bluuebunny/crossref_metadata_2025 huggingface dataset:
Diffraction of SH-Wave by Interacting Matrix Crack and an Inhomogeneity
Authors: Wang X. D. , Meguid S. A.
Published: February 2008

This article presents an analytical treatment of the dynamic interaction between a crack and an arbitrarily located circular inhomogeneity under antiplane incident wave. The method is based upon the use of a pseudo-incident wave technique which reduces the interaction problem into a coupled solution of a single crack and a single inhomogeneity problems. The newly proposed pseudo-incident wave technique avoids the numerical integration commonly used in the boundary element and volume integral methods and thus provides reliable and accurate analytical solutions. The resulting dynamic stress intensity factor of the crack is verified by comparison with existing results and numerical examples are provided to show the dependence of dynamic shielding and amplification upon the frequency of the incident wave, the material combination and the location of the inhomogeneity. The results show that the toughening associated with special geometric configurations under quasi-static loading may provide undesirable weakening effect upon the crack under dynamic loading in a certain frequency region.
On the Existence of Mayer’s Potential
Authors: Cˇovic´ V. M. , Lukacˇevic´ M. M.
Published: February 2008

A complete solution of the well-known Mayer’s problem, which is concerned with the possibility of extending Hamilton’s principle expressed in the form valid for conservative dynamical systems to one special case of nonconservative systems (Appell, 1911), is obtained. Namely, the necessary and sufficient conditions which have to be satisfied by the coefficients of the given nonconservative generalized forces so that the Mayer’s potential (and, as a consequence, the descriptive function of the system) can be constructed, are established. This result is illustrated by an example.
An Eigenvector Expansion Method for the Solution of Motion Containing Fractional Derivatives
Authors: Suarez L. E. , Shokooh A.
Published: February 2008

The use of fractional derivatives has proved to be very successful in describing the behavior of damping materials, in particular, the frequency dependence of their parameters. In this article the three-parameter model with fractional derivatives of order 1/2 is applied to single-degree-of-freedom systems. This model leads to second-order semidifferential equations of motion for which previously there were no closed-form solutions available. A new procedure that permits to obtain simple closed-form solutions of these equations is introduced. The method is based on the transformation of the equations of motions into a set of first-order semidifferential equations. The closed-form expression of he eigenvalues and eigenvectors of an associated eigenproblem are used to uncouple the equations. Using the Laplace transform method, closed-form expressions to calculate the impulse response function, the step response function and the response to initial conditions are derived.
Nonseparable Solutions to the Hamilton-Jacobi Equation
Authors: Leech C. M. , Tabarrok B.
Published: February 2008

The Hamilton-Jacobi partial differential equation is solved for potential energy functionals of constant, linear, and quadratic form using a class of nonseparable solutions; these solutions give a geometric property to the generating solution, embedding it into the class of conics. These solutions have two basic components, that designated as a kernel component which belongs to the system regardless of the specific dynamics of the system and the primary and secondary system functions that are dependent on the specific initial conditions. Solutions are obtained for the linear oscillator, a rheonomic oscillator and a two-degree-of-freedom system, the latter suggesting an approach for general multidegree-of-freedom systems.
Nonlinear System Response for Impulsive Parametric Input
Authors: Caddemi S. , Paola M. Di
Published: February 2008

In engineering applications when the intensity of external forces depends on the response of the system, the input is called parametric. In this paper dynamical systems subjected to a parametric deterministic impulse are dealt with. Particular attention has been devoted to the evaluation of the discontinuity of the response when the parametric impulse occurs. The usual forward difference and trapezoidal integration schemes have been shown to provide only approximated solutions of the jump of the response; hence, the exact solution has been pursued and presented under the form of a numerical series. The impulse is represented throughout the paper by means of a classical Dirac’s delta function; however, a new model of Dirac’s delta is presented and adopted in order to validate the results provided by the numerical series.
Stochastic Vibration of a Mobile Manipulator
Authors: Akpan U. O. , Kujath M. R.
Published: February 2008

The stochastic vibration of a flexible, articulated, and mobile manipulator is studied. The manipulator is mounted on a vehicle which is supported by a suspension system. Stochastic excitation of the manipulator is induced by the uniform horizontal motion of the vehicle on a traction surface. The power spectral density representation and the state-space representation are used to derive expressions for the covariance matrices of the manipulator tip motions. Sensitivity of the variance of the tip motion to the manipulator configuration, length, vehicle velocity, surface roughness coefficient, and structural damping and stiffness are explored. Suggestions for mobile manipulator design to minimize the influence of the stochastic base vibration on the manipulator tip motion are proposed.
Linear Systems Excited by Polynomials of Filtered Poission Pulses
Authors: Paola M. Di
Published: February 2008

