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TECHNICAL PAPERS

J. Appl. Mech. 1995;62(3):557-565. doi:10.1115/1.2895981.

This paper considers point force or point moment loading applied to the surface of a three-dimensional wedge. The wedge is two-dimensional in geometry but the loading may vary in a direction parallel to the wedge apex, thus creating a three-dimensional problem within the realm of linear elasticity. The wedge is homogeneous, isotropic, and the assumption of incompressibility is taken in order for solutions to be obtained. The loading cases considered presently are as follows: point normal loading on the wedge face, point moment loading on the wedge face, and an arbitrarily directed force or moment applied at a point on the apex of the wedge. The solutions given here are closed-form expressions. For point force or point moment loading on the wedge face, the elastic field is given in terms of a single integral containing associated Legendre functions. When the point force or moment is at the wedge tip, closed-form (nonintegral) expressions are obtained in terms of elementary functions. An interesting result of the present research indicates that the wedge paradox in two-dimensional elasticity also exists in the three-dimensional case for a concentrated moment at the wedge apex applied in one direction, but that it does not exist for a moment applied in the other two directions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):566-572. doi:10.1115/1.2895982.

The determination of the effective moduli for a material containing elliptical inclusions is the objective of this paper. This is done by incorporating an inclusion/matrix/composite model into a general energy equivalence framework. Through the evaluation of the average strain in each individual inclusion, the current approach can handle the inclusion’s orientation dependency in a straightforward manner. The case of an in-plane isotropic distribution of elliptical inclusions is addressed in detail. For the case of reinforcements, or hard inclusions, the effect of the inclusion aspect ratio on in-plane effective moduli is small if the aspect ratio is larger than 0.5. For aspect ratios less than 0.3, the effective moduli increase dramatically, which implies that flat reinforcements are much more effective than traditional cylindrical reinforcements. It is also established that the generalized self-consistent method predicts a stronger dependence of effective moduli on the inclusion aspect ratio than does the Mori-Tanaka method, especially for shear moduli.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):573-578. doi:10.1115/1.2895983.

It is difficult to obtain explicit expressions of Green’s function for elastic medium with general anisotropy. The difficulty is associated with an integration of functions with high degrees of singularity. In this paper, we propose a method employing extend functions. This method avoids the difficulty of singularities and renders an explicit series expression of Green’s function for general anisotropic conditions. Analytical expression of the coefficients in the series are provided. Numerical examples are given to evaluate the applicability of this method.

Topics: Anisotropy , Functions
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):579-584. doi:10.1115/1.2895984.

The displacement and stress fields caused by uniform eigenstrains in a circular cylindrical inclusion are analyzed inside the region x12 + x22 < a2, −∞ < x3 < ∞ and are given in terms of nonsingular surface integrals. Analytical solutions can be expressed as functions of the complete elliptic integrals of the first, second and third kind. The corresponding elastic fields in the region x12 + x22 > a2, −∞ < x3 < ∞ are solved by using the same technique (by Green’s functions) in the companion paper (Part II).

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):585-589. doi:10.1115/1.2895985.

Analytical solutions are presented for the displacement and stress fields caused by a circular cylindrical inclusion with arbitrary uniform eigenstrains in an infinite elastic medium. The expressions obtained and those presented in Part I constitute the solutions of the whole elastic field, −∞ < x1, x2, x3 < ∞. In the present paper, it is found that the analytical solutions within the region x12 + x22 > a2, −∞ < x3 < ∞ can also be expressed as functions of the complete elliptic integrals of the first, second, and third kind. When the length of inclusion tends towards the limit (infinity), the present solutions agree with Eshelby’s results. Finally, numerical results are shown for the stress field.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):590-594. doi:10.1115/1.2895986.

A pair of two new tensors called GPS tensors S and D is proposed for the concentric cylindrical inclusion problem. GPS tensor S relates the strain in the inclusion constrained by the matrix of finite radius to the uniform transformation strain (eigenstrain), whereas tensor D relates the strain in the matrix to the same eigenstrain. When the cylindrical matrix is of infinite radius, tensor S reduces to the appropriate Eshelby’s tensor. Explicit expressions to evaluate thermal residual stresses σr , σθ and σz in the matrix and the fiber using tensor D and tensor S , respectively, are developed. Since the geometry of the present problem is of finite radius, the effect of fiber volume fraction on the stress distribution can be easily studied. Results for the thermal residual stress distributions are compared with Eshelby’s infinite domain solution and finite element results for a specified fiber volume fraction.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):595-600. doi:10.1115/1.2895987.

