Showing papers on "Displacement field published in 1982"

Diffracted waves and displacement field over two-dimensional elevated topographies

Abstract: Summary The Aki-Larner technique is used to perform, in both the time and frequency domains, an analysis of the effects of two-dimensional elevated topography on ground motion. Incident plane SH-, SV- and P-waves are considered and the respective influences of surface geometry, elastic parameters and the incident wave characteristics, as long as they remain within the limits of applicability of the A-L technique, are investigated in some detail. Besides the well-known amplification/deamplfication effect related to the surface curvature, wave scattering phenomena on the convex parts of the surface are shown to contribute significantly to the disturbances in the displacement field around the topographic structure. These scattered waves are SH in the case of incident SH-waves, and mainly Rayleigh waves in the P case, while both Rayleigh and horizontal P-waves, sometimes of large amplitude, develop in the SV case. The frequency dependence of this scattering, though complex, seems to be mainly controlled by the horizontal scale of the topographic structure. The parameter study points out the regular and intuitive behaviour of this wave scattering in both SH and P cases, while it exhibits a puzzling complexity for incident SV-waves, which is interpreted as resulting from the importance of the S-P reflections on mountain slopes in that case. As to the ground motion, some general features may be pointed out. The amplification on mountain tops, which is systematically greater for incident S-waves than for P-waves, generally decreases as the average slope decreases or as the angle of incidence increases. Mountain slopes undergo either amplification or deamplification depending on site location, frequency and incidence angle, but they always undergo strong differential motion due to the lateral propagation of the scattered waves and their interference with the primary wave. Finally, all these effects may be greatly enhanced in the case of complex topographies, which moreover give rise to a significant prolongation of ground motion because of the large number of scattered waves.

Simulation of the (001) plane crack in α-iron employing a new boundary scheme

Abstract: A new boundary scheme for atomic-level computer simulations in solid mechaisms has been developed which is based on the finite-element method and which provides several advantages over previous boundary schemes. This has been applied to the simulation of (001) plane two-dimensional cracks in ac-Fe having crack line directions of [010] and [110]. Significant differences between the cracks in these two directions were observed. Lattice-trapping limits and some information on the magnitude and shape of the crack-tip displacement field is provided for both cases. No dislocations were emitted at low temperatures, but warming the model to 400 K apparently resulted in the emission of a dislocation from the crack-tip.

Flow visualization of steady streaming in oscillatory flow through a bifurcating tube

Abstract: A steady streaming displacement of fluid elements is observed to occur during oscillatory flow through a Y-shaped tube bifurcation model at Womersley and Reynolds numbers that can exist in the human bronchial tree. The cause of the displacement is the effect of the asymmetric geometry on the oscillating velocity vector field. The steady streaming displacement is greatest for fluid elements that experience the highest velocity through the bifurcation junction. The maximum displacement observed increases with Re and a up to a Re of about 100 and a of about 5, after which a levelling off and gradual decline occur. Photographs of low-Re and low-a: cxpcrimcnts show the effects of secondary components of the steady-streaming displacement field which contribute to a complex circulation.

Scattering of SH Waves by Subsurface Topography

Abstract: Horizontally polarized shear waves in an elastic alluvial valley of arbitrary shape perfectly bonded to a linearly elastic, homogeneous and isotropic half space are considered. The valley is subjected to a steady state horizontal displacement field. Total displacement field is evaluated along the interface between the half space and alluvial valey. Comparison with known exact solutions for simple geometry provided the following conclusions: 1) the method provides excellent results for wide range of frequencies, 2) for a fixed number of sources, the results are more accurate at lower frequencies, and 3) as the number of sources increases, the accuracy increases.

Geometrically nonlinear formulation for the axisymmetric shell elements

Abstract: A geometrically nonlinear formulation using total Lagrangian approach is presented for the axisymmetric shell elements. The basic element is formulated using the co-ordinates of the mid-surface nodes and the mid-surface nodal point normals. An important aspect of the formulation presented here is that the restriction on the magnitude of the nodal rotations is eliminated. This is accomplished by retaining true nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties based on this displacement field. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the element behaviour and the accuracy.

The Born approximation for the scattering theory of elastic waves by two‐dimensional flaws

Abstract: First, we present formal aspects of the scattering of plane elastic waves by a single elastic cylindrical inclusion or a cavity of an arbitrary cross section embedded in an isotropic homogeneous elastic medium of different properties. An integral equation is used to derive expressions for the displacement field valid in the entire domain. Thereafter the Born approximation for the solution is derived. Formulas for the scattered amplitudes and the scattering cross sections are presented. The validity of the approximation is examined by comparing the results with those of the simple bodies for which the exact solutions are available in the literature. Some new results for the corresponding three‐dimensional case are also presented.

A note on two-dimensional finite-deformation theories of shells

Abstract: We supplement an earlier consideration of two-dimensional finite-deformation shell theory in terms of independent descriptions of states of translational and rotational displacement by the avoidance of the previously made a priori assumption concerning the form of components of force strain. We furthermore introduce a relatively elementary description of the state of rotational displacement, in place of the known description in terms of a Rodriguez vector, which involves a symmetric treatment of the rotations about the two surface tangent vectors, without a participation in this of the rotation about the surface normal vector.

