Showing papers in "Journal of Applied Mechanics in 2002"
TL;DR: An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented in this paper, which provides dimensionless expressions for the contact load, contact area and mean contact pressure, covering a large range of interference values from yielding inception to fully plastic regime of the spherical contact zone.
Abstract: An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented. The evolution of the elastic-plastic contact with increasing interference is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. The model provides dimensionless expressions for the contact load, contact area, and mean contact pressure, covering a large range of interference values from yielding inception to fully plastic regime of the spherical contact zone. Comparison with previous elastic-plastic models that were based on some arbitrary assumptions is made showing large differences. ©2002 ASME
867 citations
TL;DR: In this article, a generalized isoparametric formulation of graded finite elements is presented for boundary value problems involving continuously nonhomogeneous isotropic and orthotropic materials, and the performance of graded elements is compared to that of conventional homogeneous elements with reference to analytical solutions.
Abstract: Graded finite elements are presented within the framework of a generalized isoparametric formulation. Such elements possess a spatially varying material property field, e.g. Young's modulus (E) and Poisson's ratio () for isotropic materials; and principal Young's moduli (E11,E22), in-plane shear modulus (G12), and Poisson's ratio (12) for orthotropic materials. To investigate the influence of material property variation, both exponentially and linearly graded materials are considered and compared. Several boundary value problems involving continuously nonhomogeneous isotropic and orthotropic materials are solved, and the performance of graded elements is compared to that of conventional homogeneous elements with reference to analytical solutions. Such solutions are obtained for an orthotropic plate of infinite length and finite width subjected to various loading conditions. The corresponding solutions for an isotropic plate are obtained from those for the orthotropic plate. In general, graded finite elements provide more accurate local stress than conventional homogeneous elements, however, such may not be the case for four-node quadrilateral (Q4) elements. The framework described here can serve as the basis for further investigations such as thermal and dynamic problems in functionally graded materials. ©2002 ASME
380 citations
TL;DR: In this paper, the authors link the indentation size effect (ISE) to a ratio between the energy of newly created surface and plastic strain energy dissipation, and propose an analytical model of hardness versus depth.
Abstract: For very shallow indentations in W, Al, Au, and Fe-3wt%Si single crystals, hardness decreased with increasing depth irrespective of increasing or decreasing strain gradients. As such, strain gradient theory appears insufficient to explain the indentation size effect (ISE) at depths less than several hundred nanometers. Present research links the ISE to a ratio between the energy of newly created surface and plastic strain energy dissipation. Also, the contact surface to plastic volume ratio was nearly constant for a range of shallow depths. Based on the above, an analytical model of hardness versus depth provides a satisfactory fit to the experimental data and correlates well with embedded atom simulations. ©2002 ASME
253 citations
TL;DR: In this article, a four-parameter constitutive model for lap-type joints is proposed to predict the force/displacement results from arbitrary load histories, based on matching joint stiffness under low load, the force necessary to initiate macroslip, and experimental values of energy dissipation in harmonic loading.
Abstract: The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in built-up structures. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured through direct numerical simulation (DNS) of the contact mechanics within a structural dynamics analysis. The difficulties of DNS manifest themselves either in terms of Courant times that are orders of magnitude smaller than that necessary for structural dynamics analysis or as intractable conditioning problems. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. In this way, development of constitutive models for joint response is a prerequisite for a predictive structural dynamics capability. A four-parameter model, built on a framework developed by Iwan, is used to reproduce the qualitative and quantitative properties of lap-type joints. In the development presented here, the parameters are deduced by matching joint stiffness under low load, the force necessary to initiate macroslip, and experimental values of energy dissipation in harmonic loading. All the necessary experiments can be performed on real hardware or virtually via fine-resolution, nonlinear quasistatic finite elements. The resulting constitutive model can then be used to predict the force/displacement results from arbitrary load histories.
244 citations
TL;DR: In this paper, a constitutive model is developed to characterize a general class of polymer and polymer-like materials that display hyperelastic orthotropic mechanical behavior and the strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules.
