simulation of Solids
Authors: Scagnetti P. A. , Nagem R. J. , Sandri G. V. H. , Bifano T. G.
Published: February 2008

Molecular dynamics simulation of solid materials is applied to a two-dimensional indentation problem. Methods are presented for calculating the stress and strain tensors at interior points within the model. The stress calculations corresponding to the elastic deformation portion of the indentation process are compared with an analytical continuum solution. Stress calculations are also presented for the plastic deformation portion of the indentation process. The methods are derived independently so that future work can be directed at determining the constitutive relationship between stress and strain throughout the development of plastic flow and fracture in a solid material.
On the Growth-of-Waviness in Fiber-Reinforced Polymer Composites: Viscoelastic Bifurcation and Imperfection Sensitivity
Authors: Bhalerao M. S. , Moon T. J.
Published: February 2008

The time-dependent, local microbuckling of fibers in polymer composites is modeled in the context of viscoelasticity. The instability or “growth-of-waviness”-type analysis is carried out for bifurcation (initially straight fibers), as well as for imperfection sensitivity (initially wavy fibers). The concept of dominant wavelength, previously defined for viscoelastic bifurcation by Biot, is generalized for viscoelastic imperfection sensitivity. A parametric study is presented to encompass a wide range of physically useful values to study the effects of matrix properties, fiber-matrix interfacial conditions, and time-dependent loads on dominant wavelengths. A marked difference is observed between the viscoelastic bifurcation and imperfection sensitivity dominant wavelength results. The bifurcation dominant wavelength is seen to depend negligibly on matrix properties, yet highly on the applied load and the interfacial conditions. On the other hand, the imperfection sensitive dominant wavelength is strongly dependent on matrix properties, while negligibly on load and interface conditions.
An Analysis of Cracking in a Layered Medium With a Functionally Graded Nonhomogeneous Interface
Authors: Choi Hyung Jip
Published: February 2008

The plane elasticity solution is presented in this paper for the crack problem of a layered medium. A functionally graded interfacial region is assumed to exist as a distinct nonhomogeneous transitional layer with the exponentially varying elastic property between the dissimilar homogeneous surface layer and the substrate. The substrate is considered to be semi-infinite containing a crack perpendicular to the nominal interface. The stiffness matrix approach is employed as an efficient method of formulating the proposed crack problem. A Cauchy-type singular integral equation is then derived. The main results presented are the variations of stress intensity factors as functions of geometric and material parameters of the layered medium. Specifically, the influences of the crack size and location and the layer thickness are addressed for various material combinations.
A Simple Model of a Stiffened Shell-Type Structure for an Investigation Into the Vibration-Buckling Correlation
Authors: Ryaboy V. M. , Weller T.
Published: February 2008

A nonlinear two-degree-of-freedom system is considered to simulate the peculiar behavior of stringer-stiffened cylindrical shells under nonuniform axial compression, which was observed in recent tests where the characteristic curves (eigenfrequency squared versus load) were nonmonotonic and decreasing steeply when approaching the critical load. Correlation is traced between the characteristic curves and equilibrium paths. It is shown that for particular nonzero values of load eccentricity, bifurcations are observed instead of the usual limit points. Nonunique stable post-buckling equilibrium paths are pointed out. The general properties of characteristic curves are discussed.
A Simplified Displacement-Rotation Form for the Equations of Motion of Nonlinearly Elastic Shells of Revolution Undergoing Combined Bending and Torsion
Authors: Simmonds J. G.
Published: February 2008

By appropriately defining two displacements and a rotation, it is shown that the equations of motion of a shell of revolution undergoing combined axisymmetric bending and torsion, in which the extensional strains and the rotations may be arbitrarily large, can be given a form in which there are three effective extensional strains and two effective bending strains, each of which is only linear or quadratic in the displacements and rotation.
A Yield Criterion for Porous Ductile Media at High Strain Rate
Authors: Wang Ze-Ping , Jiang Qing
Published: February 2008