The stochastic differential equations for quasi-linear systems excited by parametric non-normal Poisson white noise are derived. Then it is shown that the class of memoryless transformation of filtered non-normal delta correlated process can be reduced, by means of some transformation, to quasi-linear systems. The latter, being excited by parametric excitations, are frst converted into ltoˆ stochastic differential equations, by adding the hierarchy of corrective terms which account for the nonnormality of the input, then by applying the Itoˆ differential rule, the moment equations have been derived. It is shown that the moment equations constitute a linear finite set of differential equation that can be exactly solved.
On Bonded Circular Inclusions in Plane Thermoelasticity
Authors: Chao C. K. , Shen M. H.
Published: February 2008

A general solution to the thermoelastic problem of a circular inhomogeneity in an infinite matrix is provided. The thermal loadings considered in this note include a point heat source located either in the matrix or in the inclusion and a uniform heat flow applied at infinity. The proposed analysis is based upon the use of Laurent series expansion of the corresponding complex potentials and the method of analytical continuation. The general expressions of the temperature and stress functions are derived explicitly in both the inclusion and the surrounding matrix. Comparison is made with some special cases such as a circular hole under remote uniform heat flow and a circular disk under a point heat source, which shows that the results presented here are exact and general.
Spherical Cavity Expansion in a Drucker-Prager Solid
Authors: Durban D. , Fleck N. A.
Published: February 2008

A finite strain analysis is presented for the pressurized spherical cavity embedded in a Drucker-Prager medium. Material behavior is modeled by a nonassociated deformation theory which accounts for arbitrary strain-hardening. The governing equations of spherically symmetric response are reduced to a single differential equation with the effective stress as the independent variable. Some related topics are discussed including the elastic-perfectly plastic solid, the thin-walled shell, and the Mohr-Coulomb material. Spontaneous growth (cavitation limit) of an internally pressurized cavity is treated as a self-similar process and a few numerical examples are presented. These illustrate, for different hardening characteristics, the pressure sensitivity of material response and that deviations from normality always reduce the caviation pressure.
A Multicontinuum Approach to Structural Analysis of Linear Viscoelastic Composite Materials
Authors: Garnich M. R. , Hansen A. C.
Published: February 2008

A “multicontinuum” approach to structural analyses of composites is described. A continuum field is defined to represent each constituent material along with the traditional continuum field associated with the composite. Finite element micromechanics is used to establish relationships between composite and constituent field variables. These relationships uncouple the micromechanics from structural solutions and render an efficient means of extracting constituent information during the course of a finite element structural analysis. Equations are developed for the case of a linear elastic reinforcing material embedded in a linear viscoelastic matrix and verified by comparison with results of finite element micromechanics.
Crack Initiation From Homogeneous and Bimaterial Corners
Authors: Grenestedt J. L. , Hallstrom S.
Published: February 2008

Fracture initiated at a corner between two different isotropic materials is considered. A “small” crack, well within the region dominated by the asymptotic stress fields of the noncracked corner, is modeled and the stress intensities associated with the tip of the small crack are determined. Different criteria for the direction of crack propagation are studied.
Viscoelastic Model of Finitely Deforming Rubber and Its Finite Element Analysis
Authors: Kim Seung Jo , Kim Kyeong Su , Cho Jin Yeon
Published: February 2008

A viscoelastic model of finitely deforming rubber is proposed and its nonlinear finite element approximation and numerical simulation are carried out. This viscoelastic model based on continuum mechanics is an extended model of Johnson and Quigley’s one-dimensional model. In the extended model, the kinematic configurations and measures based on continuum mechanics are rigorously defined and by using these kinematic measures, constitutive relations are introduced. The obtained highly nonlinear equations are approximated by the nonlinear finite element method, where a mixture of the total and updated Lagrangian descriptions is used. To verify the theory and the computer code, uniaxial stretch tests are simulated for various stretch rates and compared with actual experiments. As a practical example, an axisymmetric rubber plate under various time-dependent pressure loading conditions is analyzed.
Total Deformation, Plane-Strain Contact Analysis of Macroscopically Homogeneous, Compositionally Graded Materials With Constant Power-Law Strain Hardening
Authors: Giannakopoulos A. E.
Published: February 2008

Plane-strain contact analysis is presented for compositionally graded materials with power-law strain hardening. The half-space, y≤0, is modeled as an incompressible, nonlinear elastic material. The effective stress, σe, and the effective total strain, εe, are related through a power-law model, σe=K0εeμ;0<μ≤min(1,(1+k)). The material property K0 changes with depth, |y|, as K0=A|y|k;A>0,0≤|k|<1. This material description attempts to capture some features of the plane-strain indentation of elastoplastic or steady-state creeping materials that show monotonically increasing or decreasing hardness with depth. The analysis starts with the solution for the normal line load (Flamant’s problem) and continues with the rigid, frictionless, flat-strip problem. Finally, the general solution of normal indentation of graded material by a convex, symmetric, rigid, and frictionless two-dimensional punch is given. Applications of the present results range from surface treatments of engineering structures, protective coatings for corrosion and fretting fatigue, settling of beam type foundations in the context of soil and rock mechanics, to bioengineering as well as structural applications such as contact of railroad tracks.
Enrichment of the Finite Element Method With the Reproducing Kernel Particle Method
Authors: Liu Wing Kam , Uras R. A. , Chen Y.
Published: February 2008

