Showing papers in "Journal of Applied Mechanics in 1986"

Laminated Composite Plate Theory With Improved In-Plane Responses

Abstract: In order to improve the accuracy of the in-plane response of the shear, deformable laminated composite plate theory, a new laminated plate theory has been developed based upon a new variational principle proposed by Reissner (1984). The improvement is achieved by including a zigzag-shaped C 0 function to approximate the thickness variation of in-plane displacements. The accuracy of this theory is examined by applying it to a problem of cylindrical bending of laminated plates which has been solved exactly by Pagano (1969). The comparison of the in-plane response with the exact solutions for symmetric three-ply and five-ply layers has demonstrated that the new theory predicts the in-plane response very accurately even for small span-to-depth ratios.

Stresses in Bi-Metal Thermostats

Abstract: Determination de l'amplitude et de la distribution des contraintes dans les thermostats bi-metalliques soumis a des echauffements et des refroidissements uniformes

On the Variational Foundations of Assumed Strain Methods

Abstract: On montre que cette classe de methodes tombe dans la classe des methodes variationnelles basee sur le principe de Hu-Washizu

Impact With Friction

Abstract: A theory of the impact or collision of two rigid bodies, taking account of friction, is presented. It determines how the direction of sliding varies during the impact, which must be known to calculate the direction of the frictional force and thence the frictional impulse. This is accomplished by analyzing the equations of motion of the bodies during the collision. The normal impulse is determined by using a coefficient of restitution. When the direction of sliding is constant throughout the collision, the theory agrees with that given by Whittaker, which is correct only in this case.

Parametric Random Vibration

Abstract: PARAMETRIC random vibration is an applied scientific discipline that covers problems from the broad field of applied dynamics, e.g. structural dynamics, aerodynamics, naval architecture etc. The system equations are characterized by random perturbed parameters while, in many practical situations, non-linearities and random forcing terms create additional complications. Various textbooks have appeared covering the field of random vibration of time-invariant systems. This monograph, a state of the art presentation of parametric random vibration, based on an enormous number of published papers and reports, is a great credit to the author. In the first chapter the reader is introduced to the basic definitions of parametric and autoparametric instabilities, chaotic motion, pseudo-random excitation and crypto-deter-ministic systems and a brief review of parametric random vibration is given. In random vibrations, the emphasis is on the response and stability of systems under wide band random parametric excitations. Unfortunately system equations with physical wide band noise excitation are very difficult to handle, therefore physical Gaussian wide band noise is often replaced by idealized white noise, or the wide band noise is generated by a shaping filter driven by white noise. This is usually the point where many engineers get lost. They are referred to books on stochastic processes and stochastic differential equations and are encouraged to go into theories which are embedded in mathematical abstraction. For these engineers the root of all evil (which is at the same time a source of pleasure for many mathematicians) is the unbounded variation of the Brownian motion, which has white noise as its derivative, in a formal sense. For these processes a new stochastic calculus is needed. In Chapters 2-4 the author provides the necessary tools for deriving response statistical functions and techniques for examining stochastic parameter stability, as required in later chapters. The author has chosen an engineering approach without mathematical abstraction, which implies that some important theorems are verified in a heuristic way, while many others are only mentioned. The result is a nice reference frame for readers with a reasonable background in stochastic processes and stochastic differential equations. Readers without this background will certainly get into trouble, for example, when reading the definitions of random variables and random processes. Obviously, the author could not resist the temptation to give some flavour of mathematical abstraction by introducing a random variable as a function of a sample space f~, which is confusing in the context it is used. …

Handbook of Heat Transfer Fundamentals (Second Edition)

Abstract: Recent advances in heat transfer are discussed, providing data and methodology to solve a wide range of heat transfer problems. The topics considered include: basic concepts of heat transfer, mathematical methods, thermophysical properties, conduction, numerical methods in heat transfer, natural convection, and internal duct flow and external flows in forced convection. Also addressed are: rarefied gases, electric and magnetic fields, condensation, boiling, two-phase flow, and radiation.

The Poisson Function of Finite Elasticity

Abstract: The Poisson function is introduced to study in a simple tension test the lateral contractive response of compressible and incompressible, isotropic elastic materials in finite strain. The relation of the Poisson function to the classical Poisson’s ratio and its behavior for certain constrained materials are discussed. Some experimental results for several elastomers, including two natural rubber compounds of the same kind studied in earlier basic experiments by Rivlin and Saunders, are compared with the derived relations. A special class of compressible materials is also considered. It is proved that the only class of compressible hyperelastic materials whose response functions depend on only the third principal invariant of the deformation tensor is the class first introduced in experiments by Blatz and Ko. Poisson functions for the Blatz-Ko polyurethane elastomers are derived; and our experimental data are reviewed in relation to a volume constraint equation used in their experiments.

