Elastic displacements for various edge-cracked plate specimens
Elastic displacements for various edge-cracked plate specimens using boundary collocation computing procedures
FRACTURE TOUGHNESS↗
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An approximate three-dimensional theory of plates with application to crack problems
Approximative three dimensional solution for crack in elastic plates
Hartranft, R. J.↗
Evaluation of the use of a singularity element in finite element analysis of center-cracked plates
Two different methods are applied to the analyses of finite width linear elastic plates with central cracks. Both methods give displacements as a primary part of the solution. One method makes use of Fourier transforms. The second method employs a coarse mesh of triangular second-order finite elements in conjunction with a single singularity element subjected to appropriate additional constraints. The displacements obtained by these two methods are in very good agreement. The results suggest considerable potential for the use of a cracked element for related crack problems, particularly in connection with the extension to nonlinear material behavior.
Mendelson, A.↗
Noise transmission through plates into an enclosure
An analytical model is presented to predict noise transmission through elastic plates into a hard-walled rectangular cavity at low frequencies, that is, frequencies up through the first few plate and cavity natural frequencies. One or several nonoverlapping and independently vibrating panels are considered. The effects on noise transmission of different external-pressure excitations, plate boundary conditions, fluid parameters, structural parameters, and geometrical parameters were investigated.
Mcdonald, W. B.↗
An elastic-perfectly plastic analysis of the bending of the lithosphere at a trench
A number of authors have modeled the flexure of the lithosphere at an oceanic trench using a thin elastic plate with a hydrostatic restoring force. In some cases good agreement with observed topography is obtained but in other cases the slope of the lithosphere within the trench is greater than that predicted by the elastic theory. In this paper the bending of a thin plate is considered using an elastic-perfectly plastic rheology. It is found that the lithosphere behaves elastically seaward of the trench, but that plasticity decreases the radius of curvature within the trench. The results are compared with a number of observed trench profiles. The elastic-perfectly plastic profiles are in excellent agreement with those profiles that deviate from elastic behavior.
Turcotte, D. L.↗
Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory
A higher-order shear deformation theory is used to demonstrate the natural frequencies and buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia. Exact solutions of simply supported plates are obtained and the results are compared with the exact solutions of three-dimensional elasticity theory, the first-order shear deformation theory, and the classical plate theory. The present theory predicts the frequencies and buckling loads more accurately when compared to the first-order and classical plate theories.
Reddy, J. N.↗
Nonlinear vibrations of rectangular plates.
A finite-difference method is developed to determine the large amplitude dynamic responses of thin elastic plates subjected to uniform pressure pulse-type loads. Four different sets of boundary conditions are considered. Some specific problems are solved. The results are compared with approximate solutions obtained by Yamaki (1961). The numerical method presented provides an accurate and efficient approximate solution to the problem, and should be useful as a check on other approximate methods. The grid-size and the time-step necessary for obtaining numerical stability depend on the particular problem. For many cases the method converges rapidly and a rather large grid-size and time-step is adequate.
Bayles, D. J.↗
A theory for the fracture of thin plates subjected to bending and twisting moments
Stress fields near the tip of a through crack in an elastic plate under bending and twisting moments are reviewed assuming both Kirchhoff and Reissner plate theories. The crack tip displacement and rotation fields based on the Reissner theory are calculated. These results are used to calculate the J-integral (energy release rate) for both Kirchhoff and Reissner plate theories. Invoking Simmonds and Duva's (1981) result that the value of the J-integral based on either theory is the same for thin plates, a universal relationship between the Kirchhoff theory stress intensity factors and the Reissner theory stress intensity factors is obtained for thin plates. Calculation of Kirchhoff theory stress intensity factors from finite elements based on energy release rate is illustrated. It is proposed that, for thin plates, fracture toughness and crack growth rates be correlated with the Kirchhoff theory stress intensity factors.
Hui, C. Y.↗
Line-spring model for surface cracks in a Reissner plate
In this paper the line-spring model developed by Rice and Levy for a surface crack in elastic plates is reconsidered. The problem is formulated by using Reissner's plate bending theory. For the plane strain problem of a strip containing an edge crack and subjected to tension and bending new expressions for stress intensity factors are used which are valid up to a depth-to-thickness ratio of 0.8. The stress intensity factors for a semi-elliptic and a rectangular crack are calculated. Considering the simplicity of the technique and the severity of the underlying assumptions, the results compare rather well with the existing finite element solutions.