The reproducing kernel particle method (RKPM) has attractive properties in handling high gradients, concentrated forces, and large deformations where other widely implemented methodologies fail. In the present work, a multiple field computational procedure is devised to enrich the finite element method with RKPM, and RKPM with analytical functions. The formulation includes an interaction term that accounts for any overlap between the fields, and increases the accuracy of the computational solutions in a coarse mesh or particle grid. By replacing finite element method shape Junctions at selected nodes with higher-order RKPM window functions, RKPM p-enrichment is obtained. Similarly, by adding RKPM window functions into a finite element method mesh, RKPM hp-enrichment is achieved analogous to adaptive refinement. The fundamental concepts of the multiresolution analysis are used to devise an adaptivity procedure.
Koiter-Based Solution for the Initial Post-buckling Behavior of Moderately Thick Orthotropic and Shear Deformable Cylindrical Shells Under External Pressure
Authors: Kardomateas G. A.
Published: February 2008

The initial post-buckling behavior of moderately thick orthotropic shear deformable cylindrical shells under external pressure is studied by means of Koiter’s general post-buckling theory. To this extent, the objective is the calculation of imperfection sensitivity by relating to the initial post-buckling behavior of the perfect structure, since it is generally recognized that the presence of small geometrical imperfections in some structures can lead to significant reductions in their buckling strengths. A shear deformation theory, which accounts for transverse shear strains and rotations about the normal to the shell midsurface, is employed to formulate the shell equations. The initial post-buckling analysis indicates that for several combinations and geometric dimensions, the shell under external pressure will be sensitive to small geometrical imperfections and may buckle at loads well below the bifurcation predictions for the perfect shell. On the other hand, there are extensive ranges of geometrical dimensions for which the shell is insensitive to imperfections, and, therefore it would exhibit stable post-critical behavior and have a load-carrying capacity beyond the bifurcation point. The range of imperfection sensitivity depends strongly on the material anisotropy, and also on the shell thickness and whether the end pressure loading is included or not. For example, for the circumferentially reinforced graphite/epoxy example case studied, it was found that the structure is not sensitive to imperfections for values of the Batdorf length parameter z˜ above ≃270, whereas for the axially reinforced case the structure is imperfection-sensitive even at the high range of length values; for the isotropic case, the structure is not sensitive to imperfections above z˜ ≃ 1000.
In-Plane Stress and Displacement Distributions in a Spinning Annular Disk Under Stationary Edge Loads
Authors: Chen Jen-San , Jhu Jhi-Lu
Published: February 2008

It is well known that the in-plane stress and displacement distributions in a stationary annular disk under stationary edge tractions can be obtained through the use of Airy stress function in the classical theory of linear elasticity. By using Lame’s potentials, this paper extends these solutions to the case of a spinning disk under stationary edge tractions. It is also demonstrated that the problem of stationary disk-spinning load differs from the problem of spinning disk-stationary load not only by the centrifugal effect, but also by additional terms arising from the Coriolis effect. Numerical simulations show that the amplitudes of the stress and displacement fields grow unboundedly as the rotational speed of the disk approaches the critical speeds. As the rotational speed approaches zero, on the other hand, the in-plane stresses and displacements are shown, both numerically and analytically, to recover the classical solutions derived through the Airy stress function.
Air Entrainment During Steady-State Web Winding
Authors: Keshavan M. B. , Wickert J. A.
Published: February 2008

As a web is wound at speed onto a roll, a thin layer of air becomes entrapped between it and the incoming web stream. The resulting spiral-shaped air bearing separates adjacent web layers and can extend many wraps into the roll. The air entrained during the winding process increases the propensity for lateral interlayer slippage and damage to the edges of the web. In the present paper, an in situ technique is developed for measuring the thickness of the entrained air film during winding, and parameter studies quantify the effects of such winding variables as tension, width, transport speed, and surface roughness. With a view towards evaluating different transport designs and operating conditions, three measures of air entrainment are discussed: (i) the cumulative thickness of all air layers, (ii) the thickness of the outermost air layer at the nip, and (iii) the rate at which air bleeds from the roll once it comes to rest. Measured values of the first two metrics are compared with those predicted by a derived two-dimensional reduced-order model for steady-state winding. The analysis treats the two bounding configurations of symmetric and asymmetric stacking of web layers by specifying appropriate cross-web pressure profiles.
A Quasi-Decoupling Approach for Nonclassical Linear Systems in State Space
Authors: Ren Gexue , Zheng Zhaochang
Published: February 2008