It is well known that a thin elastic shell under external pressure may undergo buckling and collapse. Less well known is that a hollow beam under internal pressure may buckle as an Euler column. This is the subject of the present study. The buckled deflection and natural frequency about the buckled configuration of a vertical pipe with clamped (y -axis) and hinged (z -axis) boundary conditions at the lower support location, considering the influence of internal pressure and initial (manufactured) curvature, has been studied analytically and experimentally. The buckling and post-buckling behavior of the pipe beam with an initial static deflection depends upon the nonlinear coupling due to deflection in the two directions including the anisotropic boundary condition at the one support location. The coupling effects increase as the internal pressure and the initial static deflection increase. When the initial static deflection is zero, the coupling effect disappears. The theoretical results agree reasonably well with the experiments.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):601-606. doi:10.1115/1.2895988.

The problem of non-coplanar crack propagation in homogeneous and bimaterial sheets is investigated within the framework of the nonlinear theory of plane stress and for the Generalized Neo-Hookean class of hyperelastic solids. The analysis is performed numerically using a boundary layer approach and the maximum energy release rate criterion. The influence of the large deformation effect on the limiting process associated with the concept of “infinitesimal virtual crack extension” is examined, together with the possible relation between the size of the nonlinear zone and the additional length parameter appearing in the linearized analysis of the interfacial crack propagation problem. As the virtual crack extension is gradually shortened to a size comparable to that of the nonlinear zone, a transition is observed between the nonunique value of the kink angle predicted by the linearized theory and a single “nonlinear” value, which is independent of the crack extension length but also independent of the far-field loading conditions. In the limit of homogeneous properties this angle is zero and is corroborated by experiments on natural rubber undergoing large deformations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):607-613. doi:10.1115/1.2895989.

The strip element method (SEM) has been extended to investigate wave scattering by cracks in anisotropic laminated plates. The cracked plates are divided into domains in which the extended SEM is applied. For each domain a set of SEM equations is obtained which gives a relationship between the traction and displacement vectors on the vertical boundaries. These equations are solved by using the conditions at the junctures of the domains. To obtain the time domain response a Fourier transform technique is used, and an exponential window method is introduced to avoid singularities in the Fourier integration. For composite plates with horizontal and vertical cracks, scattered wave fields in both the time and frequency domains are computed, and discussed in comparison with results for uncracked plates. A technique for determining the length of a crack in a plate is also presented. It is shown that the SEM is an efficient technique for the calculation of elastodynamic fields in cracked anisotropic laminated plates.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):614-619. doi:10.1115/1.2895990.

This paper presents the plane elastostatics analysis of a semi-infinite crack perpendicular to a perfectly bonded bimaterial interface. Both cases of the crack approaching the interface and penetrating the interface are addressed. The distance from the tip of the crack to the interface is δ. A singular integral equation approach is used to calculate the stress intensity factor, K I , and the crack-opening displacement at the interface, η, as functions of δ, the Dundurs parameters α and β, and the stress intensity factor k I associated with the same crack terminating at the interface (the case δ = 0). The results are presented as KI = kIδ1/2−λf(α, β) and η = CkIδ1−λη̃(α, β) where λ is the strength of the stress singularity associated with δ = 0, f and η̃ are functions calculated numerically and C is a material constant. These results can be used to determine the stress intensity factor and crack opening displacement of cracks of finite length 2a with one tip at a distance δ from the interface for δ/a ≪ 1. The selected results presented for a crack loaded by a uniform far-field tension in each half-plane show that the stress intensity factors approach their limits at a relatively slow rate.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):620-625. doi:10.1115/1.2895991.

A buckling instability in a system where a straight edge crack lies at the interface between a thin elastic film and a substrate is analysed theoretically and experimentally. The buckling, which can occur also under remote tensile loads, may result in crack growth before the conventional criterion for fracture is met on the straight crack front by enhancing the mode adjusted crack driving force. If crack growth occurs, buckling will cause a wavy crack front to develop.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):626-632. doi:10.1115/1.2895992.

