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TECHNICAL PAPERS

J. Appl. Mech. 1998;65(1):1-6. doi:10.1115/1.2789026.

This paper addresses the question of how to assess the errors made when the exact three-dimensional linear elasticity solution for the axisymmetric dynamic deformation of an elastic plate is approximated by a solution inferred from the classical plate theory of Kirchhoff. Following the strategy used by Ladevèze and Simmonds for beams, the exact solution of a “nearby” three-dimensional problem, which differs from the original problem by the addition of incremental, computable body forces, face shears, and initial conditions—error increments, for short—is expressed in terms of the solution of a wave equation in which distance normal to the plate’s midplane plays the role of a time-like variable while the physical time itself enters only as a parameter. The error increments which, ultimately, can be computed in terms of the solution delivered by plate theory, can be regarded as an “engineering norm” because with them an engineer can decide if such a shift in the external data lies within acceptable bounds.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):7-16. doi:10.1115/1.2789050.
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):17-24. doi:10.1115/1.2789023.

A dynamic vibration absorber with a viscoelastic element is studied. The viscoelastic element is modeled as a material with memory in which the internal dissipative force depends on current, as well as previous deformations. The viscoelastic behavior is governed by two parameters: the relaxation modulus Go , and the relaxation time γ. We apply the principle of time-temperature superposition to affect a dependence of the relaxation time γ on temperature. This temperature dependence can be used to tune a vibration absorber so as to be effective at more than one excitation frequency.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):25-29. doi:10.1115/1.2789035.

An asymmetric increase in the apparent values of the interfacial fracture toughness with increasing mode II component of loading has been observed by several investigators. In this study, cracks were grown in a steady-state manner along the glass/epoxy interface in sandwich specimens in order to determine the mechanisms responsible for the shielding effect. Finite element analysis using a hydrostatic stress and strain rate dependent plasticity model for the epoxy and a cohesive zone model for the interface shows that plastic dissipation in the epoxy accounts for the asymmetric shielding seen in these experiments which cover a wide range of mode mix. Numerical predictions of normal crack-opening displacements yielded results that were consistent with measured values which were made as close as 0.3 μm from the crack tip.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):30-38. doi:10.1115/1.2789042.

A general method is presented to obtain the rigorous solution for a circular inclusion embedded within an infinite matrix with a circumferentially inhomogeneous sliding interface in plane elastostatics. By virtue of analytic continuation, the basic boundary value problem for four analytic functions is reduced to a first-order differential equation for a single analytic function inside the circular inclusion. The finite form solution is obtained that includes a finite number of unknown constants determined by the analyticity of the solution and certain other auxiliary conditions. With this method, the exact values of the average stresses within the circular inclusion can be calculated without solving the full problem. Several specific examples are used to illustrate the method. The effects of the circumferential variation of the interface parameter on the mean stress at the interface and the average stresses within the inclusion are discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):39-45. doi:10.1115/1.2789043.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):46-50. doi:10.1115/1.2789044.

The Mullins effect (Mullins, 1947), also known as stress softening, is exhibited by certain rubberlike materials and refers to changes of the mechanical properties, due to prior deformation. Johnson and Beatty (1995) have investigated the Mullins effect in equibiaxial tension by performing cycles of static inflation and deflation experiments on latex balloons. These experiments show that stress softening results in a decrease in the pressure necessary to inflate a balloon, and in addition, indicate inelastic effects of hysteresis and permanent set. The objective of this paper is to investigate the finite deformation static inflation from the virgin state, followed by quasi-static removal of the internal pressure, of a thick-walled homogeneous spherical shell composed of an incompressible isotropic rubberlike material which exhibits stress softening and permanent set. Since the initial inflation of the shell, due to application of an internal pressure, does not result in a homogeneous deformation, a state of residual stress is present after complete removal of the internal pressure. A procedure is presented for the determination of the response of the shell for the first cycle of inflation and deflation from the virgin state, and the analysis includes strain softening and the inelastic effects of hysteresis and permanent set. It is assumed that, for the initial static inflation of the shell from the virgin state, the internal pressure and stress distribution for a monotonically increasing internal or external radius are the same as for a hyperelastic shell, and also that the magnitude of the permanent set of an element of the material is related monotonically to the deformation at the end of the inflation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):51-58. doi:10.1115/1.2789045.