By adopting the orthogonal transformations provided by the generalized real Schur decomposition, it is shown that every nonclassical linear system in state space can be transformed into block upper triangular form, to which the quasi-decoupling solution can be progressively carried out by solving the either first or second-order component equations with the “back substitution.” The distinct characteristics of generalized eigenvalue problems from those of standard ones are discussed. Favorable properties of the proposed method include: no inverting of any system matrix, indiscriminate applicability to both defective and nondefective systems, the simultaneous decoupling of the adjoint problem, and numerical stability. Illustrative examples are also presented.
Stochastic Averaging of Quasi-Integrable Hamiltonian Systems
Authors: Zhu W. Q. , Huang Z. L. , Yang Y. Q.
Published: February 2008

A stochastic averaging method is proposed to predict approximately the response of quasi-integrable Hamiltonian systems, i.e., multi-degree-of-freedom integrable Hamiltonian systems subject to lightly linear and (or) nonlinear dampings and weakly external and (or) parametric excitations of Gaussian white noises. According to the present method an n-dimensional averaged Fokker-Planck-Kolmogrov (FPK) equation governing the transition probability density of n action variables or n independent integrals of motion can be constructed in nonresonant case. In a resonant case with α resonant relations, an (n + α)-dimensional averaged FPK equation governing the transition probability density of n action variables and α combinations of phase angles can be obtained. The procedures for obtaining the stationary solutions of the averaged FPK equations for both resonant and nonresonant cases are presented. It is pointed out that the Stratonovich stochastic averaging and the stochastic averaging of energy envelope are two special cases of the present stochastic averaging. Two examples are given to illustrate the application and validity of the proposed method.
Time-Integral Variational Principles for Nonlinear Nonholonomic Systems
Authors: Papastavridis J. G.
Published: February 2008

This is a comprehensive treatment of the time-integral variational “principles” of mechanics for systems subject to general nonlinear and possibly nonholonomic velocity constraints (i.e., equations of the form f(t, q, q˙) = 0, where t = time and q/q˙ = Lagrangean coordinates/velocities), in general nonlinear nonholonomic coordinates. The discussion is based on the Maurer-Appell-Chetaev-Hamel definition of virtual displacements and subsequent formulation of the corresponding nonlinear transitivity (or transpositional) equations. Also, a detailed analysis of the latter supplies a hitherto missing clear geometrical interpretation of the well-known discrepancies between the equations of motion obtained by formal application of the calculus of variations (mathematics) and those obtained from the principle of d’Alembert-Lagrange (mechanics); i.e., admissible adjacent paths (mathematics) are locally nonvirtual; and adjacent paths built from locally virtual displacements (mechanics) are not admissible. (These discrepancies, although revealed about a century ago, for systems under Pfaffian constraints (Hertz (1894), Ho¨lder (1896), Hamel (1904), Maurer (1905), and others) seem to be relatively unknown and/or misunderstood among today’s engineers.) The discussion includes all relevant nonlinear nonholonomic variational principles, in both unconstrained and constrained forms of their integrands, and the corresponding nonlinear nonholonomic equations of motion. Such time-integral formulations are useful both conceptually and computationally (e.g., multibody dynamics).
The Fiber-Matrix Interface Crack
Authors: Chao R. , Laws N.
Published: February 2008

The problem of an interface crack between a circular fiber and the surrounding matrix is considered. The problem is formulated and solved with the help of complex variable methods. It is essential to take into account the existence of contact zones at the crack tips. The solution procedure relies on the use of crack opening displacements as the primary variables. Ultimately the governing equations are shown to consist of two coupled singular integral equations together with contact and single valuedness conditions. In general these equations must be solved by numerical methods. Attention is focused on the lengths of the contact zones. It is shown that the lengths of these contact zones are essentially independent of one of the Dundurs parameters.
A Theoretical Prediction of Natural Frequency of a Ferromagnetic Beam Plate With Low Susceptibility in an In-Plane Magnetic Field
Authors: Zhou You-He , Miya Kenzo
Published: February 2008

In order to simulate the experimental phenomenon of increase of natural frequency to a cantilevered ferromagnetic beam plate in in-plane magnetic fields, a theoretical model for behaving the magnetoelastic interaction is proposed in this paper based on the variational principle of energy functional of the system. It is found that the expression of magnetic force is distinctly different from those of the existing theoretical models in publications, and the experimental phenomenon is successfully simulated by this theoretical model. After the increase of natural frequency is quantitatively considered in the predictions of magnetic damping, the theoretical predictions of magnetic damping ratio are agreement with the corresponding experimental data well.
Chaotic Motions of a Dual-Spin Body
Authors: Or A. C.
Published: February 2008