Experiments to study the yield surface of 304 stainless steel with either 20 percent tension or 20 percent shear prestrain have been conducted. Explicit transformation equations have also been derived to convert the experimentally determined first Piola-Kirchhoff stress components into the Cauchy stresses and the second Piola-Kirchhoff stresses for combined axial-torsional experiments. It has been found that, in the phenomenological approach, the stress measure and the definition of yield have significant effect on the degree of anisotropy of strain-hardening. In particular, the strain-hardening rule is extremely complicated if the second Piola-Kirchhoff stress is used. Also, the equivalent stress-strain curves have been investigated by means of different stress measures.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):633-639. doi:10.1115/1.2895993.

The present work examines the inertial effects on void growth in viscoplastic materials which have been largely neglected in analyses of dynamic crack growth and spallation phenomena using existing continuum porous material models. The dynamic void growth in porous materials is investigated by analyzing the finite deformation of an elastic/viscoplastic spherical shell under intense hydrostatic tensile loading. Under typical dynamic loading conditions, inertia is found to have a strong stabilizing effect on void growth process and consequently to delay coalescence even when the high rate-sensitivity of materials at very high strain rates is taken into account. Effects of strain hardening and thermal softening are found to be relatively small. Approximate relations are suggested to incorporate inertial effects and rate sensitivity of matrix materials into the porous viscoplastic material constitutive models for dynamic ductile fracture analyses for certain loading conditions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):640-645. doi:10.1115/1.2895994.

Continuum damage mechanics (CDM) is considered as a general method to treat the progressive deterioration of materials and structures in the framework of continuum mechanics. The damage-coupled creep mechanics based on CDM is discussed in the paper first, including the description of effective stress concept and the expression of all field equations in creep. The general formulation of a constitutive relation is presented after simplifying treatment for the sake of the modeling of creep damage problem in computational mechanics. The parametric variational principle (PVP) developed from the idea of optimal theory is introduced to establish the numerical principle of structural analysis for damage-coupled creep mechanics, including both the associated potential variational principle and the corresponding FEM formulations. The possibility of applying the principle presented by this paper to the life and damage prediction of structural components is finally illustrated by some examples on creep experiments for three kinds of materials.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):646-653. doi:10.1115/1.2895995.

A straightforward procedure is demonstrated for measuring local cyclic elastoplastic biaxial stresses at notch roots. First, the biaxial cyclic strains are measured over short gage lengths (150 or 200 micrometers) with a laser-based strain measuring system. Then, cyclic stresses are computed from those measured strains by using an elastoplastic constitutive model. The material selected for this study is HY-80 steel which has a fine grain size and is isotropic. Double-notched specimens were prepared with two different notch geometries: a U-shaped notch with a 4.76 mm radius and a V-shaped notch with a 1.0 mm radius. Two thicknesses, 2.54 and 12.7 mm, were tested for each notch geometry to produce four different amounts of notch constraint. The results of cyclic biaxial strain measurements show good reproducibility. Stress computations based on two different constitutive models were used to compute stresses for the first cycle and a stable cycle. One of the constitutive models is the classical J 2 flow theory and the other is a two-surface cyclic plasticity model. The results computed using these two models show good agreement with each other. The measured stresses show the effect of constraint on the elastoplastic behavior at notch roots under cyclic loading conditions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):654-661. doi:10.1115/1.2895996.

Axial rates of diffusion of the symmetrical state of stress caused by equal but opposed normal forces acting on opposite sides of an indefinitely long strip or plate, are examined in the context of orthotropic elastic materials. To obtain the stress components for this boundary value problem, the imposed surface tractions are represented by a Fourier integral. At distances larger than one quarter of the thickness, the normal stress on the middle surface is closely represented by the sum of eigenfunctions for this problem, up to, and including the first complex eigenfunction as well as its conjugate. Each eigenfunction is a product of exponentially decreasing and oscillatory terms. The exponential term is more significant for determining the rate of diffusion of stress in materials with a large ratio of axial to transverse Young’s moduli E x /Ey ≥ 3; this term shows a strong dependence on the ratio of transverse Young’s modulus to shear modulus E y /G.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):662-666. doi:10.1115/1.2895997.

A finite solid cylinder rotates inside a larger, fluid-filled cylindrical casing. The Stokes equation is solved by an efficient method using domain decomposition, eigenfunction expansion, and collection. The resistive torque is found as a function of the geometric parameters. The torque due to the rotation of a finite cylinder in an infinite fluid is extrapolated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):667-673. doi:10.1115/1.2895998.