Abstract: A constitutive model is developed to characterize a general class of polymer and polymer-like materials that displays hyperelastic orthotropic mechanical behavior. The strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules and the strain energy change associated with the deformation of a representative orthotropic unit cell. The ability of this model to predict nonlinear, orthotropic elastic behavior is examined by comparing the theory to experimental results in the literature. Simulations of more complicated boundary value problems are performed using the finite element method. ©2002 ASME
192 citations
TL;DR: In this article, the authors studied the problem of a finite crack in a strip of functionally graded piezoelectric material (FGPM) and showed that the singular stresses and electric displacements at the tip of the crack in the FGPM carry the same forms as those in a homogeneous piezolectric materials but that the magnitudes of the intensity factors are dependent upon the gradient of the FG PM properties.
Abstract: In this paper the problem of a finite crack in a strip of functionally graded piezoelectric material (FGPM) is studied. It is assumed that the elastic stiffness, piezoelectric constant, and dielectric permitivity of the FGPM vary continuously along the thickness of the strip, and that the strip is under an antiplane mechanical loading and in-plane electric loading. By using the Fourier transform, the problem is first reduced to two pairs of dual integral equations and then into Fredholm integral equations of the second kind. The near-tip singular stress and electric fields are obtained from the asymptotic expansion of the stresses and electric fields around the crack tip. It is found that the singular stresses and electric displacements at the tip of the crack in the functionally graded piezoelectric material carry the same forms as those in a homogeneous piezoelectric material but that the magnitudes of the intensity factors are dependent upon the gradient of the FGPM properties. The investigation on the influences of the FGPM graded properties shows that an increase in the gradient of the material properties can reduce the magnitude of the stress intensity factor. ©2002 ASME
173 citations
TL;DR: In this paper, the shape of the incident pulse and the specimen thickness must be designed such that the specimens are in dynamic equilibrium and deform homogeneously at constant strain rates, and a sensitive transmission bar is required to detect the weak transmitted pulses.
Abstract: Low-strength and low-impedance materials pose significant challenges in the design of experiments to determine dynamic stress-strain responses. When these materials are tested with a conventional split Hopkinson pressure bar, the specimen will not deform homogeneously and the tests are not valid. To obtain valid data, the shape of the incident pulse and the specimen thickness must be designed such that the specimens are in dynamic equilibrium and deform homogeneously at constant strain rates. In addition, a sensitive transmission bar is required to detect the weak transmitted pulses. Experimental results show that homogeneous deformations at nearly constant strain rates can be achieved in materials with very low impedances, such as a silicone rubber and a polyurethane foam, with the experimental modifications presented in this study. ©2002 ASME
170 citations
TL;DR: In this article, scale-dependent hierarchies of bounds are extended to dissipative/irreversible phenomena within the framework of thermomechanics with internal variables in particular, the free-energy function and the dissipation function become stochastic functionals whose scatter tends to decrease to zero as the volume is increased.
Abstract: Continuum thermomechanics hinges on the concept of a representative volume element (RVE), which is well defined in two situations only: (i) unit cell in a periodic microstructure, and (ii) statistically representative volume containing a very large (mathematically infinite) set of microscale elements (eg, grains) Response of finite domains of material, however, displays statistical scatter and is dependent on the scale and boundary conditions In order to accomplish stochastic homogenization of material response, scale-dependent hierarchies of bounds are extended to dissipative/irreversible phenomena within the framework of thermomechanics with internal variables In particular, the free-energy function and the dissipation function become stochastic functionals whose scatter tends to decrease to zero as the material volume is increased These functionals are linked to their duals via Legendre transforms either in the spaces of ensemble average velocities or ensemble-average dissipative forces In the limit of infinite volumes (RVE limit (ii) above) all the functionals become deterministic, and classical Legendre transforms of deterministic thermomechanics hold As an application, stochastic continuum damage mechanics of elastic-brittle solids is developed ©2002 ASME
137 citations
TL;DR: In this article, a continuum theory of fracture nucleation in single-walled carbon nanotubes was developed by incorporating interatomic potentials between carbon atoms into a continuum constitutive model for the nanotube wall.