The dynamics of a dual-spinner subject to the action of an internal oscillatory torque and Coulomb friction between the two linked bodies is investigated. The conditions for existence of transverse homoclinic points and homoclinic tangency of chaotic motions are obtained using Melnikov’s method. Through long-term numerical integration of the equations of motion, steady-state chaotic attractors are also found and studied numerically by varying the forcing amplitude.
A Two-Dimensional Model of the Fluid Dynamics of an Air Reverser
Authors: Mu¨ftu¨ S. , Lewis T. S. , Cole K. A. , Benson R. C.
Published: February 2008

A theoretical analysis of the fluid mechanics of the air cushion of the air reversers used in web-handling systems is presented. A two-dimensional model of the air flow is derived by averaging the equations of conservation of mass and momentum over the clearance between the web and the reverser. The resulting equations are Euler’s equations with nonlinear source terms representing the air supply holes in the surface of the reverser. The equations are solved analytically for the one-dimensional case and numerically for the two-dimensional case. Results are compared with an empirical formula and the one-dimensional airjet theory developed for hovercraft. Conditions that maximize the air pressure supporting the web are analyzed and design guidelines are deduced.
Three-Dimensional Axisymmetric Piezothermoelastic Solution of a Transversely Isotropic Piezoelectric Clamped Circular Plate
Authors: Kapuria S. , Dumir P. C. , Segupta S.
Published: February 2008

Three-dimensional solution in terms of potential functions is presented for a transversely isotropic piezoelectric clamped circular plate subjected to axisymmetric ther-moelectromechanical load. The boundary conditions are satisfied using Fourier-Bessel expansions yielding two uncoupled infinite systems of algebraic equations for the arbitrary constants. These are solved to any desired degree of accuracy by truncating to finite set of equations. Results are presented to illustrate the effect of the thickness parameter. These would help assess two-dimensional theories of piezoelectric plates.
The Dependence of the Time Scale of Relative Lagrangian Motion on the Initial Separation
Authors: Fung J. C. H.
Published: February 2008

Kinematic simulation of homogeneous isotropic turbulence are used to compute Lagrangian statistics of turbulence and, in particular, its time scales. The computed pseudo-Lagrangian velocity autocorrelation functions Rˆ11L(l,t) compare well with theory for a small initial separation l and short time t. We also demonstrate the feasibility of using kinematic simulation as a means of constructing Lagrangian statistics.
Canonical Perturbation of a Fast Time-Periodic Hamiltonian via Liapunov-Floquet Transformation
Authors: Butcher E. A. , Sinha S. C.
Published: February 2008

In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic, the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent canonical perturbation theory may be successfully applied. For this purpose, the Liapunov-Floquet (L-F) transformation and its inverse associated with the unperturbed time-periodic quadratic Hamiltonian are computed using a recently developed technique. Action-angle variables and time-dependent canonical perturbation theory are then utilized to find the solution in the original coordinates. The results are compared for accuracy with solutions obtained by both numerical integration and by the classical method of directly applying the time-dependent perturbation theory in which the time-periodic quadratic part is treated as another perturbation term. A strongly excited Mathieu-Hill quadratic Hamiltonian with a cubic perturbation and a nonlinear time-periodic Hamiltonian without a constant quadratic part serve as illustrative examples. It is shown that, unlike the classical method in which the internal excitation must be weak, the proposed formulation provides accurate solutions for an arbitrarily large internal excitation.
Paradoxes in Rigid-Body Kinematics of Structures
Authors: Mentrasti L.
Published: February 2008

The paper discusses two paradoxes appearing in the kinematic analysis of interconnected rigid bodies: there are structures that formally satisfy the classical First and Second Theorem on kinematic chains, but do not have any motion. This can arise when some centers of instantaneous rotation (CIR) relevant to two bodies coincide with each other (first kind paradox) or when the CIRs relevant to three bodies lie on a straight line (second kind paradox). In these cases two sets of new theorems on the CIRs can be applied, pointing out sufficient conditions for the nonexistence of a rigid-body motion. The question is clarified by applying the presented theory to several examples.
On the Dynamics of Vibration Absorbers With Motion-Limiting Stops
Authors: Luo H. , Hanagud S.
Published: February 2008

The dynamics of a class of vibration absorbers with elastic stops is discussed in this paper. The mechanical model proposed in previously published papers are modified to explain certain nonlinear effects, chaotic vibrations, and lower damping observed in our studies. Refined contact-noncontact criteria are presented. Exact steady-state solutions are obtained for a piecewise linear system by using the proposed contact-noncontact criteria. Numerical simulations are presented and compared with the results of the previous work. Significant differences that have been found include some chaotic responses of the system. Experiments are conducted to validate the theoretical results. Chaotic and period-2 responses are also detected experimentally.
A Variational Framework for Solution Method Developments in Structural Mechanics
Authors: Park K. C. , Felippa C. A.
Published: February 2008

