Showing papers in "Journal of Applied Mechanics in 1985"

Computational Methods for Transient Analysis

Abstract: Preface. 1 . An Overview of Semidiscretization and Time Integration Procedures (T. Belytschko). 2 . Analysis of Transient Algorithms with Particular Reference to Stability Behavior (T.J.R. Hughes). 3 . Partitioned Analysis of Coupled Systems (K.C. Park and C.A. Felippa). 4 . Boundary-Element Methods for Transient Response Analysis (T.L. Geers). 5 . Dynamic Relaxation (P. Underwood). 6 . Dispersion of Semidiscretized and Fully Discretized Systems (H.L. Schreyer). 7 . Silent Boundary Methods for Transient Analysis (M. Cohen and P.C. Jennings). 8 . Explicit Lagrangian Finite-Difference Methods (W. Hermann and L.D. Bertholf). 9 . Implicit Finite Element Methods (M. Geradin, M. Hogge and S. Idelsohn). 10 . Arbitrary Lagrangian-Eulerian Finite Element Methods (J. Donea). Indices.

The Plastic Spin

Abstract: On presente une formulation macroscopique des grandes deformations elastoplastiques avec des variables de structure tensorielles

Dynamics of Viscoelastic Structures—A Time-Domain, Finite Element Formulation

Abstract: Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M , K ” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.

Prediction of Impact Force and Duration Due to Low-Velocity Impact on Circular Composite Laminates

Abstract: Two simple and improved models--energy-balance and spring-mass--were developed to calculate impact force and duration during low velocity impact of circular composite plates. Both models include the contact deformation of the plate and the impactor as well as bending, transverse shear, and membrane deformations of the plate. The plate was transversely isotropic graphite/epoxy composite laminate and the impactor was a steel sphere. Calculated impact forces from the two analyses agreed with each other. The analyses were verified by comparing the results with reported test data.

Use of Statical Indentation Laws in the Impact Analysis of Laminated Composite Plates

Abstract: The low-velocity impact response of graphite/epoxy laminates was investigated theoretically and experimentally. A nine-node isoparametric plate finite element in conjunction with an empirical contact law was used for the theoretical investigation. Theoretical results are in good agreement with strain-gage experimental data. The results of the investigation indicate that the present theoretical procedure describes the impact response of laminate for low-impact velocities.

Reflection and Transmission of Elastic Waves by a Periodic Array of Cracks

Abstract: Etude de l'interaction d'ondes elastiques avec une serie plane de fissures a espacements periodiques d'egales longueurs. Pour une incidence normale, on considere la reflexion et la transmission des ondes longitudinales et transversales. La solution numerique est verifiee par une application de l'equilibre des taux d'energie

The Crack Problem for Bonded Nonhomogeneous Materials Under Antiplane Shear Loading

Abstract: The singular nature of the crack tip stress field in a nonhomogeneous medium having a shear modulus with a discontinuous derivative was investigated. The problem is considered for the simplest possible loading and geometry, namely the antiplane shear loading of two bonded half spaces in which the crack is perpendicular to the interface. It is shown that the square-root singularity of the crack tip stress field is unaffected by the discontinuity in the derivative of the shear modulus. The problem is solved for a finite crack and extensive results are given for the stress intensity factors.

A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part 1: Development of Appropriate Equations

Abstract: A two surface stress space model is introduced with internal state variable repositories for fading memory of maximum plastic strain range and non-proportionality of loading Evolution equations for isotropic hardening variables are prescribed as a function of these internal variables and accumulated plastic strain, and reflect dislocation interactions that occur in real materials The hardening modulus is made a function of prior plastic deformation and the distance of the current stress point from the limit surface The kinematic hardening rules of Mroz and Prager are used for the yield and limit surfaces, respectively The structure of the model is capable of representing essential aspects of complex nonproportional deformation behavior, including direction of the plastic strain rate vector, memory of plastic strain range, cross-hardening effects, variation of hardening modulus, cyclic hardening or softening, cyclic racheting, and mean stress relaxation

Continuous Damage Mechanics Revisited: Basic Concepts and Definitions

Abstract: On propose une representation geometriquement coherente pour l'ensemble de variables internes definissant une distribution arbitraire de microfissures planes

On the Comparison Between Microscopic and Macroscopic Instability Mechanisms in a Class of Fiber-Reinforced Composites

Abstract: To investigate the relation between the macroscopic and microscopic instability predictions for certain microstructured media, we study the stability of an axially stretched fiber-reinforced composite under plane strain conditions. The microstructural instability is attributed to a bifurcation buckling of the fibers while the corresponding macroscopic one occurs at the loss of ellipticity in the homogenized incremental equilibrium equations of the material. The effects of geometry and material properties on those phenomena are analyzed. The macroscopic approach consistently and sometimes considerably overestimates the stable region of the composite. The attractive feature in this work is that all the investigations can be done by using analytical solutions instead of the numerical ones employed in similar investigations so far.

Singular Value Decomposition for Constrained Dynamical Systems

Abstract: On montre que la methode de decomposition des valeurs singulieres est utile dans le probleme de reduction des equations de mouvement pour une classe de systemes dynamiques contraints, a leur dimension minimale

A Beam Theory for Anisotropic Materials

Abstract: Beam theory plays an important role in structural analysis. The basic assumption is that initially plane sections remain plane after deformation, neglecting out-of-plane warpings. Predictions based on these assumptions are accurate for slender, solid, cross-sectional beams made out of isotropic materials. The beam theory derived in this paper from variational principles is based on the sole kinematic assumption that each section is infinitely rigid in its own plane, but free to warp out of plane. After a short review of the Bernoulli and Saint-Venant approaches to beam theory, a set of orthonormal eigenwarpings is derived. Improved solutions can be obtained by expanding the axial displacements or axial stress distribution in series of eigenwarpings and using energy principles to derive the governing equations. The improved Saint-Venant approach leads to fast converging solutions and accurate results are obtained considering only a few eigenwarping terms.