A hybrid spectral/finite difference method is developed in this paper for the analysis of three-dimensional unsteady viscous flows between concentric cylinders subjected to fully developed laminar flow and executing transverse oscillations. This method uses a partial spectral collocation approach, based on spectral expansions of the flow parameters in the transverse coordinates and time, in conjunction with a finite difference discretization of the axial derivatives. The finite difference discretization uses central differencing for the diffusion derivatives and a mixed central-upwind differencing for the convective derivatives, in terms of the local mesh Reynolds number. This mixed scheme can be used with coarser as well as finer axial mesh spacings, enhancing the computational efficiency. The hybrid spectral/finite difference method efficiently reduces the problem to a block-tridiagonal matrix inversion, avoiding the numerical difficulties otherwise encountered in a complete three-dimensional spectral-collocation approach. This method is used to compute the unsteady fluid-dynamic forces, the real and imaginary parts of which are related, respectively, to the added-mass and viscous-damping coefficients. A parametric investigation is conducted to determine the influence of the Reynolds and oscillatory Reynolds (or Stokes) numbers on the axial variation of the real and imaginary components of the unsteady forces. A semi-analytical method is also developed for the validation of the hybrid spectral method, in the absence of previous accurate solutions or experimental results for this problem. Good agreement is found between these very different methods, within the applicability domain of the semi-analytical method.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):674-678. doi:10.1115/1.2895999.

A bulk-flow thermohydrodynamic (THD) analysis is developed for prediction of the static and dynamic performance characteristics of turbulent-flow, process-liquid, hydrostatic journal bearings (HJBs). Pointwise evaluation of temperature and hence liquid properties is achieved through the solution of the energy equation in the fluid film with insulated boundaries, and justified for fluid film bearings with external pressurization. Fluid inertia within the film lands and at recess edges is preserved in the analysis. Flow turbulence is accounted through turbulence shear parameters based on friction factors derived from Moody’s formulae. The effects of fluid compressibility and temperature variation in the bearing recesses are included. Numerical solution and results are presented in the second part of this work and compared with some limited experimental data for a liquid hydrogen (LH2 ) bearing.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):679-684. doi:10.1115/1.2896000.

A finite difference scheme is implemented to solve the nonlinear differential equations describing the turbulent bulk-flow on the film lands of a hydrostatic journal bearing (HJB). A Newton-Raphson scheme is used to update the recess pressures and to satisfy the mass continuity requirement at each bearing recess. Comparisons of numerical predictions from the thermohydrodynamic (THD) model with experimental measurements of mass flow rate, fluid temperature, and static stiffness coefficient from a LH2 test HJB article show very good agreement. In particular, the exit temperature of the bearing is lower than the supply temperature; i.e., the liquid temperature decreases along the bearing length. Similar values of direct stiffness and damping coefficients are predicted by the adiabatic THD model and other considering isothermal flow characteristics. However, the THD model predicts lower cross-coupled stiffness and whirl frequency ratio (WFR < 0.5). The results show that for the application presented, the LH2 hydrostatic bearing is more stable than previously thought.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):685-691. doi:10.1115/1.2896001.

The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to systems with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):692-698. doi:10.1115/1.2896002.

A method to identify both the impact location and the transverse impact force history from the strain responses at certain points on a rectangular plate is presented. The governing equations of the plate were obtained by applying the Reissner-Mindlin plate theory and the Rayleigh-Ritz method. The strain response was related to the impact force by solving the above equations using the eigenmode expansion method. A mutuality relationship among any pairs of strain responses was used to find the impact location without knowing in advance the impact force history. The force history was subsequently determined after the impact location was identified. The conjugate gradient method was adopted to search for the optimal impact location as well as the force history. Numerical verification was performed using randomly generated impact locations and force histories to simulate impact events. The excellent agreement showed the effectiveness and the validity of the proposed method.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):699-705. doi:10.1115/1.2896003.

Experimental verification of the method developed in Part 1 to identify both the impact location and the force history from strain responses on a rectangular plate was performed. Results showed the validity of the method in a real impact event. Also, a method was developed to further identify the initial velocity and the mass of an impactor by which a transverse impact was induced. This was accomplished by solving algebraic equations obtained from the assumption that the lateral displacements of both the impactor and the plate at the impact point were coincident during the contact period. Moreover, the inverse problem using incomplete response signals as the given data was investigated. A procedure to temporarily reconstruct the lost portions of the recorded signals was first presented, and the identification problem could then be solved by similar methods as that used for the complete response signals. Experimental verification was also performed. The agreement between the measured and the identified results was very satisfactory.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):706-708. doi:10.1115/1.2897003.