Nonreciprocal surface-acoustic-wave propagation in aluminum

Abstract: Nonreciprocal effects in surface-acoustic-wave (SAW) velocities for single-crystal aluminum have been observed at low temperatures in the presence of a magnetic field. They are of the order of 0.1% in the relative velocity change. This effect is due to coupling of the SAW displacement field to the conduction electrons moving on cyclotron orbits. We give a quantitative explanation for this effect.

Interaction of elastic waves by a Griffith crack in an infinite transversely-isotropic medium

Abstract: The paper deals with the problem of finding the stress distribution near a Griffith crack located in an infinite transversely-isotropic medium. The crack is opened by the interaction of a plane harmonic elastic wave incident normally on the crack. A Fredholm integral equation is derived for the determination of diffracted field. From the integral equation asymptotic solution is obtained which is valid for wavelength long compared to the crack length. For wave lengths comparable with the size of the crack, the integral equation is solved numerically. The stress intensity factor and displacement field in the vicinity of crack are computed for a range of values of the frequency. The approximate solution is compared with exact solution.

On extending Biot's theory of multiple scattering at low frequencies from acoustic to elastic media

Abstract: Summary. We derive a linear, inhomogeneous boundary condition that approximately describes long-wavelength multiple scatter about a plane of spherical inclusions embedded in an elastic wholespace. This boundary condition relates the discontinuity in the displacement-stress vector to a description of the material properties of the inclusions and to spatial derivatives up to fourth order of the average displacement field across the plane. The boundary condition is an elastic medium analogue to Biot’s boundary condition for scattering in an acoustic medium. While the acoustic theory predicts that a plane of rigid, fixed inclusions can support a boundary wave, our results suggest that in elastic media analogous modes are leaky.

A time dependent theory of crazing behavior in polymers

Abstract: The development of crazing is not only a function of stress, but also a function of time. Under a simple state of tension, a craze opening displacement is closely associated with the viscoelastic behavior of the original bulk polymer medium in which individual crazes initiate and develop. Within each craze region, molecular orientation takes place when conditions permit, and a new phase of rearranged molecules governs its local behavior. Based upon a time‐dependent viscoelastic two‐dimensional model, using a computer program the craze opening displacement field has been calculated, time‐dependent craze length was also computed by taking into consideration the molecular orientation mechanism and large deformations in the craze region. Examples are given for simple viscoelastic media with simplified stress distributions. It is interesting to find out that the occurrence of crazing may be interpreted in terms of the stability or instability of the constitutive behavior of the bulk polymer.

A numerical analysis on stable crack growth under increasing load

Abstract: A simple and flexible method of analysis on stable crack growth in ductile materials is presented. The analysis is based on an elastic-plastic finite element method to calculate the stress and displacement fields in the vicinity of a growing crack under monotonically increasing load. A special type of element known as a “breakable element” and a nodal force relaxation technique have been adopted in a usual elastic-plastic analysis to simulate stable crack growth. A new fracture criterion which is suitable for mixed mode fracture is also used. The computational scheme was verified by excellent correlation with some experimental results.

Interior and exterior solutions for boundary value problems in composite elastic media. I. Two‐dimensional problems

Abstract: We study two‐dimensional problems of elasticity when a homogeneous and isotropic solid of an arbitrary shape is embedded in an infinite homogeneous isotropic medium of different properties. Solutions are obtained both inside the guest and host media. These solutions are derived by first transforming the boundary value problems to the equivalent integral equations. The interior displacement field is obtained by a simple method of truncation. By this method the integral equations are recast into an infinite number of algebraic equations and a systematic scheme of solutions is constructed by an appropriate truncation. The exterior solutions are obtained by substituting the interior solutions in the integral equations valid for the entire medium. The boundaries considered are rectangular cylinder, equilateral triangular prism, and elliptic cylinder and its limiting configurations. It emerges that the solutions for the elliptic cylinder and its limiting configurations are exact.

Tidal deformation of a viscoelastic body

Abstract: Summary. The tidal deformation of a homogeneous viscoelastic sphere due to the gravitational attraction of an external body is calculated. The sphere is modelled as an incompressible Kelvin-Voigt solid. An equation for the displacement field is obtained assuming that strains are small and inertia is negligible. This equation has a series solution in terms of Legendre polynomials. The resulting expression for the displacement field reduces to that for an elastic solid and a viscous fluid in the appropriate limits of the material constants. The first term in the viscoelastic solution is used to calculate the moments induced by tidal deformation assuming a circular orbit. In the absence of obliquity and precession, these moments reduced to a torque about the spin axis. This torque is compared to that predicted by a phase lag analysis. These two approaches are formally equivalent if the tidal dissipation function Q-' depends in a specific way on the difference of the spin and orbital angular velocities.

