Showing papers on "Displacement field published in 1980"
TL;DR: In this paper, the authors apply the method of asymptotic expansions to the nonlinear, three-dimensional, equations for the equilibrium of a special class of elastic plates under suitable loads.
Abstract: The method of asymptotic expansions, with the thickness as the parameter, is applied to the nonlinear, three-dimensional, equations for the equilibrium of a special class of elastic plates under suitable loads. It is shown that the leading term of the expansion is the solution of a system of equations equivalent to those of von Karman. The existence of solutions of this system is established. It is also shown that the displacement and stress corresponding to the leading term of the expansion have the specific form generally assumed in the usual derivations of the von Karman equations; in particular, the displacement field is of Kirchhoff-Love type. This approach also clarifies the nature of admissible boundary conditions for both the von Karman equations and the three-dimensional model from which these equations are obtained. A careful discussion of the limitations of this approach is given in the conclusion.
255 citations
TL;DR: In this article, a general representation of the displacement field of an AE event is given in terms of the double-couple response to a distribution of moment density tensors in the source region.
Abstract: The theory of elastic wave emission (i.e., acoustic emission; AE) from damage processes such as slip and microcracking is discussed. Analogous developments in the literature on earth-quake seismology and dynamic dislocation theory are noted and utilized. A general representation of the displacement field of an AE event is given in terms of the double-couple response to a distribution of “moment density tensor” in the source region. Results are specialized to a point source model and to a general far-field analysis of outgoing elastic waves, and conditions for validity of such representations and their low-frequency specializations are noted. Emitted wave fields are compared for tensile opening and slip events, and procedures which might enable the approximate determination of the size or area increase of tensile microcracks are discussed.
58 citations
TL;DR: In this paper, a finite element solution for a circular ring or curved beam is developed for a polynomial displacement function, which gives high accuracy for an element which subtends an angle as great as 90°.
55 citations
TL;DR: The theory of Brillouin scattering from the surface of a semi-infinite medium is presented in this article, where the electromagnetic field is calculated to first order in the phonon displacements using the Rayleigh method.
Abstract: The theory of Brillouin scattering from the surface of a semi-infinite medium is presented. The electromagnetic field is calculated to first order in the phonon displacements using the Rayleigh method. Both s and p polarisations are considered and the scattering geometry is not limited to the plane of incidence. The cross-section formulae can be interpreted in terms of the ripple and elasto-optic mechanisms. The effects on the displacement field due to the surface are investigated in both the discrete and the continuous part of the frequency spectrum. In particular, a detailed analysis of the so-called 'mixed modes' belonging to the continuum is analytically given for the isotropic medium. The application of the theory to GaAs and the comparison with experimental data (including A1 coated surfaces) will be discussed in paper II.
53 citations
TL;DR: In this paper, the spacial variation of displacement due to carbon in the c-oriented octahedral site coupled with the assumption that such carbon is dispersed randomly then allows computation of the displacement of the two nearest neighbors as 0.6A in the direction, corresponding to a carbon-iron distance of 2.0A.
Abstract: The ratio of the X-ray intensity in the 002 to that in the 200, 020 in martensite formed in fine-grained 18 pct Ni ∼ 1 pct C austenite provides a measure of the strength of the carbon displacement field. Theoretical calculation of the spacial variation of displacement due to carbon in the c-oriented octahedral site coupled with the assumption that such carbon is dispersed randomly then allows computation of the displacement of the two nearest neighbors as 0.6A in the c-direction, corresponding to a carbon-iron distance of 2.0A. Aging the martensite for one hour at temperatures above −40 °C, the temperature of the above measurements, results in a decrease in the 002 intensity with little or no change in the 200 or 020 intensity, and little change in the lattice parameters until +40 °C when precipitation starts. This behavior is expected if clustering of carbon occurs and is contrary to expectations if carbon changes site during aging. If the absence of aging at —40 °C is assumed, then aging corresponds to formation of clusters of two to four carbon atoms.
45 citations
TL;DR: In this article, the problem of finding the elastic stress and displacement field around a straight dislocation at the interface separating two media with the most general anisotropic properties, similarly to a treatment by Barnett and Lothe (1974), was reduced to the inversion of twelve linear equations with twelve unknowns, using the classical formulations of elasticity.