We present a variational framework for the development of partitioned solution algorithms in structural mechanics. This framework is obtained by decomposing the discrete virtual work of an assembled structure into that of partitioned substructures in terms of partitioned substructural deformations, substructural rigid-body displacements and interface forces on substructural partition boundaries. New aspects of the formulation are: the explicit use of substructural rigid-body mode amplitudes as independent variables and direct construction of rank-sufficient interface compatibility conditions. The resulting discrete variational functional is shown to be variation-ally complete, thus yielding a full-rank solution matrix. Four specializations of the present framework are discussed. Two of them have been successfully applied to parallel solution methods and to system identification. The potential of the two untested specializations is briefly discussed.
Finite Element Analysis of Rolling Contact Problems Using Minimum Dissipation of Energy Principle
Authors: Rathore S. K. , Kishore N. N.
Published: February 2008

In steady rolling motion, the loads and the fields of strain, stress, and deformations do not change with time at the contact region, as the contact region is continuously being formed by a new rolling surface. The principle of minimum dissipation of energy and the concept of traveling finite elements are made use of in solving such problems and the determination of micro-slips. The conditions of contact are discovered by use of the kinematic constraints and the Coulomb’s law of friction. A two-dimensional plane-strain finite element method along with the iterative procedure is used. The results obtained are in good agreement with expected behavior.
Use of “Simple Solutions” in Regularizing Hypersingular Boundary Integral Equations in Elastoplasticity
Authors: Poon H. , Mukherjee S. , Ahmad M. Fouad
Published: February 2008

The subject of this paper is the use of “simple solutions” or “modes” to regularize a hypersingular boundary integral equations (HBIE) for small strain elastoplasticity. A particularly simple form of the regularized HBIE is obtained by the use of three global “modes” of deformation: rigid-body displacement, linear displacement, and a fully constrained plastic solution. The resulting regularized HBIE is used in an implicit boundary element method (BEM) scheme for solving elastoplasticity problems. Numerical results are presented for an illustrative plane-strain example.
Effect of the T-Stress in Microcrack Shielding Problems
Authors: Zhao LiGuo , Chen YiHeng
Published: February 2008

The effect of the T-stress in microcrack shielding problems is studied by solving the interaction problem of a macrocrack with near tip microcracks applying a discrete model. The T-stress has no effect on the results for the parallel microcrack cases; however, it plays an important role for the oriented microcrack cases, especially for large values of the T-stress and large distances of the microcrack center from the macrocrack tip. In determining the shielding or amplification effect of the oriented microcracks, it is necessary to consider the effect of the T-stress. The effect of the T-stress on microcrack shielding or amplification is substantially dependent on the sign and magnitude of the T-stress as well as on the geometry of the microcrack arrangement. The contribution to the J-integral induced from the microcracks is reexamined by considering the T-stress and shown to be still in a consistent relation with those induced from the macrocrack tip and the remote stress field.
Analysis of Conducting Rigid Inclusion at the Interface of Two Dissimilar Piezoelectric Materials
Authors: Deng Wei , Meguid S. A.
Published: February 2008

This paper is concerned with the electro-elastic analysis of a conducting rigid line inclusion at the interface of two bonded piezoelectric materials. By combining the analytic function theory and the Stroh formalism, we were able to obtain closed-form expressions for the field variables. Both the mechanical stresses and the electric displacement are shown to have at least one of the following behaviors: (i) traditional square root singularity; (ii) nonsquare root singularity; and (iii) oscillatory singularity, which depend upon the electro-elastic mismatch at the interface. By using the static equilibrium conditions, the rigid rotation vector of the inclusion is determined and the extended stress singularity factors (ESSF) are evaluated.
The Energy Release Rate in the General Delamination Problem of Anisotropic Laminates Under Thermomechanical Loads
Authors: Yin Wan-Lee
Published: February 2008

A simple formulation, directly in terms of the local variables of the laminated plate theory, is used to derive the general expression of the energy release rate at a boundary point of an arbitrarily shaped delamination in a multilayered anisotropic laminate under combined mechanical and temperature loads. The intact and de-bonded sublaminates are modeled using the first-order shear deformation theory. If the thermoelastic constitutive equations of the sublaminates are linear and uncoupled, then the expression of the energy release rate may be reduced to a simple form depending only on the sublaminate stiffness coefficients and the local values of the midplane strains and curvatures. The expression does not explicitly involve the temperature load, and is also independent of the strain and curvature parameters tangential to the delamination front. The corresponding expression for delamination in classical laminated plates is also given. The results are applied to the problem of a laminated strip with a fully developed edge delamination loaded under axial extension, bending, and twisting.
Kinematic Description of Damage
Authors: Park Taehyo , Voyiadjis G. Z.
Published: February 2008