Abstract: Carbon nanotubes show great promise for applications ranging from nanocomposites, nanoelectronic components, nanosensors, to nanoscale mechanical probes. These materials exhibit very attractive mechanical properties with extraordinarily high stiffness and strength, and are of great interest to researchers from both atomistic and continuum points of view. In this paper, we intend to develop a continuum theory of fracture nucleation in single-walled carbon nanotubes by incorporating interatomic potentials between carbon atoms into a continuum constitutive model for the nanotube wall. In this theory, the fracture nucleation is viewed as a bifurcation instability of a homogeneously deformed nanotube at a critical strain. An eigenvalue problem is set up to determine the onset of fracture, with results in good agreement with those from atomistic studies. ©2002 ASME
117 citations
TL;DR: In this article, a boundary element method without internal cells is presented for the analysis of elastoplastic problems, based on an effective transformation technique from domain integrals to boundary integrals.
Abstract: In this paper, a new and simple boundary element method without internal cells is presented for the analysis of elastoplastic problems, based on an effective transformation technique from domain integrals to boundary integrals. The strong singularities appearing in internal stress integral equations are removed by transforming the domain integrals to the boundary. Other weakly singular domain integrals are transformed to the boundary by approximating the initial stresses with radial basis functions combined with polynomials in global coordinates. Three numerical examples are presented to demonstrate the validity and effectiveness of the proposed method. ©2002 ASME
111 citations
TL;DR: In this article, nonlinear finite element analyses using the von Mises (yielding is independent of hydrostatic stress) and the Drucker-Prager (Yielding is linearly dependent on hydrostatic tensile stress) yield functions were performed.
Abstract: P. W. Bridgman's early work on flow and fracture in the presence of hydrostatic pressure showed no systematic effect on strain hardening. This experimental observation led to the conclusions that yielding does not depend on hydrostatic stress and that the yielded material is incompressible. Classical plasticity theory was largely built on these observations. New experiments and nonlinear finite element analyses of 2024-T351 aluminum notched round bars has quantified the effect of hydrostatic tensile stresses on yielding. Nonlinear finite element analyses using the von Mises (yielding is independent of hydrostatic stress) and the Drucker-Prager (yielding is linearly dependent on hydrostatic stress) yield functions was performed. The von Mises results overestimated experimental load-displacement curves by 10?65 percent. The Drucker-Prager results essentially matched the experimental results. The only additional data requirement for the Drucker-Prager yield function is the compressive yield strength. ©2002 ASME
TL;DR: In this article, the authors present the general form of the explicit equations of motion for mechanical systems with holonomic and nonholonomic constraints, and the constraint forces may or may not satisfy D'Alembert's principle at each instant of time.
Abstract: This paper presents the general form of the explicit equations of motion for mechanical systems. The systems may have holonomic and/or nonholonomic constraints, and the constraint forces may or may not satisfy D'Alembert's principle at each instant of time. The explicit equations lead to new fundamental principles of analytical mechanics. ©2002 ASME
TL;DR: In this article, a new solution for the identification of physical parameters of mechanical systems from identified state space formulations is presented, where the restriction of having a full set of sensors or actuators for a complete identification is relaxed, and a solution can be achieved by utilizing mixed types of information.
Abstract: In this study a new solution for the identification of physical parameters of mechanical systems from identified state space formulations is presented. With the proposed approach, the restriction of having a full set of sensors or a full set of actuators for a complete identification is relaxed, and it is shown that a solution can be achieved by utilizing mixed types of information. The methodology is validated through numerical examples, and conceptual comparisons of the proposed methodology with previously presented approaches are also discussed. ©2002 ASME
TL;DR: In this paper, the aeroelastic stability of simply supported, circular cylindrical shells in supersonic flow is investigated by using both linear aerodynamics (first-order piston theory) and nonlinear aerodynamic (third order piston theory), and geometric nonlinearities due to finite amplitude shell deformations, and the effect of viscous structural damping is taken into account.