Theoretical Estimation of the Response of Helically Armored Cables to Tension, Torsion, and Bending

Abstract: Etude du comportement mecanique des conducteurs en aluminium renforces a l'acier dans des conditions de charge statique pouvant etre composee de n'importe quelle combinaison de charges de torsion, de tension et de flexion. On obtient une matrice de rigidite et on donne des relations pour les rigidites axiale, de torsion et de flexion et pour les parametres de couplage

Chute Flows of Granular Material: Some Computer Simulations

Abstract: A computer simulation has been developed to describe unidirectional flows of granular materials. Results are presented for a simulation of the two-dimensional flow of disks or cylinders down an inclined plane or chute. Velocity and solid fraction profiles were measured from the simulated systems and compared with theoretical analyses and are compared with the limited experimental results now available. The behavior is shown to be critically dependent on a third field quantity -- the "granular temperature" -- a measure of the kinetic energy contained in the random motions of the particles.

Counterintuitive Behavior in a Problem of Elastic-Plastic Beam Dynamics

Abstract: In a particular example of short pulse loading on a pin-ended beam, the permanent deflection is predicted by a numerical solution to be in the direction opposite that of the load. Analysis of a Shanley-type model shows that this surprising behavior may occur as a consequence of plastic irreversibility combined with geometric nonlinearity, when the peak deflection produced by the pulse lies in a certain range of small magnitudes. Results from a number of well-known structural dynamics codes are shown. These exhibit a wide spread in the predicted final deflections, indicating strong sensitivities of both physical and computational nature.

Response of an Elastic Plate to Localized Transient Sources

Abstract: The surface response of an infinite, homogeneous elastic plate to an internal dislocation across an infinitestimal area is investigated. As a companion problem, the normal displacement of the plate surface due to a time-dependent surface load is also calculated. The first problem is relevant for the detection of crack initiation in structural materials through the analysis of high-frequency elastic waves generated by the event. The solution to the second problem is needed for the calibration of test equipment used in the detection of the waves. The problems are formulated by means of a classical integral transform in the frequency domain and the spectral response of the plate is expressed in terms of the modal contributions due to the real, imaginary, and complex roots of the Rayleigh-Lamb equation. Time histories of the response are obtained through the inversion of the spectra by a Fast Fourier Transform (FFT) routine.

Stochastic Response of Nonlinear Dynamic Systems Based on a Non-Gaussian Closure

Abstract: The random response of nonlinear dynamic systems involving stochastic coefficients is examined. A non-Gaussian closure scheme is outlined and employed to resolve an observed contradiction of the results obtained by other techniques. The method is applied to a system possessing nonlinear damping. The stationary response is obtained by numerical integration of the closed differential equations of the moments (up to fourth order). An interesting feature of the numerical results reveals the existence of a jump in the response statistic functions. This new feature may be attributed to the fact that the non-Gaussian closure more adequately models the nonlinearity, and thus results in characteristics that are similar to those of deterministic nonlinear systems. The results are compared with solutions derived by the Gaussian closure and stochastic averaging method.

On the Theory of a Cosserat Point and Its Application to the Numerical Solution of Continuum Problems

Abstract: The theory of a Cosserat point is developed to describe motion of a body that is essentially a material point surrounded by some small volume. The development of this theory is motivated mainly by its applicability to the numerical solution of continuum problems. Attention is confined to the purely mechanical theory and nonlinear balance laws are proposed for Cosserat points with arbitrary constitutive properties. The linearized theory is developed and constitutive equations for an elastic material are discussed within the context of both the nonlinear and linear theories. Explicit constitutive equations for a linear-elastic isotropic Cosserat point are developed to model a parallelepiped composed of a linear-elastic homogeneous isotropic material.

A Finite Element Study of Low Reynolds Number Two-Phase Flow in Cylindrical Tubes

Abstract: Resolution par elements finis du probleme d'une bulle sans viscosite s'ecoulant a faible nombre de Reynolds dans un tube cylindrique capillaire occupe par une seconde phase liquide visqueuse. Etude des effets du nombre capillaire sur la forme de la bulle et le champ d'ecoulement. Comparaison des resultats numeriques avec les theories et les experiences publiees

A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part 2: Comparison of Theory With Experiments

Abstract: For the two surface cyclic plasticity model introduced in Part 1, methods for determination of model parameters are described. The model is specialized to axial-torsional loading of a thin-walled tubular specimen, and applied to non-proportional, room-temperature cycling of type 304 stainless steel. Computer simulations for two complex histories show good general agreement with experimental data obtained by the author.

An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading, Part 1: Theory

Abstract: An attempt is made to derive simple procedures for distinguishing between structural problems involving substantial thermal loading, where structural ratchetting can occur at moderate levels of thermal loading, and problems where very high levels of thermal loading may be tolerated. This distinction is of particular importance in the design of liquid metal fast breeder reactors. It is shown that a conservative estimate of the boundary between plastic shakedown and the ratchetting region can be found by overestimating the cyclic hardening of the material. The resulting theory yields a very simple procedure for identifying circumstances where thermal stresses are a potential source of structural ratchetting. Interactive diagrams are constructed for a sequence of sample problems which imply that for many shell problems where temperature variations occur along the surface, ratchetting occurs in two distinct ways, depending on the level of thermal loading. 18 references.