In this paper the kinematics of damage for finite elastic deformations is introduced using the fourth-order damage effect tensor through the concept of the effective stress within the framework of continuum damage mechanics. However, the absence of the kinematic description of damage deformation leads one to adopt one of the following two different hypotheses. One uses either the hypothesis of strain equivalence or the hypothesis of energy equivalence in order to characterize the damage of the material. The proposed approach in this work provides a relation between the effective strain and the damage elastic strain that is also applicable to finite strains. This is accomplished in this work by directly considering the kinematics of the deformation field and furthermore it is not confined to small strains as in the case of the strain equivalence or the strain energy equivalence approaches. The proposed approach shows that it is equivalent to the hypothesis of energy equivalence for finite strains. In this work, the damage is described kinematically in the elastic domain using the fourth-order damage effect tensor which is a function of the second-order damage tensor. The damage effect tensor is explicitly characterized in terms of a kinematic measure of damage through a second-order damage tensor. The constitutive equations of the elastic-damage behavior are derived through the kinematics of damage using the simple mapping instead of the other two hypotheses.
The Axisymmetric Deformation of Linearly and Nonlinearly Elastic Spinning Tubes Under End Thrusts and Torques
Authors: McDevitt T. J. , Simmonds J. G.
Published: February 2008

We consider the steady-state deformations of elastic tubes spinning steadily and attached in various ways to rigid end plates to which end thrusts and torques are applied. We assume that the tubes are made of homogeneous linearly or nonlinearly anisotropic material and use Simmonds” (1996) simplified dynamic displacement-rotation equations for shells of revolution undergoing large-strain large-rotation axisymmetric bending and torsion. To exploit analytical methods, we confine attention to the nonlinear theory of membranes undergoing small or large strains and the theory of strongly anisotropic tubes suffering small strains. Of particular interest are the boundary layers that appear at each end of the tube, their membrane and bending components, and the penetration of these layers into the tube which, for certain anisotropic materials, may be considerably different from isotropic materials. Remarkably, we find that the behavior of a tube made of a linearly elastic, anisotropic material (having nine elastic parameters) can be described, to a first approximation, by just two combined parameters. The results of the present paper lay the necessary groundwork for a subsequent analysis of the whirling of spinning elastic tubes under end thrusts and torques.
Dynamic Fracture Criteria for Crack Growth Along Bimaterial Interfaces
Authors: Kavaturu M. , Shukla A.
Published: February 2008

Dynamic fracture criteria based on experimental observations are proposed for subsonic crack growth along bimaterial interfaces. These criteria are based on the premise that the crack-face displacements at a point behind the crack tip increase exponentially with the instantaneous crack-tip velocity. This assumption establishes a generalized relationship between the dynamic energy release rate and the instanta-neous crack-tip velocity. Experiments are performed on PSM-1/aluminum bimaterial systems for both shear dominated and opening-mode dominated crack growth to verify the proposed criteria. Two different bimaterial specimen geometries are employed to obtain the complete range of crack-tip speeds in the subsonic regime. The dynamic loading is achieved either by detonating two explosive charges on the specimen or by impacting the specimen in one-point bend configuration. Dynamic photoelasticity in conjunction with high-speed photography is used to analyze the fracture event. Explosive loading of the interface crack results in crack propagation speeds on the order of 65 percent of the shear wave speed of PSM-1 and the crack growth is observed to be stable and opening-mode dominated. In contrast, the impact loading results in very high crack propagation speeds on the order of shear wave speed of PSM-1 and the crack growth is observed to be shear dominated.
On Random Field Discretization in Stochastic Finite Elements
Authors: Zeldin B. A. , Spanos P. D.
Published: February 2008

Several traditional methods for discretizing random fields in stochastic mechanics applications are considered; they are the midpoint method, the interpolation method, and the local averaging method. A simple and computationally convenient criterion for estimating the accuracy of these discretization methods is developed. Also, the Volterra series representation of nonlinear input/output relationships is utilized to assess the effect of the random field discretization methods on the response variability of stochastic mechanics problems. The theoretical developments are elucidated by a numerical example involving a beam problem.
Refined Dynamic Stability Theory of Laminated Isotropic Circular Plates
Authors: Krizhevsky G. , Stavsky Y.
Published: February 2008

Hamilton’s variational principle is used for the derivation of transversally isotropic laminated circular plates motion. Nonlinear strain-displacements relations are considered. Linearized dynamic stability equations are obtained for circular plates subjected to the same uniformly distributed periodic radial loads. The effects of transverse shear and rotational inertia are included. The exact solutions of vibrations and buckling problems are given initially in the terms of Bessel, power, and trigonometric functions. The vibrational modal functions are used then as a basis in the Galerkin method that reduced the study of dynamic stability to investigation of bounds of instability of Mathieu’s equations. Analytic expressions for the bounds of both principal and combination-type instability regions are obtained using the methods of Bolotin and Tamir. A new effect—sensitivity of certain instability regions to slight imperfections in the symmetry of lamination—is found out and discussed here.
Stress and Deformation Fields Around a Cylindrical Cavity Embedded in a Pressure-Sensitive Elastoplastic Medium
Authors: Bradford I. D. R. , Durban D.
Published: February 2008