Use of Ĵ-Integral in Dynamic Analysis of Cracked Linear Viscoelastic Solids by Finite-Element Method

Abstract: A computational method using the path (area)-independent J-integral is developed to analyze viscoelastic problems. Since the displacement field near the crack tip of a viscoelastic solid is dependent upon the complete past history of the dynamic stress-intensity factors, the J-integral is represented by a hereditary integral of the dynamic stress-intensity factors. We assume that the stress and strain rates vary in proportion to time during each increment of time and derive a formula to obtain the current value of the dynamic stress-intensity factor from the time increment of the J-value. Both pure and mixed mode problems of a suddenly loaded crack are analyzed by making use of the formula together with the conventional finite-element method. In order to demonstrate the capability and reliability of the present method, problems of a center crack and an oblique crack in viscoelastic rectangular plates are solved.

Three-dimensional elastic wave scattering and diffraction due to a rigid cylinder embedded in an elastic medium by a point source

Abstract: The formal solutions of displacement field to the problem of elastic wave scattering and diffraction due to an infinitely long rigid cylinder embedded in an infinite elastic medium by an impulsive point source have been obtained in the integral form. The integrals for the reflected and the diffracted waves both in the shadow zone and in the illuminated zone are evaluated asymptotically for the early time motion by the Reisdue-Cagniard method and the Saddle-point-Cagniard method.

A general solution procedure in elastostatics with multiply-connected regions with applications to mode III fracture mechanics problems

Abstract: A new variational method recently proposed by Ho is extended to the general boundaryvalue problems of elasticity involving multiply-connected regions, including those of fracture mechanics. The method presents the approximate displacement functions in “series” form, the coefficients of which are obtained through minimizing the strain energy of the difference displacement field, resulting in the solution of a system of linear algebraic equations. Formulations are derived for all four types of boundary conditions (displacement, traction, mixed, dual). The method is applied to the anti-plane shear deformation of a finite elastic medium with a line crack. Surprisingly elegant exact solutions are obtained for two different problems. Further applications are included for infinite strips with parallel, perpendicular, as well as inclined cracks. Results show good convergence characteristics. Since the strain energy norm used in this method is actually proportional to the stress intensity factor, this method is indeed ideally suited for studies of Fracture Mechanics problems.

Differential gear housing support device

Abstract: PURPOSE: To improve the characteristics of a spring by coupling a car body and a differential case using an elastic body that is sheared and deformed for the vertical and horizontal displacement and an elastic body that is sheared, compressed, and deformed for the vertical displacement and that is sheared and deformed for the horizontal displacement. CONSTITUTION: A first elastic body 12 is provided at an opposed location that is parallel to the horizontal direction between first and second brackets 7 and 10. This first elastic body 12 is sheared and deformed for the vertical and horizontal displacement and is compressed and deformed for the vertical displacement. In addition, a second elastic body 13 is provided at an opposed direction that is parallel to the tilting direction between the said both brackets 7 and 10. This second elastic body 13 is sheared, compressed, and deformed for the vertical and horizontal displacement and is sheared and deformed for the horizontal displacement. Furthermore, an auxiliary elastic body 14 is provided between both brackets 7 and 10. Then the bracket 7 adheres to a differential crossmember 5 and the bracket 10 adheres to a differential housing 6. COPYRIGHT: (C)1984,JPO&Japio

Fundamental aspects in quantitative ultrasonic determination of fracture toughness: The scattering of a single ellipsoidal inhomogeneity

Abstract: The scattering of a single ellipsoidal inhomogeneity is studied via an eigenstrain approach. The displacement field is given in terms of volume integrals that involve eigenstrains that are related to mismatch in mass density and that in elastic moduli. The governing equations for these unknown eigenstrains are derived. Agreement with other approaches for the scattering problem is shown. The formulation is general and both the inhomogeneity and the host medium can be anisotrophic. The axisymmetric scattering of an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the scattered displacement field, the differential and total cross sections are formally given in series expansions for the case of uniformly distributed eigenstrains.

A new penalty function element for thin shell analysis

Abstract: In this paper a triangular thin shell element is presented where C1 continuity is introduced by means of the penalty function technique. The displacement field has complete cubic polynomials for each component. The introduced constraint condition is the continuity of normal slopes of the transverse displacements along interelement boundaries. Classical thin shell theory for small deformations is applied. Several analyses of thin plates and shells are performed, including a large problem of practical interest, to study the effect of an increasing penalty factor. The accuracy of the results is estimated and compared to the actually occurred error. In the conclusions a recommended value for the penalty factor is given.

The solution of the dynamic field of the Haskell fault model reconsidered

Abstract: A method of obtaining the displacement field of the Haskell model of an earthquake source, based on the well-known equivalence of seismic dislocations and body force, is described. It is shown that the solution of Madariaga (1978) can be generalized and that the two methods are equivalent for the problem of a rectangular dislocation expanding on a plane in an infinite space with a variable rupture speed and variable slip in the direction of rupture. One of the advantages of the equivalent body force method is that it can be used to readily obtain the transformed solution to the Haskell model in a half-space for a rectangular dislocation, expanding with variable rupture speed and variable slip.