Showing papers in "Journal of Applied Mechanics in 1993"

A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method

Abstract: A new family of time integration algorithms is presented for solving structural dynamics problems. The new method, denoted as the generalized-α method, possesses numerical dissipation that can be controlled by the user. In particular, it is shown that the generalized-α method achieves high-frequency dissipation while minimizing unwanted low-frequency dissipation. Comparisons are given of the generalized-α method with other numerically dissipative time integration methods; these results highlight the improved performance of the new algorithm. The new algorithm can be easily implemented into programs that already include the Newmark and Hilber-Hughes-Taylor-α time integration methods.

Identification of Nonlinear Dynamic Systems Using Neural Networks

Abstract: This paper explores the potential of using parallel distributed processing methodologies (artificial neural networks) to identify the internal forces of structure unknown non linear dynamic systems

Cyclic Viscoplastic Constitutive Equations, Part I: A Thermodynamically Consistent Formulation

Abstract: The purpose of the paper is to show how the classical models can be modified in order to follow the general principles of thermodynamics with internal variables. Using the restrictive framework of standard generalized materials, the state variables associated to various kinds of kinematic and isotropic hardening are selected. The evolution equations for these internal variables are then formulated in a slightly less restrictive form

Tunneling Cracks in Constrained Layers

Abstract: A thin, brittle layer bonded between tougher substrates is susceptible to cracking under residual and applied stresses. Such a crack initiates from an equi-axed flaw, confined by the substrates, tunneling in the brittle layer. Although tunneling is a three-dimensional process, the energy release rate at the front of a steady-state tunnel can be computed using plane strain fields. Several technically important problems are analyzed, including tunnels in adhesive joints, shear fracture, and kinked tunnels in a reaction product layer. The concept is finally applied to microcracking in brittle matrix composites caused by thermal expansion mismatch.

Dynamics of Bipedal Gait: Part I—Objective Functions and the Contact Event of a Planar Five-Link Biped

Abstract: This article presents an approach that can be followed to formulate objective functions which can be used to prescribe the gait of a planar, five element, bipedal automaton during single support phase. The motion of the biped is completely characterized in terms of progression speed, step length, maximum step height, and stance knee bias. Kinematic relations have been derived and the inverse problem has been solved to perform a parametric study that correlates the regions of the four dimensional parameter space with the respective gait patterns

Statistical Properties of Residual Stresses and Intergranular Fracture in Ceramic Materials

Abstract: The problem addressed in this paper concerns the statistical characterization of the state of residual stress generated in polycrystalline ceramics during cooling from the fabrication temperature. Detailed finite element simulations are carried out for an ensemble of large numbers of randomly oriented, planar hexagonal grains with elastic and thermal expansion anisotropy, and brittle grain interfaces. The calculations show that the distribution of normal and shear tractions induced by thermal contraction mismatch among grains is gaussian and that these tractions are statistically independent random variables. Although the gaussian nature of the distributions remains unaffected by the introduction of elastic anisotropy, the results indicate that elastic anisotropy has a significant effect on the residual stresses for finite departures from isotropy. When the hexagonal grains are randomly distorted, the magnitude and distribution of residual stresses are found to be insignificantly altered. Spontaneous microfracture due to the generation of internal stresses is also simulated in the analysis by allowing for the nucleation and growth of intergranular microcracks when the fracture energy along the grain facets exceeds a certain critical value. When such microcracking is incorporated into the computation, the levels of residual stress are markedly reduced as a consequence of stress dissipation. The dependence of intergranular microcracking on grain size and temperature variation is examined and the predicted trends on material degradation or the complete suppression of microfracture are discussed in the light of available experimental results.

Active Stiffness Control of Cable Vibration

Abstract: Changing the tension as a positive use of parametric excitation is studied. An optimal algorithm is obtained from energy analysis and verified by experiment on a scale model

A Geometrically Nonlinear Theory of Elastic Plates

Abstract: A set of kinematical and intrinsic equilibrium equations are derived for plates undergoing large deflection and rotation but with small strain

Singular Stress Field Near the Corner of Jointed Dissimilar Materials

Abstract: In this paper, the characteristics of the stress field near a corner of jointed dissimilar materials are studied as a plane problem. It is found that the order of singularity is dependent not only on the elastic constants of materials and the local geometry of corner, but also on the deformation mode. The dependence of the order of singularity was established for the case of mode I and the case of mode II. An explicit closed-form expression is given for the singular stress field at the close vicinity of the corner, in which the stress field is expressed as a sum of the symmetric state with a stress singularity of 1/r 1-λ1 and the skew symmetric state with a stress singularity of 1/r 1-λ2 . When both λ1 and λ2 are real the singular stress field around the point singularity is defined in terms of two constants K 1 , λ1 , K 11 , λ2 , as in the case of crack problems.