Abstract: The aeroelastic stability of simply supported, circular cylindrical shells in supersonic flow is investigated by using both linear aerodynamics (first-order piston theory) and nonlinear aerodynamics (third-order piston theory). Geometric nonlinearities, due to finite amplitude shell deformations, are considered by using the Donnell's nonlinear shallow-shell theory, and the effect of viscous structural damping is taken into account. The system is discretized by Galerkin method and is investigated by using a model involving up to 22 degrees-of-freedom, allowing for travelling-wave flutter around the shell and axisymmetric contraction of the shell. Asymmetric and axisymmetric geometric imperfections of circular cylindrical shells are taken into account. Numerical calculations are carried out for a very thin circular shell at fixed Mach number 3 tested at the NASA Ames Research Center. Results show that the system loses stability by travelling-wave flutter around the shell through supercritical bifurcation. Nonsimple harmonic motion is observed for sufficiently high post-critical dynamic pressure. A very good agreement between theoretical and existing experimental data has been found for the onset of flutter, flutter amplitude, and frequency. Results show that onset of flutter is very sensible to small initial imperfections of the shells. The influence of pressure differential across the shell skin has also been deeply investigated. The present study gives, for the first time, results in agreement with experimental data obtained at the NASA Ames Research Center more than three decades ago. ©2002 ASME
TL;DR: In this paper, the authors proposed a new theoretical solution for elastic wave propagation in anisotropic curved plates in the circumferential direction in a pipe wall and compared the results with those available in the literature.
Abstract: Ultrasonic nondestructive inspection of large-diameter pipes is important for health monitoring of ailing infrastructure. Longitudinal stress-corrosion cracks are detected more efficiently by inducing circumferential waves; hence, the study of elastic wave propagation in the circumferential direction in a pipe wall is essential. The current state of knowledge lacks a complete solution of this problem. Only when the pipe material is isotropic a solution of the wave propagation problem in the circumferential direction exists. Ultrasonic inspections of reinforced concrete pipes and pipes retrofitted by fiber composites necessitate the development of a new theoretical solution for elastic wave propagation in anisotropic curved plates in the circumferential direction. Mathematical modeling of the problem to obtain dispersion curves for curved anisotropic plates leads to coupled differential equations. Unlike isotropic materials for which the Stokes-Helmholtz decomposition technique simplifies the problem, in anisotropic case no such general decomposition technique works. These coupled differential equations are solved in this paper. Dispersion curves for anisotropic curved plates of different curvatures have been computed and presented. Some numerical results computed by the new technique have been compared with those available in the literature. ©2002 ASME
TL;DR: In this paper, the first six terms of the stress field were obtained for both opening mode and shear mode loading, and it was observed that the structure of the terms other than r?1/2 and r0 are influenced by nonhomogeneity.
Abstract: Stress field for stationary cracks, aligned along the gradient, in functionally graded materials is obtained through an asymptotic analysis coupled with Westergaard's stress function approach. The first six terms of the stress field are obtained for both opening mode and shear mode loading. It is observed that the structure of the terms other than r?1/2 and r0 are influenced by the nonhomogeneity. Using this stress field, contours of constant maximum shear stress are generated and the effect of nonhomogeneity on these contours is discussed. ©2002 ASME
TL;DR: In this paper, an analysis of the frictional mechanics of a steadily rotating belt drive is carried out using a physically appropriate creep-rate-dependent friction law, which predicts no adhesion zones in the belt-pulley contact region.