A Ritz approach, with simple polynomials as trial functions, is used to obtain the natural frequencies of vibration of a class of solids. Each solid is modeled by means of a segment which is described in terms of Cartesian coordinates and is bounded by the yz , zx , and xy orthogonal coordinate planes as well as by a fourth curved surface, which is defined by a polynomial expression in the coordinates x , y , and z . By exploiting symmetry, a number of three-dimensional solids previously considered in the open literature are treated, including a sphere, a cylinder and a parallelepiped. The versatility of the approach is then demonstrated by considering several solids of greater geometric complexity, including an ellipsoid, an elliptical cylinder, and a cone.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):709-717. doi:10.1115/1.2897004.

The main difference between a linear system and a nonlinear system is in the non-uniqueness of solutions manifested by the singular Jacobian matrix. It is important to be able to express the Jacobian accurately, completely, and efficiently in an algorithm to analyze a nonlinear system. For periodic response, the incremental harmonic balance (IHB) method is widely used. The existing IHB methods, however, requiring double summations to form the Jacobian matrix, are often extremely time-consuming when higher order harmonic terms are retained to fulfill the completeness requirement. A new algorithm to compute the Jacobian is to be introduced with the application of fast Fourier transforms (FFT) and Toeplitz formulation. The resulting Jacobian matrix is constructed explicitly by three vectors in terms of the current Fourier coefficients of response, depending respectively on the synchronizing mass, damping, and stiffness functions. The part of the Jacobian matrix depending on the nonlinear stiffness is actually a Toeplitz matrix. A Toeplitz matrix is a matrix whose k , r position depends only on their difference k-r . The other parts of the Jacobian matrix depending on the nonlinear mass and damping are Toeplitz matrices modified by diagonal matrices. If the synchronizing mass is normalized in the beginning, we need only two real vectors to construct the Toeplitz Jacobian matrix (TJM), which can be treated in one complex fast Fourier transforms. The present method of TJM is found to be superior in both computation time and storage than all existing IHB methods due to the simplified explicit analytical form and the use of FFT.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):718-724. doi:10.1115/1.2897005.

A three-dimensional elasticity solution to the vibrations of stress-free hollow cylinders of arbitrary cross section is presented. The natural frequencies and deformed mode shapes of these cylinders are obtained via a three-dimensional displacement-based energy formulation. The technique is applied specifically to the parametric investigation of hollow cylinders of different cross sections and sizes. It is found that the cross-sectional property of the cylinder has significant effects on the normal mode responses, particularly, on the transverse bending modes. By varying the length-to-width ratio of these elastic cylinders, interesting results demonstrating the dependence of frequencies on the length of the cylinder have been concluded.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):725-732. doi:10.1115/1.2897006.

This article deals with three-dimensional collisions of rigid, kinematic chains with an external surface while in contact with other surfaces. We concentrate on a special class of kinematic chain problems where there are multiple contact points during the impact process. A differential formulation based algorithm is used to obtain solutions that utilize the kinematic, kinetic, and the energetic definitions of the coefficient of restitution. Planar and spatial collisions of a three-link chain with two contact points are numerically studied to compare the outcomes predicted by each approach. Particular emphasis is placed on the relation between the post and pre-impact energies, slippage and rebounds at the contact points, and differences among planar and nearly planar three-dimensional solutions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):733-739. doi:10.1115/1.2897008.

A constitutive model for finite elastoplastic deformations is presented. This model incorporates two novel features: first, a strain-hardening law that is applicable to complex loading paths and histories; and second, an objective stress-rate measure that is based on the spin of an orthogonal triad of material unit vectors which instantaneously coincides with the principal directions of the stress tensor. Problems of shear superposed on triaxial tension, cyclic shear deformation, and biaxial nonproportional loading are studied. It is shown that realistic predictions for the aforementioned problems are obtained by using the proposed constitutive model.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):740-746. doi:10.1115/1.2897009.