Stochastic Dynamics of Nonlinear Systems Driven by Non-normal Delta-Correlated Processes

Abstract: In this paper, nonlinear systems subjected to external and parametric non-normal delta-correlated stochastic excitations are treated. A new interpretation of the stochastic differential calculus allows first a full explanation of the presence of the Wong-Zakai or Stratonovich correction terms in the Ito’s differential rule. Then this rule is extended to take into account the non-normality of the input. The validity of this formulation is confirmed by experimental results obtained by Monte Carlo simulations.

Convex Models of Uncertainty in Radial Pulse Buckling of Shells

Abstract: The buckling of shells subject to radial impulse loading has been studied by many investigators, and it is well known that the severity of the buckling response is greatly amplified by initial geometrical imperfections in the shell shape. Traditionally, these imperfections have been modeled stochastically. In this study convex models provide a convenient alternative to probabilistic representation of uncertainty. Convex models are well suited to the limitations of the available information on the nature of the geometrical uncertainties. A n ellipsoidal convex model is employed and the maximum pulse response is evaluated. The ellipsoidal convex model is based on three types of information concerning the initial geometrical uncertainty of the shell: (1) which mode shapes contribute to the imperfections, (2) bounds on the relative amplitudes of these modes, and (3) the magnitude of the maximum initial deviation of the shell from its nominal shape. The convex model analysis yields reasonable results in comparison with a probabilistic analysis due to Lindberg (1992a,b). We also consider localized imperfections of the shell. Results with a localized envelope-bound convex model indicate that very small regions of localized geometrical imperfections result in buckling damage which is a substantial fraction of the damage resulting from full circumferential initial imperfection.

Dynamics of Bipedal Gait: Part II—Stability Analysis of a Planar Five-Link Biped

Abstract: A general approach based on discrete mapping techniques is presented to study stability of bipedal locomotion. The approach overcomes difficulties encountered by others on the treatment of discontinuities and nonlinearities associated with bipedal gait. A five-element bipedal locomotion model with proper parametric formulation is considered to demonstrate the utility of the proposed approach. Changes in the stability of the biped as a result of bifurcations in the fourdimensional parameter space are investigated. The structural stability analysis uncovered stable gait patterns that conform to the prescribed motion. Stable non-symmetric locomotion with multiple periodicity was also observed, a phenomenon that has never been considered before. Graphical representation of the bifurcations are presented for direct correlation of the parameter space with the resulting walking patterns. The bipedal model includes some idealizations such as neglecting the dynamics of the feet and assuming rigid bodies. Some additional simplifications were performed in the development of the controller that regulates the motion of the biped.

On the anisotropic elastic inclusions in plane elastostatics

Abstract: By combining the method of Stroh`s formalism, the concept of perturbation, the technique of conformal mapping and the method of analytical continuation, a general analytical solution for the elliptical anisotropic elastic inclusions embedded in an infinite anisotropic matrix subjected to an arbitrary loading has been obtained in this paper. The inclusion as well as the matrix are of general anisotropic elastic materials which do not imply any material symmetry. The special cases when the inclusion is rigid or a hole are also studied. The arbitrary loadings include in-plane and antiplane loadings. The shapes of ellipses cover the lines or circles when the minor axis is taken to be zero or equal to the major axis. The solutions of the stresses and deformations in the entire domain are expressed in complex matrix notation. Simplified results are provided for the interfacial stresses along the inclusion boundary. Some interesting examples are solved explicitly, such as point forces or dislocations in the matrix and uniform loadings at infinity. Since the general solutions have not been found in the literature, comparison is made with some special cases of which the analytical solutions exists, which shows that our results are exact and universal.

Rudnicki and Rice's analysis of strain localization revisited

Abstract: In a celebrated paper published in 1975, Rudnicki and Rice (RR) analyzed the conditions for strain localization in pressure-sensitive dilatant materials. This paper corrects certain results in their work that are relevant in exceptional cases. RR found that the normal to the plane of localization was generally orthogonal to the direction of the intermediate principal stress; however, when a certain inequality was satisfied, it was orthogonal to the direction of the minimum principal stress. In contrast, it is shown here that the normal to the plane of localization is always orthogonal to the direction of the intermediate principal stress; but there is a special case where it is parallel to the direction of either the maximum or the minimum principal stress, and in this case the expression of the critical hardening modulus at localization differs from that given by RR.

Chaotic Vibrations of Beams: Numerical Solution of Partial Differential Equations

Abstract: A simply supported buckled beam governed by a Euler Bernoulli beam equation with transverse loading and non linear membrane stretching effect has been studied. By using a stable, explicit finite difference scheme to solve the governing partial differential equation it has been demonstrated that various problems are easily handled

Buckling and Post-buckling of Composite Plates and Shells Subjected to Elevated Temperature

Abstract: Effects of temperature on buckling and post-buckling behavior of reinforced and unstiffened composite plates or cylindrical shells are considered. First, equilibrium equations are formulated for a shell subjected to the simultaneous action of a thermal field and an axial loading. These equations are used to predict a general form of the algebraic equations describing the post-buckling response of a shell. Conditions for the snap-through of a shell subjected to thermomechanical loading are formulated. As an example, the theory is applied to prediction of post-buckling response of flat large-aspect-ratio panels reinforced in the direction of their short edges. 19 refs.