Abstract: An analysis of the frictional mechanics of a steadily rotating belt drive is carried out using a physically appropriate creep-rate-dependent friction law. Unlike in belt-drive mechanics analyzed using a Coulomb friction law, the current analysis predicts no adhesion zones in the belt-pulley contact region. Regardless of this finding, for the limiting case of a creep-rate law approaching a Coulomb law, all predicted response quantities (including the extent of belt creep on each pulley) approach those predicted by the Coulomb law analysis. Depending on a slope parameter governing the creep-rate profile, one or two sliding zones exist on each pulley, which together span the belt-pulley contact region. Closed-form expressions are obtained for the tension distribution, the sliding-zone arc magnitudes, and the frictional and normal forces per unit length exerted on the belt. A sample two-pulley belt drive is analyzed further to determine its pulley angular velocity ratio and belt-span tensions. Results from this analysis are compared to a dynamic finite element solution of the same belt drive. Excellent agreement in predicted results is found. Due to the presence of arbitrarily large system rotations and a numerically friendly friction law, the analytical solution presented herein is recommended as a convenient comparison test case for validating friction-enabled dynamic finite element schemes. ©2002 ASME
TL;DR: Based on the fractal particle size distribution, a fragmentation theory for quasi-brittle materials is developed in this paper, where three simple and powerful universal laws for the multiscale energy dissipation under impact and explosion fragmentation for one, two, and three-dimensional bodies, respectively.
Abstract: Based on the fractal particle size distribution, a fragmentation theory for quasi-brittle materials is herein developed. The results are three simple and powerful universal laws for the multiscale energy dissipation under impact and explosion fragmentation for one, two, and three-dimensional bodies, respectively. The three-dimensional law unifies the most important and well-known fragmentation theories. As an example, it has been applied to the prediction of the devastated area due to asteroid impacts on earth as a function of the energy released in the collision. ©2002 ASME
TL;DR: In this paper, a phenomenological cohesive fracture model is proposed to control the transition of fracture behavior between the constituents of a TiB/Ti FGM, and the model is applied to analyze crack growth in compact tension, C(T), and single-edge notch bend, SE(B).
Abstract: This work studies mode I crack growth in ceramic/metal functionally graded materials (FGMs) using three-dimensional interface-cohesive elements based upon a new phenomenological cohesive fracture model. The local separation energies and peak tractions for the metal and ceramic constituents govern the cohesive fracture process. The model formulation introduces two cohesive gradation parameters to control the transition of fracture behavior between the constituents. Numerical values of volume fractions for the constituents specified at nodes of the finite element model set the spatial gradation of material properties with standard isoparametric interpolations inside interface elements and background solid elements to define pointwise material property values. The paper describes applications of the cohesive fracture model and computational scheme to analyze crack growth in compact tension, C(T), and single-edge notch bend, SE(B), specimens with material properties characteristic of a TiB/Ti FGM. Young's modulus and Poisson's ratio of the background solid material are determined using a self-consistent method (the background material remains linear elastic). The numerical studies demonstrate that the load to cause crack extension in the FGM compares to that for the metal and that crack growth response varies strongly with values of the cohesive gradation parameter for the metal. These results suggest the potential to calibrate the value of this parameter by matching the predicted and measured crack growth response in standard fracture mechanics specimens. ©2002 ASME
TL;DR: In this paper, an exact solution and an approximate solution using the expansion of transient wave functions in a series of eigenfunctions for the transient response of an infinitely long and multilayered circular cylinder subjected to uniformly distributed dynamic pressures at the boundaries are presented.
Abstract: This paper presents an exact solution and an approximate solution, using the expansion of transient wave functions in a series of eigenfunctions, for the transient response of an infinitely long and multilayered circular cylinder subjected to uniformly distributed dynamic pressures at the boundaries. Numerical results are given to illustrate the effects of the layer properties on the interfacial stresses and the spatial and temporal variations of the displacement and stresses. In particular, the exact solution is used to examine the applicability of the thin shell theories to the transient response of multilayered cylinders. ©2002 ASME
TL;DR: In this article, the authors considered the problem of determining the elastic field in an infinite elastic solid induced by an ellipsoidal inclusion with a distribution of eigenstrains, and the particular type of distribution considered in the article is characterized by a polynomial in the Cartesian coordinates of the points of the inclusion.