An approximate yield criterion for porous ductile media at high strain rate is developed adopting energy principles. A new concept that the macroscopic stresses are composed of two parts, representing dynamic and quasi-static components, is proposed. It is found that the dynamic part of the macroscopic stresses controls the movement of the dynamic yield surface in stress space, while the quasi-static part determines the shape of the dynamic yield surface. The matrix material is idealized as rigid-perfectly plastic and obeying the von Mises yield. An approximate velocity field for the matrix is employed to derive the dynamic yield function. Numerical results show that the dynamic yield function is dependent not only on the rate of deformation but also on the distribution of initial micro-damage, which are different from that of the quasi-static condition. It is indicated that inertial effects play a very important role in the dynamic behavior of the yield function. However, it is also shown that when the rate of deformation is low (≤103/sec), inertial effects become vanishingly small, and the dynamic yield function in this case reduces to the Gurson model.
A Layer-Wise Laminate Theory Rationally Deduced From the Three-Dimenstonal Elasticity
Authors: Bisegna P. , Sacco E.
Published: February 2008

A layer-wise theory of laminated plates, which accounts for piecewise constant shear strain in the thickness, is derived from the three-dimensional elasticity theory by imposing suitable constraints on the strain and stress fields. At this aim, the functional of the three-dimensional elasticity is modified according to the Lagrange multipliers theory. In fact, a nonstandard application of the Lagrange theory is presented, because of the simultaneous presence of constraints on dual spaces. The imposed constraints make reactive strain and stress fields arise. Thus, it is necessary to distinguish between elastic and total strain and stress fields. The difference between them is emphasized in a numerical application.
In-Plane and Out-of-Plane Free Vibration Analysis of Archimedes-Type Spiral Springs
Authors: Yıldırım V.
Published: February 2008

The in-plane and out-of-plane free vibration frequencies of Archimedes-type spiral springs are computed by the transfer matrix method. Taking into account the effects of the axial and the shear deformations and the rotary inertia, the overall dynamic transfer matrix is computed up to any desired numerical accuracy by the complementary functions method. Since there are no restrictions for the number of coils and for the form of the spring (close-coiled or open-coiled), the presented method is general. After having verified the soundness of the computer program devised, the effects of the number of coils, of the axial and shear deformations, of rotary inertia and of the boundary conditions on the frequencies are also investigated.
A Least-Squares Approach to the Practical Use of the Hole Method in Photoelasticity
Authors: Cardenas-Garcia J. F. , Tian Y. L. , Hashemi J. , Durelli A. J.
Published: February 2008

The use of a small circular hole in elastostatic photoelasticity to determine the stress tensor for any two-dimensional general loading situation is well known. The original application required fringe-order information at four points on the boundary, on opposite sides, along the axes of symmetry or principal stress directions. Later, to obtain greater precision, it was adapted so that fringe information inside the field could be used. This led to the also limited use of fringe-order information from four points at 1.4 and two times the radius of the hole, along the principal axes of symmetry. More recent work has even allowed the use of fringe-order information, at a fixed radius, anywhere along the two principal axes of symmetry. The greatest limitation of all of these approaches is that the majority of the fringe-order information that is available, away. from the axes of symmetry, is not utilized at all. The current work presents a least-squares approach to the hole method that allows the simultaneous use of information anywhere and at any radial distance from the center of the hole inside the stress field. The objectives of this paper are: to apply the use of the least-squares approach to the hole method in photoelasticity; and, to show the consistent and practical application of this least-squares approach to the hole method. The achievement of this last objective permits the use of the values of specimen birefringence at a large number of points, taken from anywhere in the field around the hole.
Critical Velocities of a Harmonic Load Moving Uniformly Along an Elastic Layer
Authors: Dieterman H. A. , Metrikine A.
Published: February 2008

The critical (resonance) velocities of a harmonically varying point load moving uniformly along an elastic layer are determined as a function of the load frequency. It is shown that resonance occurs when the velocity of the load is equal to the group velocity of the waves generated by the load. The critical depths of the layer are determined as function of the load velocity in the case the load frequency is proportional to the load velocity. This is of importance for high-speed trains where the loading frequency of the train wheel excitations is mainly determined by the ratio between the train velocity and the distance between the sleepers (ties). It is shown that the critical depths are decreasing with increasing train velocity. It is concluded that the higher the train velocity, the more important are the properties of the ballast and the border between the ballast and the substrate.
A Symmetric Inverse Vibration Problem for Nonproportional Underdamped Systems
Authors: Starek L. , Inman D. J.
Published: February 2008