The problem of an internally pressurized cylindrical cavity under remote nonequibiaxial compression is examined within the framework of small strain theory. The cavity is embedded in a medium with a pressure-sensitive elastoplastic, strain-hardening and nonassociative response. The stress and deformation fields around the cavity are derived using a Drucker-Prager type deformation theory under the assumption of plane strain. The symmetry conditions allow the solution to be expanded as a Fourier cosine series in the circumferential direction. The Fourier coefficients are functions of the radial coordinate and are governed by a coupled system of ordinary differential equations. Numerical examples illustrate the evolution of the elastoplastic interface, together with the variation in both the stress concentration factor and the displacements at the cavity surface, due to increasing remote load.
Linear and Nonlinear Elasticity of Granular Media: Stress-Induced Anisotropy of a Random Sphere Pack
Authors: Johnson D. L. , Schwartz L. M. , Elata D. , Berryman J. G. , Hornby B. , Norris A. N.
Published: February 2008

We develop an effective medium theory of the nonlinear elasticity of a random sphere pack based upon the underlying Hertz-Mindlin theory of grain-grain contacts. We compare our predictions for the stress-dependent sound speeds against new experimental data taken on samples with stress-induced uniaxial anistropy. We show that the second-order elastic moduli, Cijkl, and therefore the sound speeds, can be calculated as unique path-independent functions of an arbitrary strain environment, {εkl}, thus generalizing earlier results due to Walton. However, the elements of the stress tensor, σij, are not unique functions of {εkl} and their values depend on the strain path. Consequently, the sound speeds, considered as functions of the applied stresses, are path dependent. Illustrative calculations for three cases of combined hydrostatic and uniaxial strain are presented. We show further, that, even when the additional applied uniaxial strain is small, these equations are not consistent with the usual equations of third-order hyperelasticity. Nor should they be, for the simple reason that there does not exist an underlying energy function which is simply a function of the current state of the strain. Our theory provides a good understanding of our new data on sound speeds as a function of uniaxial stress.
Interaction and Microfracturing Pattern for Successive Origination (Introduction) of Pores in Elastic Bodies: Finite Deformation
Authors: Levin V. A. , Zingerman K. M.
Published: February 2008

The elastic interaction of holes, micropores, and narrow slots (cracks), introduced (originated) successively or simultaneously in previously loaded bodies, is analyzed under finite deformations. Their origination raises an additional finite deformations superimposed on the finite initial ones. The influence of mutual positions of holes, distances between them, their eccentricities and sizes on interaction is investigated. Qualitative and quantitative effects concerned with the finiteness of strains are considered.
Response of a Nonconservative Continuous System to a Moving Concentrated Load
Authors: Pesterev A. V. , Bergman L. A.
Published: February 2008

The problem of calculating the response of a general class of nonconservative linear distributed parameter systems excited by a moving concentrated load is investigated. A method of solution based on the series expansion of the response in terms of complex eigenfunctions of the continuous system is proposed. A set of ordinary differential equations in the time-dependent coefficients of the expansion is established in terms of the unknown force of interaction on the continuum, which allows one to investigate different models of concentrated loads. For the case of a conservative oscillator moving with arbitrarily varying speed, the coefficients of the equations are obtained in explicit terms. Some results of numerical experiments involving a proportionally damped beam are presented.
How the Raleigh Flow Transits to Blasius Numerically
Authors: Sarma G. N.
Published: February 2008

This paper answers the question numerically how a two-dimensional incompressible Rayleigh boundary layer started impulsively past a semi-infinite flat plate with uniform velocity in the mainstream transits to steady Blasius flow. It is shown that the transition is a convective transition and smooth with no discontinuities. It is effected by the parameters called the convective and angular parameters. The velocity field gets disintegrated into discrete dissimilar diffusive layers of different convective orders. This is an example based on modified boundary layer theory of Sarma. Polynomial solutions are found using the theory of definite thickness boundary layers and the method of weighted residuals. This modifies the numerical works of Hall and Dennis, which are based on Stewartson’s theory of propagation of disturbances.
Stress Singularities at the Apex of a Dissimilar Anisotropic Wedge
Authors: Lin Y. Y. , Sung J. C.
Published: February 2008

The complex form of the characteristic equation for the stress singularities of the order rλ-1(0<Re[λ]<1) for the dissimilar anisotropic wedges is derived. Special attention is then focused on the problems that are composed by two orthotropic materials. For such problems the characteristic equation is expressed in real forms from which the dependence of the singularities on the material parameters and wedge angles is investigated. The case of a single free-fixed wedge problem is particularly studied in detail. Numerical results for several special wedge geometries are also presented.