Abstract: We consider the problem of determining the elastic field in an infinite elastic solid induced by an ellipsoidal inclusion with a distribution of eigenstrains. The particular type of distribution considered in the article is characterized by a polynomial in the Cartesian coordinates of the points of the inclusion. Eshelby showed that in such a situation the induced strain field within the inclusion is also characterized by a polynomial of the same order. However, the explicit expression for this polynomial seems to have not yet been reported in the literature. The present study fills this gap. ©2002 ASME
TL;DR: In this paper, a clamped circular film is adhered to a rigid cylindrical punch and an external force pulls the punch away causing delamination at the punch-plate interface.
Abstract: A clamped circular film is adhered to a rigid cylindrical punch. An external force pulls the punch away causing delamination at the punch-plate interface. The deflections of the film are discussed for a range of film thickness and stiffness, detailing the continuous transition from a plate under bending to a membrane under stretching. An equilibrium theory of delamination mechanics is derived based on an energy balance. A complete separation at the punch-film interface, or the "pull-off" event, is predicted when the contact circle shrinks to approximately 0.18 of the film diameter. The values and trends, presented in dimensionless normalized form here, should have implications in biological and colloidal sciences in relation to thin-walled capsules and in electronics in relation to thin encapsulating films. ©2002 ASME
TL;DR: In this article, the orthotropic constitutive model is recast using the wormlike chain model in place of the freely jointed chain model and the effects of this alternation are examined.
Abstract: There are many statistical mechanical models of long-chain models, two of which are the freely jointed chain model and the wormlike chain model. A continuum constitutive law for hyperelastic orthotropic materials has recently been developed using the freely jointed chain model as its basis. In this note, the continuum strain energy function is recast in general terms allowing for the incorporation of an arbitrary macromolecular constitutive model. In particular, the orthotropic constitutive model is recast using the wormlike chain model in place of the freely jointed chain model and the effects of this alternation are examined. ©2002 ASME
TL;DR: In this paper, the first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrably Hamiltonian systems subject to light dampings and weakly random excitations) is investigated.
Abstract: The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.
TL;DR: In this article, the authors considered a piezoelectric material strip containing an embedded crack or an edge crack perpendicular to its boundaries and solved the mixed boundary value problem numerically.
Abstract: Considered in this paper is a piezoelectric material strip containing an embedded crack or an edge crack perpendicular to its boundaries. The problem is solved for a strip that is suddenly heated or cooled from the top surface. The bottom surface is assumed to be zero temperature or thermally insulated. First the transient temperature and the stress distributions in an uncracked strip are calculated. Then, these stresses are used as the crack surface traction with opposite sign to formulate the mixed boundary value problem. This leads to a singular integral equation of Cauchy-type, which is then solved numerically. The numerically results for stress intensity factor are computed as a function of the normalized time and the crack size. The temperature and the thermal stress distributions for the uncracked problem are also included. ©2002 ASME
TL;DR: In this article, the authors considered the problem of a surface crack in a semi-infinite elastic graded medium under general loading conditions and solved the problem by approximating the normal and shear tractions on the crack surfaces by polynomials and the normalized modes I and II stress intensity factors.
Abstract: In this study the problem of a surface crack in a semi-infinite elastic graded medium under general loading conditions is considered. It is assumed that first by solving the problem in the absence of a crack it is reduced to a local perturbation problem with arbitrary self-equilibrating crack surface tractions. The local problem is then solved by approximating the normal and shear tractions on the crack surfaces by polynomials and the normalized modes I and II stress intensity factors are given. As an example the results for a graded half-plane loaded by a sliding rigid circular stamp are presented. ©2002 ASME
TL;DR: In this article, Griffith's fracture theory is generalized for cracks in micropolar solids and shown to have two possible forms, i.e., smooth or irregular, and the effect of fractality of fracture surfaces on the powers of stress and couple-stress singularity is studied.