This paper considers a symmetric inverse vibration problem for linear vibrating systems described by a vector differential equation with constant coefficient matrices and nonproportional damping. The inverse problem of interest here is that of determining real symmetric, coefficient matrices assumed to represent the mass normalized velocity and position coefficient matrices, given a set of specified complex eigenvalues and eigenvectors. The approach presented here gives an alternative solution to a symmetric inverse vibration problem presented by Starek and Inman (1992) and extends these results to include noncommuting (or commuting) coefficient matrices which preserve eigenvalues, eigenvectors, and definiteness. Furthermore, if the eigenvalues are all complex conjugate pairs (underdamped case) with negative real parts, the inverse procedure described here results in symmetric positive definite coefficient matrices. The new results give conditions which allow the construction of mass normalized damping and stiffness matrices based on given eigenvalues and eigenvectors for the case that each mode of the system is underdamped. The result provides an algorithm for determining a nonproportional (or proportional) damped system which will have symmetric coefficient matrices and the specified spectral and modal data.
Transient Analysis of a Propagating In-Plane Crack in a Finite Geometry Body Subjected to Static Loadings
Authors: Tsai Chwan-Huei , Ma Chien-Ching
Published: February 2008

In this study, a cracked body with finite boundaries subjected to static loading and the crack propagating with a constant speed are analyzed. The interaction of the propagating crack with reflected waves generated from traction-free boundaries is investigated in detail. The methodology for constructing the scattered field by superimposing the fundamental solution in the Laplace transform domain is proposed. The fundamental solutions represent the responses of applying exponentially distributed loadings in the Laplace transform domain on the surface of a half-plane or a crack. The dynamic stress intensity factors of a propagating crack induced from the interaction with the first few reflected waves generated from the traction-free boundary are obtained in an explicit closed form. The analytical solutions of dynamic stress intensity factors are compared with available numerical and experimental results and the agreement is quite good. We find one thing very interesting: the dynamic stress intensity factor for a long time period is a universal function of the instantaneous extending rate of a crack tip times the static stress intensity factor for an equivalent stationary crack for the finite strip problem. It was also found that the reflected waves generated from free boundaries always increase the stress intensity factor, and the influence from reflected waves generated from the boundary, which is perpendicular to the crack, are weaker than those generated from the boundary, which is parallel to the crack.
Response and Stability of Square Tubes Under Bending
Authors: Vaze S. P. , Corona E.
Published: February 2008

This paper addresses the response and stability of elastic-plastic steel tubes with square cross section under pure bending. An analytical model with sufficiently nonlinear kinematics to capture the development of ripples in the compression flange was developed. the results indicate that collapse of such tubes is imperfection sensitive for tubes with “high” height-to-thickness ratio (h/t), but the sensitivity decreases as h/t decreases. Experimentally, the tubes collapse due to a limit moment instability which is followed by the formation of a kink on the compression flange of the tubes. The limit moment and the development of the kink are captured well by the analytical model.
Finite Element Method for Stochastic Beams Based on Variational Principles
Authors: Ren Y.-J. , Elishakoff I. , Shinozuka M.
Published: February 2008

This paper proposes a new version (fundamentally different from the existing ones) of finite element method for the mean and covariance functions of the displacement for bending beams with spatially random stiffness. Apart from the conventional finite element method for stochastic problems, which utilizes either perturbation or series expansion technique or the Monte Carlo simulation, the present method is based on the newly established variational principles. The finite element scheme is formulated directly with respect to the mean function and covariance function, rather than perturbed components of the displacement. It takes into account an information on joint probability distribution function of the random stiffness to obtain the covariance function of the displacement. Therefore, the accurate solution can be obtained even if the coefficient of variation of the random stiffness is large, in contrast to conventional technique. Several examples are given to illustrate the advantage of the proposed method, compared with the conventional ones.
Closed-Form Solutions and the Eigenvalue Problem for Vibration of Discrete Viscoelastic Systems
Authors: Muravyov A. , Hutton S. G.
Published: February 2008