32 citations
TL;DR: In this article, the problem of scattering of plane compressional wave by an elastic sphere embedded in an isotropic elastic medium of different material properties is solved, and approximate formulas are derived for the displacement field, stress tensor, stress intensity factors, far-field amplitudes and the scattering cross-section.
22 citations
TL;DR: In this paper, the displacement field of the screw dislocation, the interaction energy of two parallel screw dislocations and their self-energy were calculated for a smectic C liquid crystal in the approximation of the self-power of a single screw.
Abstract: The displacement field of the screw dislocation, the interaction energy of two parallel screw dislocations and their self-energy is calculated for a smectic C liquid crystal in the approximation of...
17 citations
TL;DR: In this article, the axisymmetry problem of a penny-shaped crack opened out by thermal loads is studied and the linear theory of micropolar elasticity is employed.
16 citations
TL;DR: In this article, the authors used a dual-beam illumination and a single point of observation to obtain quantitative data for the components of the displacement vector, which is then used to obtain moire patterns for the out-of-plane and in-plane displacements of flat surfaces.
Abstract: Geometrical considerations are used to obtain quantitative data for the components of the displacement vector. Use is made of a dual-beam illumination and a variant is described, using point light sources and a single point of observation. Contour lines for the displacement vector in the viewing direction and in a perpendicular direction are obtained as the algebraic sum and difference of two interference patterns. Densification of the initial pattern is used to obtain moire patterns for the out-of-plane and in-plane displacements of flat Surfaces and for the derivatives of these displacements. To determine the complete displacement field of objects of arbitrary shape, one holographic plate is sufficient, using two times two-point light sources.
15 citations
TL;DR: In this article, a nonlinear equation governing large amplitude oscillation in a thin hyperelastic tube is reduced for a four-parameter class of strain energy potentials to a canonical form amenable to exact solution via an extension of Pinney's theorem.
Abstract: A non-linear equation governing large amplitude oscillation in a thin hyperelastic tube is reduced for a four-parameter class of strain energy potentials to a canonical form amenable to exact solution via an extension of Pinney's theorem. The displacement field associated with both free oscillation and Heaviside loading problems are thereby solved explicitly. Results due to Shahinpoor and Nowinski for Mooney-Rivlin materials emerge as special cases of the present analysis.
TL;DR: In this paper, the creep buckling of thin nonshallow spherical shells is treated, the material of which is assumed to be isotropic and linearly viscoelastic with special temperature dependence of its mechanical properties so as to fit the thermorheologically simple body model.
Abstract: The creep buckling of thin nonshallow spherical shells is treated, the material of which is assumed to be isotropic and linearly viscoelastic with special temperature dependence of its mechanical properties so as to fit the thermorheologically simple body model. The shell is subjected to uniform external pressure smaller than the classical buckling pressure for corresponding elastic shells. The prebuckling stress state is assumed to be the membrane state, and total deflections are less than or equal to the shell thickness. The classical stability criteria, uniqueness of equilibrium, is used in formulating the problem, defined by a linear integrodifferential equation in terms of displacement field W, and describing the adjacent equilibrium configuration, and it is assumed to be a function of coordinates and time. A first-step approximation to the governing equation is derived and used to determine the external critical pressure loading as a function of temperature, time, and shell geometry. For a shell made of a three-element model material a “safe load limit” is established.
Patent•
30 Jun 1980
TL;DR: A displacement machine operating according to the spiral principle has at least one parallel motion guide device provided to ensure a torsionally rigid relative movement of two displacement elements as mentioned in this paper, which is the minimum required for any displacement machine.
Abstract: A displacement machine operating according to the spiral principle has at least one parallel motion guide device provided to ensure a torsionally rigid relative movement of two displacement elements.
01 Jan 1980
TL;DR: In this article, a holographic type reconstruction technique using either 2-dimensional Fourier transform, or Rayleigh-Sommerfeld diffraction formulae, was used to reconstruct the field at the location of the defect from a knowledge of the field from an observation plane, a distance z away from the defect.