Abstract: this paper we review the fracture mechanics of smooth cracks in micropolar (Cosserat) elastic solids. Griffith's fracture theory is generalized for cracks in micropolar solids and shown to have two possible forms. The effect of fractality of fracture surfaces on the powers of stress and couple-stress singularity is studied. We obtain the orders of stress and couple-stress singularities at the tip of a fractal crack in a micropolar solid using dimensional analysis and an asymptotic method that we call "method of crack-effect zone." It is shown that orders of stress and couple-stress singularities are equal to the order of stress singularity at the tip of the same fractal crack in a classical solid. ©2002 ASME
TL;DR: In this article, a non-dimensional, periodic, linear time-varying model with torsional and lateral degrees-of-freedom is developed for a rotor shaft-disk assembly supported on a flexible bearing and driven through a U-joint.
Abstract: Understanding the instability phenomena of rotor-shaft and driveline systems incorporating universal joints is becoming increasingly important because of the trend towards light-weight, high-speed supercritical designs. In this paper, a nondimensional, periodic, linear time-varying model with torsional and lateral degrees-of-freedom is developed for a rotor shaft-disk assembly supported on a flexible bearing and driven through a U-joint. The stability of this system is investigated utilizing Floquet theory. It is shown that the interaction between torsional and lateral dynamics results in new regions of parametric instability that have not been addressed in previous investigations. The presence of load inertia and misalignment causes dynamic coupling of the torsion and lateral modes, which can result in torsion-lateral instability for shaft speeds near the sum-type combinations of the torsion and lateral natural frequencies. The effect of angular misalignment, static load-torque, load-inertia, lateral frequency split, and auxiliary damping on the stability of the system is studied over a range of shaft operating speeds. Other than avoiding the unstable operating frequencies, the effectiveness of using auxiliary lateral viscous damping as a means of stabilizing the system is investigated. Finally, a closed-form technique based on perturbation expansions is derived to determine the auxiliary damping necessary to stabilize the system for the least stable case (worst case). ©2002 ASME
TL;DR: In this paper, a numerical approach to analyze the pounding responses of adjacent buildings on subsoil to earthquakes is presented, and the nonlinear calculation of the soil-structure system is performed subsequently in the Laplace and the time domain.
Abstract: A numerical approach to analyse pounding responses of adjacent buildings on subsoil to earthquakes is presented. The nonlinear calculation of the soil-structure system is performed subsequently in the Laplace and the time domain. The adjacent buildings and the subsoil are described by finite elements and boundary elements, respectively. In the numerical investigation the effect of Kobe, Northridge and Chi-Chi near-source earthquakes is considered. The result reveals that both the subsoil and long-period pulses in the ground motions can increase the pounding potential of buildings. In addition, poundings can amplify the induced floor vibrations. In contrast, soil-structure interaction has reduction effect on the induced vibrations. In order to estimate the distance required to prevent pounding the influence of the soil-structure interaction is significant.
TL;DR: In this article, closed-form expressions for the total axial deflection and stress distribution using a superposition approach were derived for axially loaded rubber blocks of long, thin rectangular and circular cross section whose ends are bonded to rigid plates.
Abstract: Axially loaded rubber blocks of long, thin rectangular and circular cross section whose ends are bonded to rigid plates are studied. Closed-form expressions, which satisfy exactly the governing equations and conditions based upon the classical theory of elasticity, are derived for the total axial deflection and stress distribution using a superposition approach. The corresponding relations are presented for readily calculating the apparent Young's modulus, Ea, the modified modulus, E, and the deformed lateral profiles of the blocks. From these, improved approximate elementary expressions for evaluating Ea and E are deduced. These estimates, and the precisely found values, agree for large values of the shape factor, S, with those previously suggested, but also fit the experimental data more closely for small values of S. Confirmation is provided that the assumption of a parabolic lateral profile is invalid for small values of S. ©2002 ASME