A general analytical solution for the elliptical anisotropic inclusion embedded in an infinite anisotropic matrix subjected to uniform heat flow is provided in this paper. Based upon the method of Lekhnitskii formulation, the technique of conformal mapping, the method of analytical continuation, and the concept of superposition, both the solutions of the temperature and stress, functions either in the matrix or in the inclusion are expressed in complex matrix notation. Numerical results are carried out and provided in graphic form to elucidate the effect of material and geometric parameters on the interfacial stresses. Since the general solutions have not been found in the literature, comparison is made with some special cases of which the analytical solutions exist, which shows that our solutions presented here are exact and general.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):59-65. doi:10.1115/1.2789046.

This paper derives the exact frequency equation for the toroidal mode of vibrations for a spherically isotropic elastic sphere. The vibrations of spherically isotropic solids are solved by introducing two wave potentials (Φ and Ψ) such that the general solutions for free vibrations can be classified into two independent modes of vibrations, namely the “toroidal” and “spheroidal” modes. Both of these vibration modes can be written in terms of spherical harmonics of degree n. The frequency equation for the toroidal modes is obtained analytically, and it depends on both n and β [ = (C11 – C12)/(2C44)], where C11 C12, and C44 have the usual meaning of moduli and are defined in Eqs. (2)–(3); and, as expected, Lamb’s (1882) classical frequency equation is recovered as the isotropic limit. Numerical results show that the normalized frequency ωa/Cs increases with both n and β, where ω is the circular frequency of vibration, a the radius of the sphere, and Cs is the shear wave speed on the spherical surfaces. The natural frequencies for spheres of transversely isotropic minerals and crystals, with β ranging from 0.3719 to 1.8897, are also tabulated. However, two coupled differential equations are obtained for the spheroidal modes, which remain to be solved.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):66-70. doi:10.1115/1.2789047.

We formulate and solve the boundary value problem of a linearly elastic, infinite Cosserat plate which contains a circular hole and which is loaded in tension at infinity. The effect of hole radius, plate thickness, and material parameters on the stress concentration at the hole is discussed. We also discuss the stress concentration when the plate is subjected to pure shear.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):71-75. doi:10.1115/1.2789048.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):76-84. doi:10.1115/1.2789049.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):85-92. doi:10.1115/1.2789051.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):93-98. doi:10.1115/1.2789052.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):99-106. doi:10.1115/1.2789053.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):107-115. doi:10.1115/1.2789012.

The large deflections of a clamped circular plate are investigated over a wide range of transverse loadings and initial in-plane tension loads. The continuous transition from plate behavior to membrane behavior is described in detail, along with the development of the accompanying edge zone region where properties change rapidly. We give a simple approximation of this edge zone and its properties, provide limits for the validity of small deflection, linear theory, and note the similar effects of large in-plane tension and large transverse loading. The values and trends are presented in general nondimensional form, and should prove useful for the design of thin circular disks for microsensing applications.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):116-120. doi:10.1115/1.2789013.

This paper uses Lyapunov’s method to determine the critical speed of a flexible spinning disk enclosed in a housing that hydrodynamically couples the transverse motion of the disk to the motion of the thin films of air surrounding the disk. Depending on the clamping ratio, this critical speed is three to ten times higher than the critical speed in the absence of hydrodynamic coupling and does not depend on the strength of the hydrodynamic coupling. Despite the nonlinearity of the underlying model, the critical speed problem is linear and tractable. The linearized free-vibration problem is also computed to verify the stability prediction and to examine linearized damping and stiffness as possible design criteria. The results are relevant to the design of both conventional computer floppy disks and the emerging generation of 100+ MB floppies.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):121-126. doi:10.1115/1.2789014.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):127-133. doi:10.1115/1.2789015.