Abstract: We give here a theory for the nature of the image if produced by the scanning laser acoustic microscope (SLAM) at a surface in the far field of the flaw. A physical model and an exact calculation of scattering of longitudinal acoustic waves by spherical defects are presented. The total displacement field (incident plus scattered) is evaluated at planes at a distance from the defect by using the Ying and Truell scattering theory. It is found that evaluation of the exact type and size of a defect is not possible from direct observation of the total field. A holographic type reconstruction technique using either 2-dimensional Fourier transform, or Rayleigh-Sommerfeld diffraction formulae, was used to reconstruct the field at the location of the defect from a knowledge of the field at an observation plane, a distance z away from the defect. It is found that accurate defect characterization can be made using this reconstruction technique.
TL;DR: In this article, the authors measured the preferred orientation of basal planes of clay minerals at 80 points in a three-dimensional array, using an X-ray pole-figure goniometer.
TL;DR: In this article, a method for calculating the static displacements of lattice atoms near a defect atom is presented and applied to carbon occupying the octahedral site in α-iron.
Abstract: A method for calculating the static displacements of lattice atoms near a defect atom is presented and applied to carbon occupying the octahedral site in α-iron. The interaction between lattice atoms and the defect is assumed to extend to second neighbors, but a defect-lattice atom interatomic potential is neither assumed nor constructed. Instead the displacements of the first and second neighbors of the defect atom are treated as adjustable parameters, which can be determined experimentally, and the displacement field is calculated as a function of these parameters. A central, two-body Morse potential is used to describe the interaction of lattice atoms, and the lattice atom displacements are calculated for both harmonic and anharmonic (quartic) approximations of the potential. The latter calculation requires an iterative procedure that obtains self-consistent anharmonic displacements without sacrificing the convenience of the matrix inversion technique that is used to solve the harmonic problem.
TL;DR: In this paper, the displacement field within an infinite, fluid-loaded elastic plate insonified by a plane wave at arbitrary incidence angle is examined for a water-immersed steel plate which is 0·55 shear wavelengths thick.
TL;DR: In this paper, the slender body approximation is applied to a dilute system of flexibly inextensible fibres embedded in an elastic medium, and an explicit constitutive equation is derived for any arbitrary distribution of fibres in the undeformed configuration relating the bulk stress in the composite and the homogeneous displacement field.
TL;DR: In this paper, the average ratio of progressing torsional spectra versus the product of the displacement spectra and frequency, remains constant for a wide range of frequencies, and the same ratio is strongly frequency-dependent for locally standing waves.
Abstract: Horizontally polarized shear waves in an elastic layer perfectly bonded to a rigid half-space are considered. The layer is subjected to a steady-state horizontal displacement field. The displacement spectrum is evaluated in closed form. It consists of two types of waves: (1)Progressing waves; and (2)locally standing waves. The average ratio of progressing torsional spectra versus the product of the displacement spectra and frequency, remains constant for a wide range of frequencies. The same ratio is strongly frequency-dependent for locally standing waves. The contribution of locally standing waves to displacements is significant for distances from the source which are, at most, an order of one thickness of the layer.
TL;DR: For an edge dislocation loop lying in the plane parallel to the surface formulae, the features of the electron microscopical contrast are determined from the obtained displacement distribution regularities as discussed by the authors.
Abstract: For an edge dislocation loop lying in the plane parallel to the surface formulae are obtained for the displacement field gradient caused by stress relaxation on the free surface. The features of the electron microscopical contrast are determined from the obtained displacement distribution regularities. A comparison is made between theoretical images of a dipole in regard to the relaxation, and a loop without and with regard to the relaxation. It is shown that the calculated image constructed with regard to the stress relaxation on the free surface corresponds to the experiments almost exactly.
[Russian text ignored].
TL;DR: In this article, a plate thickness of 2·5 shear wavelengths was investigated, at which thickness nine Lamb modes can be excited, with consequent increase in the complexity of the evolution of the interior and exterior fields.
TL;DR: In this article, the transmitted field due to surface waves incident on a local irregularity of a plane-layered medium has been studied and a perturbation method to the first order and the Born approximation can be used if the variations in the thickness of the layers are sufficiently smooth and the wavelengths are long when compared to the size of the irregularities.