Post-buckling of geometrically imperfect shear-deformable flat panels under combined thermal and compressive edge loadings

Abstract: The static post-buckling of simply-supported flat panels exposed to a stationary nonuniform temperature field and subjected to a system of subcritical in-plane compressive edge loads is investigated. The study is performed within a refined theory of composite laminated plates incorporating the effect of transverse shear and the geometric nonlinearities. The influence played by a number of effects, among them transverse shear deformation, initial geometric imperfections, the character of the in-plane boundary conditions and thickness ratio are studied and a series of conclusions are outlined. The influence played by the complete temperature field (i.e., the uniform through thickness and thickness-wise gradient) as compared to the one induced by only the uniform one, is discussed and the peculiarities of the resulting post-buckling behaviors are enlightened.

Stresses in Narrow Regions

Abstract: A method for calculating the stress distribution in a narrow region of an elastic plate is presented. It consists in treating the narrow region by beam theory, treating the rest of the plate by any computational or analytical method, and matching the results of these two calculations. It is illustrated by finding the stress distribution in the narrow region of a plate, between a straight edge and a nearby hole, when the plate is under tension. The same method can be applied to three-dimensional bodies with thin plate-like or shell-like regions.

Universal Relations in Piezoelectric Composites With Eigenstress and Polarization Fields, Part I: Binary Media—Local Fields and Effective Behavior

Abstract: The constituent phases of the present binary composite media with arbitrary phase geometry have general anisotropic piezoelectric behavior and contain both constant eigenstress and spontaneous polarization fields. The existence of uniform strain and electric field intensity throughout the solid is used to derive exact universal relations between the local fields, as well as between the effective constants of the composite aggregate. Attention is then given to an alternative method that is based on the use of virtual work theorems in piezoelectric media. It is shown that the effective eigenstress and polarization follow from a knowledge of the influence functions related to an electromechanical loading of the composite aggregate in which neither eigenstress nor polarizations are present. 33 refs.

Transient Wave Propagation Methods for Determining the Viscoelastic Properties of Solids

Abstract: The following two solutions are proposed for deducing the viscoelastic properties of a solid from the change in the shape of a one dimensional transient mechanical wave as it propagates through the medium: the general solution (the phase velocity and the attenuation coefficient are expressed in terms of the Fourier transfors of the pulse after two distances of travel), and a filter method. This method fills a gap between the existing vibratory and ultrasonic methods

A Multiple-Scales Analysis of Nonlinear, Localized Modes in a Cyclic Periodic System

Abstract: The nonlinear localized modes of an n degree-of-freedom nonlinear cyclic system are examined by the averaging method of multiple scales. The implications of mode localization on the active or passive vibration isolation of such structures are discussed

Interfacial fracture mechanics for anisotropic bimaterials

Abstract: This paper focuses on aspects of fracture mechanics of interface cracks in anisotropic bimaterials. In this case there is a coupling of all three crack-tip fracture modes in the natural interface-crack coordinate system, whereas in the isotropic case, mode 3 is decoupled from modes 1 and 2. This paper intends to shed light on how to interpret the crack-tip fields which are given explicitly along the interface in terms of two (real 3x3) bimaterial matrices W and D . A matric function Y is defined in terms of W and D which determines the coupling and oscillations in the cracktip fields. Explicit expressions for the crack-tip fields and the associated stress intensity factors are given as well as for the energy release rate. The finite (Griffith) interface crack is considered in detail.

The Initial Post-buckling and Growth Behavior of Internal Delaminations in Composite Plates

Abstract: No restrictive assumptions regarding the delamination thickness and plate length are made. The perturbation procedure is based on an asymptotic expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica. The reduced growth resistance of these configurations is verified by experimental results on unidirectional composite specimens with internal delaminations

Localized Elasticae for the Strut on the Linear Foundation

Abstract: Localized solutions, for the. classical problem of the nonlinear strut (elastica) on the linear elastic foundation, are predicted from double-scale analysis, and confirmed from nonlinear volume-preserving Runge-Kutta runs. The dynamical phase-space analogy introduces a spatial Lagrangian function, valid over the initial post-buckling range, with kinetic and potential energy components. The indefinite quadratic form of the spatial kinetic energy admits unbounded solutions, corresponding to escape from a potential well. Numerical experimentation demonstrates that there is a fractal edge to the escape boundary, resulting in spatial chaos.