This paper presents initial results from a program to develop a “rapid screening test” for determining the in-plane fiber distributions in unidirectionally reinforced composite structures by the use of the vibration response measurements and Galerkin’s method. Theoretical models and experimental data are generated on the basis of two methods: (1) the “shifting method,” in which the effective length of the beam is changed, and (2) the “added mass method”, in which the mass distribution of the beam is changed. The elastic constants and the density are all assumed to be functions of fiber volume fraction, while the spatial distribution of the fiber volume fraction is assumed to be given by a polynomial function. The concept of an effective density is employed to obtain the appropriate solution to the coefficients of the polynomial function. Results show that the fundamental mode gives rise to better predictions of physical properties than the higher modes do. An error analysis includes discussion of the errors due to the influences of the mode number, the assumed order of the polynomial in the fiber volume fraction distribution, and the bending-extension coupling effect caused by the unsymmetrical distribution of properties about the beam middle surface.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):134-140. doi:10.1115/1.2789016.

In order to provide analytical eigenvalue estimates for general continuous gyroscopic systems, this paper presents a perturbation analysis to determine approximate eigenvalue loci and stability conclusions in the vicinity of critical speeds and zero speed. The perturbation analysis relies on a formulation of the general continuous gyroscopic system eigenvalue problem in terms of matrix differential operators and vector eigenfunctions. The eigenvalue λ appears only as λ2 in the formulation, and the smoothness of λ2 at the critical speeds and zero speed is the essential feature. First-order eigenvalue perturbations are determined at the critical speeds and zero speed. The derived eigenvalue perturbations are simple expressions in terms of the original mass, gyroscopic, and stiffness operators and the critical-speed/zero-speed eigenfunctions. Prediction of whether an eigenvalue passes to or from a region of divergence instability at the critical speed is determined by the sign of the eigenvalue perturbation. Additionally, eigenvalue perturbation at the critical speeds and zero speed yields approximations for the eigenvalue loci over a range of speeds. The results are limited to systems having one independent eigenfunction associated with each critical speed and each stationary system eigenvalue. Examples are presented for an axially moving tensioned beam, an axially moving string on an elastic foundation, and a rotating rigid body. The eigenvalue perturbations agree identically with exact solutions for the moving string and rotating rigid body.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):141-149. doi:10.1115/1.2789017.

This paper develops a theory for geometrically nonlinear waves in strings and presents analytical solutions for a traveling kink, generation of a geometric wave with its accompanying P wave, reflection of a kink at a fixed support and at a smooth sliding support, and interaction of a P wave and a kink. Conditions that must be satisfied for linear wave theory to hold are derived. The nonlinear theory is demonstrated by extending an historically important solution of the barrage balloon problem that was obtained during World War II.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):150-156. doi:10.1115/1.2789018.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):157-163. doi:10.1115/1.2789019.

In the work based on the stiffness method reported in this paper, considering the rotary inertia, the axial and shear deformation terms, the natural frequencies of conical, barrel and hyperboloidal-type helical springs fixed at both ends are calculated. The results are presented in dimensionless graphical forms for the six lowest natural frequencies of all types of noncylindrical helices for a wide range of vibrational parameters which influence the natural frequencies. A discussion about the effects of vibrational parameters on the natural frequencies is also presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):164-170. doi:10.1115/1.2789020.

A discrete vortex model based on the panel method has been developed to simulate the two-dimensional unsteady separated flow generated by the rapid deployment of a spoiler on the upper surface of an airfoil. This method represents the boundary surfaces by distributing piecewise linear-vortex and constant source singularities on discrete panels. The wake of the spoiler and airfoil is represented by discrete vortices. At each sharp edge, a vortex sheet is used to feed discrete vortices at every time-step to form the downstream wake. The length and strength of each shed vortex sheet are determined by the continuity equation and a condition such that the flow, the net force, and the pressure difference across the vortex sheet are zero. The flow patterns behind the spoiler at different time-steps are presented. The pressure distributions on the airfoil based on the unsteady Bernoulli’s equation are compared, where possible, with the experimental results and other computational results. The adverse lift effects have been obtained, and similar effects have been measured in experiments.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):171-177. doi:10.1115/1.2789021.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):178-183. doi:10.1115/1.2789022.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):184-193. doi:10.1115/1.2789024.

An elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell is presented. The solution is achieved by the proper usage of integral transforms such as the finite Hankel transform and the Laplace transform. No restrictive assumptions on the shell thickness are placed. Results are presented for the well-formed wave propagation phenomenon of elastic stresses through the thickness of an orthotropic thick cylindrical shell. Thermal shock stresses become of significant magnitude due to stress wave propagation which is initiated at the boundaries by sudden thermal loading.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):194-203. doi:10.1115/1.2789025.

Using adaptive estimation approaches, a method is presented for the on-line identification of hysteretic systems under arbitrary dynamic environments. The availability of such an identification approach is crucial for the on-line control and monitoring of nonlinear structural systems to be actively controlled. In spite of the challenges encountered in the identification of the hereditary nature of the restoring force of such nonlinear systems, it is shown through the use of simulation studies and experimental measurements that the proposed approach can yield reliable estimates of the hysteretic restoring force under a very wide range of excitation levels and response ranges.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):204-208. doi:10.1115/1.2789027.

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 11L(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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):209-217. doi:10.1115/1.2789028.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):218-222. doi:10.1115/1.2789029.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):223-233. doi:10.1115/1.2789030.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):234-241. doi:10.1115/1.2789031.

A model to predict the tension in open spans of web handling systems during transient operations has been developed. Governing equations were developed by using the White-Metzner equation to describe the material response in conjunction with mass and force balances. The governing equations were nondimensionalized and solved via the MacCormack predictor/corrector technique. Two dimensionless parameters emerged from the analysis, the Deborah number, De, and the ratio of the viscous stress to the steady state stress, N. The resulting model is the companion to a previously reported model for steady-state operations (Guan et al, 1995). The model was used to predict the behavior of a web handling system during start-up, transition between steady states, and a periodic disturbance. During start-up and transition, systems responded more rapidly at low De. The system response during a periodic disturbance was correlated to De, the frequency, and the magnitude of the disturbance.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):242-249. doi:10.1115/1.2789032.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):250-257. doi:10.1115/1.2789033.

Contact compliance, which may arise from elastic deformation near the contact point or in the surrounding structure, affects the dynamical friction behaviors in mechanical oscillators. An idealized model consisting of a mass sliding harmonically on a mass-less compliant contact produces hysteresis in friction-velocity plots. Dynamical friction features, depending on the contact stiffness, friction level, and the frequency and amplitude of oscillation, are predicted and quantified. Contact compliance can also lead to oscillations at the transition from slip to stick. Experiments and simulations verify the model and tie together phenomena of both continuous sliding and stick-slip.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):258-265. doi:10.1115/1.2789034.

The transient response of a structure is predicted using an asymptotic modal approximation of the classical modal solution. The method is aimed at estimating the impulse response problem for high frequency regimes where typical numerical methods (e.g., finite elements) are impractical. As an example, the response of a thin elastic panel is modeled in a frequency range that includes a sufficient number of modes. Both impulsive and arbitrary forms of excitation are considered. It is shown that the asymptotic modal analysis yields an excellent estimate of both the local displacement near the excitation location and of the spatially averaged transient response of the panel for moderate time spans after the excitation is applied. Furthermore, as this approach does not require that the mode shapes or natural frequencies of the structure to be calculated, it is an extremely efficient technique.

Commentary by Dr. Valentin Fuster

BRIEF NOTES

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):268-271. doi:10.1115/1.2789037.
Abstract
Topics: Plasticity
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):271-273. doi:10.1115/1.2789038.

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.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1998;65(1):273-276. doi:10.1115/1.2789039.
Abstract
Topics: Force
Commentary by Dr. Valentin Fuster

DISCUSSION

Commentary by Dr. Valentin Fuster

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