Abstract: The transmitted field due to surface waves incident on a local irregularity of a plane-layered medium has been studied. A perturbation method to the first order and the Born approximation can be used if the variations in the thickness of the layers are sufficiently smooth and the wavelengths are long when compared to the size of the irregularities. The spectrum of the perturbed part of the displacement field at the surface is a sum over the surface-wave modes for the regular medium, with an additional term involving the scattered body waves. Numerical computations have been performed for structures composed of a layer overlying a half-space. The contribution of the various modes to the transmitted Love or Rayleigh fields has been studied for several structures. A general method has been obtained to analyze the effect of a complex structure as the superposition of the fields due to simpler ones. When the layer thickness is kept unchanged, the incident mode is not perturbed to the first order. Synthetic seismograms, computed at stations sufficiently close to the irregular region, show how the perturbation of the signal depends on distance. A comparison has been made for Love waves with a finite element method. Both methods give very similar results when the stations are not too close to the irregularities so that the body-wave contribution is negligible. The local phase velocity shows departures from the curves for a regular model.
TL;DR: In this article, the displacement field is determined when a rigid spheroidal inclusion is present in an infinite, isotropic and homogeneous elastic medium under torsion.
Abstract: The displacement field is determined when a rigid spheroidal inclusion is present in an infinite, isotropic and homogeneous elastic medium under torsion. The values of the force and moment are derived. The solutions for the limiting cases of a sphere and a circular disk are also presented. The analysis is based on suitable distributions of singularities on the axis of symmetry of the inclusion.
TL;DR: In this article, an original elasto-plastic elbow element has been formulated and developed for inclusion in the library of a finite element code, based on the following theoretical aspects: theory 1. (a) Vlasov's thin shell theory13 is used to correlate generalised strains and mid-thickness displacements.
TL;DR: In this article, an extension of the common shape function concept is used to reduce hybrid elements to the basis of the simple minimum principle of potential energy with only one expansion of the displacements.
Abstract: Hybrid elements for the representation of elastic media are based upon extended variational principle. In the discretization process the hybrid deformation model requires an expansion of the displacement field as well as of the Lagrange multipliers at the boundary. Using an extension of the common shape function concept, these hybrid elements can be reduced to the basis of the simple minimum principle of potential energy with only one expansion of the displacements. An application to plate elements is given and a discussion about some consequences of the approach.
TL;DR: In this article, the utility of variational principles is indicated for certain half-space problems with an elliptical line of separation in the boundary conditions, where the displacement field at a specified but arbitrary point is constructed for certain classes of mixed boundary value problems associated with time harmonic linear elastodynamics.
TL;DR: In this paper, a curved finite element for the solution of shells of revolution is presented, where the shell geometry in general is approximated by a third order interpolation function with cubic and quintic polynomials.
Abstract: In this paper a curved finite element for the solution of shells of revolution is presented. The shell geometry in general, is approximated by a third order interpolation function. The displacement field has four components—three displacements and the rotation of the meridional plane of the of the shell. The displacement field is interpolated with cubic and quintic polynomials. The linear system involving the nodal unknowns is obtained from the principle of virtual work, together with the colateral condition relating the rotation to the other components of the displacement field. It is shown that broken generating lines for the shell surface do not limit the convergence of the solution. Finally, for numerical applications for static and dynamical problems presented.
TL;DR: In this paper, the elastic constants of fourth order lead to a variation of the displacement field along the dislocations of edge character, which is a nonlinear effect which involves the elastic constant of the fourth order.
TL;DR: In this paper, the static and dynamic critical behavior of uniaxial ferroelectrics of TGS, TGSe-type has been studied using an lsing model at d=4 in which the order parameter is coupled to the lattice displacement field.
Abstract: The static and dynamic critical behavior of uniaxial ferroelectrics of TGS, TGSe-type has been studied using an lsing model at d=4 in which the order parameter is coupled to the lattice displacement field. Assuming strong elastic anisotropy, we have solved the renormalization group equations and investigated the stability of the free energy in the one-loop approximation. The discontinuities of the elastic constants and sound damping coefficients at the transition point have been calculated.
TL;DR: In this article, earthquake occurrence is modeled as the opening of a crack in an infinite elastic medium triggered by the action of localized stress distributions and fracture is modelled as a continuum of infinitesimal dislocations.
Abstract: Some earthquake models based on the elastic theory of dislocations are presented Earthquake occurrence is modelled as the opening of a crack in an infinite elastic medium triggered by the action of localized stress distributions The fracture is modelled as a continuum of infinitesimal dislocations This approach allows us to have complete information about the stress field and the displacement field and to make a first step towards understanding the relation between source mechanism and stress distributions