The equations of motion that define three-dimensional rigid-body impact with finite friction and restitution cannot be solved in a closed form. Previous work has shown that for general shapes and initial conditions, the direction of sliding velocity keeps changing continuously throughout the duration of impact. The flow patterns defined by the trace of the sliding velocity can be classified into a finite number of qualitatively distinct physical behavior. We identify three dimensionless parameters that completely specify the sliding behavior, and determine regions in this parameter space that correspond to each of the different flow patterns. The qualitative behavior during impact can now be determined based on the region which contains the parameters for a given impact configuration. The analysis is also used to study the sensitivity of the sliding behavior to changes in shape or configuration of the body and to rule out the occurrence of certain ambiguities in the post-sticking behavior during impact.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):747-755. doi:10.1115/1.2897010.

This paper presents a general formulation of the nonlinear and linear analysis of wire ropes. In the formulation, wires, strands, and wire ropes are all considered as a kind of identical structure characterized by seven stiffness and deformation constants, and as such they can be used, in the same way, as component elements in some layered general structures. Based on such a point of view, the general formulation thus developed can be used to analyze wire ropes of various complex cross sections, and to analyze simple wire strands as well.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):756-763. doi:10.1115/1.2897011.

A new theory of sandwich beams/one-dimensional plates is presented with finite rotations and shear allowed in each layer. The layers, variable in number from one to three, need not have the same thickness and the same length, thus allowing for ply drop-off. Restricting to planar deformation, the cross section has a motion identical to that of a multibody system that consists of rigid links connected by hinges. Large deformation and large overall motion are accommodated, with the beam dynamics referred directly to an inertial frame. An important approximated theory is developed from the general nonlinear equations. The classical linear theory is recovered by consistent linearization.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):764-771. doi:10.1115/1.2897012.

The instability mechanisms of a rotating disk, coupled to a rigid surface through a viscous fluid film at the interface, are investigated analytically. The fluid in the film is driven circumferentially by the viscous shear, and it flows outwards radially under centrifugal forces. The circumferential flow component creates an equivalent viscous damping rotating at one half the disk rotation speed. This film damping dissipates all backward traveling waves where the undamped wave speeds are greater than one half the disk rotation speed. The radial flow component creates a nonsymmetric stiffness in the disk-film system that energizes any wave mode at rotation speeds above its flutter speed. Instabilities in the disk-film system are of two types. A rotating damping instability is caused by the rotating film damping at rotation speeds above a critical value that is less than the flutter speed. A combination instability is caused by the combined effect of the film stiffness and damping at rotation speeds above a threshold that is greater than the flutter speed. The maximum rotation speed of stable disk vibration is bounded above by the lowest onset speed of rotating damping instability. This speed limit is predicted for two wall enclosure designs. The maximum stable rotation speed of a 5.25-inch diameter flexible, memory disk, separated from a rigid surface by a viscous air film, is shown to be more than 15 times greater than the maximum speed of the disk without the air film.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):772-779. doi:10.1115/1.2897013.

Von Karman nonlinear plate equations are modified to describe the motion of a wide, axially moving web with small flexural stiffness under transverse loading. The model can represent a paper web or plastic sheet under some conditions. Closed-form solutions to two nonlinear, coupled equations governing the transverse displacement and stress function probably do not exist. The transverse forces arising from the bending stiffness are much smaller than those arising from the applied axial tension except near the edges of the web. This opens the possibility that boundary layer and singular perturbation theories can be used to model the bending forces near the edges of the web when determining the equilibrium solution and stress distribution. The present analysis is applied to two examples: (I) a web deflecting under its own uniformly distributed weight; (II) a web deflecting under a transverse load whose distribution is described by the product of sine functions in the axial and width directions. Membrane theory and linear plate theory solutions are used to characterize the importance of the web deformation solutions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):780-785. doi:10.1115/1.2897014.

Although most materials are anisotropic to some extent, most yield surfaces are either chosen to be isotropic or to be a smooth anisotropic surface with no connection to the elastic anisotropic features. Here, the elastic projection operators obtained from the spectral decomposition of the elasticity tensor are used to define anisotropic yield surfaces with a yield surface defined for each of the projection operators. The advantages of the approach are (1) plastic deformation modes are associated with the elastic anisotropic behavior, (2) the spectral decomposition of the tangent tensor is readily available for a bifurcation analysis, (3) the composite yield surface has vertices which are thought to be important for predicting plastic buckling, and (4) the contributions to plastic deformations from each yield surface are uncoupled. The result is a theory that is actually quite simple but yet reflects some of the observed features for materials to yield in specific modes.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):786-793. doi:10.1115/1.2897015.