A procedure for obtaining closed-form homogeneous solutions for the problem of vibration of a discrete viscoelastic system is developed for the case where the relaxation kernel characterizing the constitutive relation of the material is expressible as a sum of exponentials. The developed procedure involves the formulation of an eigenvalue problem and avoids difficulties encountered with the application of the Laplace transform approach to multi-degree-of-freedom viscoelastic systems. Analytical results computed by using the developed method are demonstrated on an example of a viscoelastic beam.
An Axisymmetric Inclusion in One of Two Perfectly Bonded Dissimilar Elastic Half-Spaces
Authors: Korsunsky A. M.
Published: February 2008

This paper introduces an effective method for the solution of axisymmetric elastic inclusions in bonded dissimilar half-spaces. The method leads to new concise expressions for the elastic fields in terms of only two scalar Papkovich potential functions. A host of earlier solutions, which were obtained using a range of alternative techniques, involving surface stress relaxation and Hankel transforms, are shown to be subsumed in the present result.
A Remarkable Tensor in Plane Linear Elasticity
Authors: He Q.-C.
Published: February 2008

It is shown that any two-dimensional elastic tensor can be orthogonally and uniquely decomposed into a symmetric tensor and an antisymmetric tensor. To within a scalar multiplier, the latter turns out to be equal to the right-angle rotation on the space of two-dimensional second-order symmetric tensors. On the basis of these facts, several useful results are derived for the traction boundary value problem of plane linear elasticity.
The, Order of Stress Singularities in Orthotropic Wedges
Authors: Selvarathinam A. , Pageau S. S.
Published: February 2008

A formulation for the determination of the order of the stress singularities at the tip of a reentrant corner for anisotropic wedges was given by Bogy (1972). Results for orthotropic wedges were obtained as a special case, and it was concluded that the order of the stress singularities at the tip of reentrant orthotropic wedges is always more severe than that of the corresponding isotropic wedge. It is shown here that the order of the stress singularities at the wedge tip can be above or below that of the corresponding isotropic wedge, depending on the material properties.
Self-Similar Crack Expansion Method for Three-Dimensional Crack Analysis
Authors: Xu Yonglin , Moran B. , Belytschko T.
Published: February 2008

The self-similar crack expansion method is developed to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique. With this method, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface, and the crack expansion rate, which is related to the crack energy release rate, is estimated by using a technique based on self-similar (virtual) crack extension. For elements on the crack surface, regular integrals and singular integrals are evaluated based on closed-form expressions, which improves the accuracy. Examples show that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than one percent as compared with exact solutions. The stress intensity factors of subsurface cracks are in good agreement with other numerical solutions.
Enhanced Elastic Buckling Loads of Composite Plates With Tailored Thermal Residual Stresses
Authors: Mu¨ller de Almeida S. F. , Hansen J. S.
Published: February 2008

Thermal residual stresses introduced during the manufacturing process and their effect on the buckling load of stringer reinforced composite plates is investigated. The principal idea is to include stiffeners on the perimeter of the plate and thereby, during manufacture, induce a favorable thermal residual-stress state in the structure; these stresses arise by considering the difference in thermal expansion coefficients and elastic properties of the plate and the stiffeners. In this manner, it is shown that thermal residual stresses can be tailored to significantly enhance the performance of the structure. The analysis is taken within the context of an enhanced Reissner-Mindlin plate theory and the finite element technique is used to analyze the problem. A 16 node bi-cubic Lagrange element is implemented in a FORTRAN code to determine the buckling load of the composite plate in the presence of thermal residual stresses. Three different plate-stiffener geometries are used as illustrations. The analyses indicate that buckling loads can be significantly increased by properly tailoring the thermal residual stresses. Therefore it may be concluded that an evaluation of these stresses and a judicious analysis of their effects must be included in the design procedure for this class of composite structure.