Shear Stress Intensity Factors for a Planar Crack With Slightly Curved Front

Abstract: Recent work (Rice, 1985a) has presented the calculations of the first order variation in an elastic displacement field associated with arbitrary incremental planar advance of the location of the front of a half-plane crack in a loaded elastic full space. That work also indicated the relation of such calculations to a three-dimensional weight function theory for crack analysis and derived an expression for the distribution of the tensile mode stress intensity factor along a slightly curved crack front, to first order accuracy in the deviation of the crack front location from a reference straight line. Here we extend the results on stress intensity factors to the shear modes, solving to similar first order accuracy for the in-plane [Mode 2) and antiplane (Mode 3) shear stress intensity factors along a slightly curved crack front. Implications of results for the configurational stability of a straight crack front are discussed. It is also shown that the concept of line tension, while qualitatively useful in characteriz­ ing the crack extension force (energy release rate) distribution exerted on a tough heterogeneity along a fracture path as the crack front begins to curve around it, does not agree with the exact first order effect that is derived here.

Effect of Yield Surface Curvature on Necking and Failure in Porous Plastic Solids

Abstract: The effect of material path dependent hardening on neck development and the onset of ductile failure is analyzed numerically. The calculations are carried out using an elastic-viscoplastic constitutive relation that has isotropic hardening and kinematic hardening behaviors as limiting cases and that accounts for the weakening due to the growth of micro-voids. Final material failure is incorporated into the constitutive model by the dependence of the plastic potential on void volume fraction. Results are obtained for both axisymmetric and plane strain tension. Failure is found to initiate by void coalescence at the neck center in axisymmetric tension and within a shear band in plane strain tension. The increased curvature of flow potential surfaces associated with the kinematic hardening solid leads to somewhat more rapid diffuse neck development than occurs for the isotropic hardening solid. However, a much greater difference between the predictions of the two constitutive models is found for the onset of ductile failure.

On the Understanding of Chaos in Duffings Equation Including a Comparison With Experiment

Abstract: Etude de la dynamique d'une poutre flambee, pour le probleme des valeurs initiales et une excitation externe forcee. On analyse principalement les oscillations choatiques dues a l'excitation forcee

On nonlinear dynamics of planar shear indeformable beams

Abstract: The planar forced oscillations of shear indeformabie beams with either movable or immovable supports are studied through a unified approach. An exact nonlinear beam model is referred to and a consistent procedure up to order three nonlinearities is followed. By eliminating the longitudinal displacement component through a constraint condition and assuming one mode, the problem is reduced to one nonlinear differential equation. A perturbational solution in the neighborhood of the resonant frequency is determined and the stability of the steady-state solutions is studied. The dependence of the phenomenon on the geometrical and mechanical characteristics of the system is put into light and the frequency-response curves for different boundary conditions are furnished.

Effect of Fiber Anisotropy on Thermal Stresses in Fibrous Composites

Abstract: An elasticity solution is utilized to analyze an orthotropic fiber in an isotropic matrix under uniform thermal load. The analysis reveals that stress distributions in the fiber are singular in the radial coordinate when the radial fiber stiffness (C-rr) is greater than the hoop stiffness (C-theta-theta). Conversely, if C-rr is less than C-theta-theta the maximum stress in the composite is finite and occurs at the fiber-matrix interface. In both cases the stress distributions are radically different than those predicted assuming the fiber to be transversely isotropic (C-rr = C-theta-theta). It is also shown that fiber volume fraction greatly influences the stress distribution for transversely isotropic fibers, but has little effect on the distribution if the fibers are transversely orthotropic.

Theoretical study of the dynamic tensile test

Abstract: A numerical investigation of the tensile test using a finite-difference, one-dimensional elasto-viscoplastic code is presented. The influence of strain rate, strain rate sensitivity, and inertia on the development of the axial particle velocity, stress, strain, and strain rate profiles in pure copper is studied. The initial stages of post-uniform deformation and the stabilizing influence of inertia and strain rate sensitivity in this regime are demonstrated. Both inertia and strain rate sensitivity are shown to decrease the rate of unloading of the uniform region of a tensile specimen past the point of instability given by the maximum load criterion. A comparison of numerically predicted and experimentally determined values of the post-uniform elongation is shown.

Mechanism of Surface Crack Growth in Lubricated Rolling/Sliding Spherical Contact

Abstract: A possible mechanism of the crack growth is described by calculating stress intensity factors for a semicircular surface crack under a spherical Hertzian contact moving over a cracked elastic half-space surface. In the analysis the crack is assumed to be inclined at an angle of 45 deg from the surface. In particular, the effects of surface traction, frictional force between crack faces, and oil hydraulic pressure caused by oil penetrated into the crack are discussed.

A One-Dimensional Numerical Model of a Drop-On-Demand Ink Jet

Abstract: On utilise un algorithme predicteur-correcteur de Mac Cormack pour resoudre les equations d'un modele unidimensionnel de developpement d'une goutte a partir d'un jet goutte a goutte. Les calculs sont effectues en coordonnees lagrangiennes