In this paper the viscoelastostatic problem of composite materials with periodic microstructure is studied. The matrix is assumed linear viscoelastic and the fibers elastic. The correspondence principle in viscoelasticity is applied and the problem in the Laplace domain is solved by using the Fourier series technique and assuming the Laplace transform of the homogenization eigenstrain piecewise constant in the space. Formulas for the Laplace transform of the relaxation functions of the composite are obtained in terms of the properties of the matrix and the fibers and in function of nine triple series which take into account the geometry of the inclusions. The inversion to the time domain of the relaxation and the creep functions of composites reinforced by long fibers is carried out analytically when the four-parameter model is used to represent the viscoelastic behavior of the matrix. Finally, comparisons with experimental results are presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):794-801. doi:10.1115/1.2897016.

Large-amplitude oscillatory shear (LAOS) experiments were conducted at different temperatures on a molten low-density polyethylene standard, designated IUPAC LDPE X. Jeyaseelan et al. (1993) have successfully employed a simplification of transient network theory to describe the LAOS behavior of this polymer melt, at 150°C. The transient network is described by two kinetic rate constants, one for the formation of entanglements due to Brownian motion (k 1 ), and another for the destruction of entanglements (k 2 ) due to the imposed deformation. Upon comparison of the predictions of this transient network theory with the measured LAOS behavior of this polymer, we find that the kinetic rate constants k 1 and k 2 are invariant in the range of temperatures examined (150 to 190°C). The temperature dependence of departures from linear viscoelasticity is fully accounted for in the equilibrium entanglement kinetics.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):802-809. doi:10.1115/1.2897017.

A common difficulty in the analysis and design of transmission and distribution lines is to determine a conductor’s tension and its static profile under concentrated loads. For relatively small concentrated loads (such as detuning pendulums on transmission lines), approximation methods may give good predictions. For large concentrated loads (such as fallen trees on distribution lines), however, exact solutions must be found. This paper presents methodologies to compute conductor tension and static profile in three-dimensional space using both approximate and exact solution procedures under concentrated loads with different boundary conditions. Practical engineering examples from galloping control of transmission lines and mechanical coordination of distribution lines are given to demonstrate the applicability of the theory.

Commentary by Dr. Valentin Fuster

ERRATA

BRIEF NOTES

J. Appl. Mech. 1995;62(3):810-811. doi:10.1115/1.2897018.

This note is concerned with thermoelastic analysis of a multilayered anisotropic medium under the state of generalized plane deformation with interlayer thermal contact resistance. The powerful flexibility/stiffness matrix method is adopted here to obtain the complete solution of the entire layered medium by introducing the thermal and mechanical boundary and layer interface conditions including interlayer imperfect thermal contact conditions. As a numerical illustration, the effects of interlayer thermal resistance on the distributions of temperatures and thermal stresses in a laminated anisotropic slab subjected to a uniform surface temperature rise are presented.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):813-816. doi:10.1115/1.2777115.

Residual internal stresses often remain in materials after thermal-mechanical processes. Considerable deformation, such as elastic buckling, may result from such stresses. Some cases of circular-plate buckling due to internal membrane forces are analyzed in this work. The internal membrane-force field is introduced with a nonuniform radial temperature distribution in the disk. Detailed analysis is performed and critical buckling criteria are tabulated for some specific sets of parameters. Although the membrane force in the plate is axially symmetric, symmetry breaking is found at buckling. When the temperature is higher at the disk center, the first buckling mode is domeshaped, which maintains the polar symmetry. The mode of buckling, however, changes to a saddle shape when the radial temperature distribution is reversed.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):818-819. doi:10.1115/1.2897021.
Abstract
Topics: Vibration , Cylinders
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):819-820. doi:10.1115/1.2897022.

If a piece of homogeneous anisotropic elastic material is subject to simple tension along a direction n for which Young’s modulus E(n ) is an extremum, then the corresponding strain field is coaxial with the simple tension stress field. An appropriate set of rectangular cartesian coordinate axes may be introduced such that three of the elastic compliances are zero. In this coordinate system the displacement field may be written explicitly and corresponds to a pure homogeneous deformation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):820-822. doi:10.1115/1.2897023.
Abstract
Topics: Motion , String , Rods
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1995;62(3):822-823. doi:10.1115/1.2897024.
Abstract
Commentary by Dr. Valentin Fuster

BOOK REVIEW

J. Appl. Mech. 1995;62(3):824. doi:10.1115/1.2897026.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

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