Delale, F.↗
Transverse elastic impact of a sphere against an anisotropic plate
Transverse elastic impact of sphere against anisotropic plate
SPHERE↗
Lithospheric flexure at fracture zones
Studies attempting to demonstrate that lithospheric flexure occurs across the Pioneer and Mendocino fracture zones, and that the flexural topography is a topographic expression at these fracture zones, are presented. The flexure is modelled and compared with predicted depths with five bathymetric profiles which cross the two fracture zones at different ages. The model uses a thin elastic plate overlying an incompressible fluid half-space, and incorporates a temperature-dependent effective elastic thickness. Several conclusions were derived from this study. First, it is found that no significant slip on the fossil fault planes of the Mendocino and Pioneer fracture zones exists. In addition, the flexural amplitude is determined to increase with age. Finally, it is concluded that there is elastic coupling between the Mendocino and Pioneer fracture zones since the separation is less than a flexural wavelength.
Sandwell, D.↗
Analysis of vibration characteristics of thin plates covered with a thin viscous layer
The equation of motion was used to examine the problem of vibrations of a thin elastic plate covered with a thin viscous layer. Mathematical formulation and the solution of the problem are given.
Damashyavichyus, A. K.↗
Alternating method applied to edge and surface crack problems
The Schwarz-Neumann alternating method is employed to obtain stress intensity solutions to two crack problems of practical importance: a semi-infinite elastic plate containing an edge crack which is subjected to concentrated normal and tangential forces, and an elastic half space containing a semicircular surface crack which is subjected to uniform opening pressure. The solution to the semicircular surface crack is seen to be a significant improvement over existing approximate solutions. Application of the alternating method to other crack problems of current interest is briefly discussed.
Hartranft, R. J.↗
Determination of Ice Crust Thickness from Flanking Cracks Along Ridges on Europa
We use equations describing the deflection of an elastic plate below a line load to estimate ice crust thickness below ridges on Europa. Using a range of elastic parameters, ice thickness is calculated to fall in the range 0.2 2.6 km. Additional information is contained in the original extended abstract.
Billings, S. E.↗
Furrow Topography and the Elastic Thickness of Ganymede's Dark Terrain Lithosphere
The effective elastic thickness of Ganymede's lithosphere tell of the satellite's thermal evolution through time. Generally it has been inferred that dark terrain, which is less tectonically deformed than grooved terrain, represents regions of cooler and thicker lithosphere [1]. The ancient dark terrain is cut by furrows, tectonic troughs about 5 to 20 km in width, which may have formed in response to large ancient impacts [1, 2]. We have applied the methods of [3] to estimate effective elastic thickness based on topographic profiles across tectonic furrows, extracted from a stereo-derived digital elevation model (DEM) of dark terrain in Galileo Regio [4]. Asymmetry in furrow topography and inferred flexure suggests asymmetric furrow fault geometry. We find effective elastic thicknesses ~0.4 km, similar to analyzed areas alongside bright grooved terrain. Data and Analysis: A broken-plate elastic model.
Pappalardo, Robert T.↗
Impact of GRM: New evidence from the Soviet Union
Gravity information released by the Soviet Union allows the quantitative assessment of how the geopotential research mission (GRM) mission might effect the ability to use global gravity data for continental tectonic interpretation. The information is of an isostatic response spectra for eight individual tectonic units in the USSR. The regions examined include the Caroathians, Caucasus, Urals, Pamirs, Tien-Shan, Altal, Chersky Ridge, and East Siberian Platform. The 1 deg x 1 deg gravity data are used to calculate the admittances are used in two different sorts of tectonic studies of mountain belts in the USSR: (1) interpretation of isostatic responses in terms of plate models of compensation for mountainous terrain. Using geologic information concerning time of the orogeny, lithospheric plates involved, and polarity of subduction in collision zones, they convert the best-fitting flexural rigidity to an elastic plate thickness for the lithospheric plate inferred to underlie the mountains; the isostatic admittance functions is an attempt to directly model gravity and topography data for a few select regions in the Soviet Union. By knowing the value of the expected correlation between topography and gravity from the admittances, the Artemjev's map in mountainous areas can be calibrated, and the maps are converted back to Bouguer gravity. This procedure is applied to the Caucasus and southern Urals.
Mcnutt, M.↗
Crustal deformation along the San Andreas, California
The goal is to achieve a better understanding of the regional and local deformation and crustal straining processes in western North America, particularly the effects of the San Andreas and nearby faults on the spatial and temporal crustal deformation behavior. Construction of theoretical models based on the mechanics of coupled elastic plate, viscoelastic foundation and large scale crack mechanics provide a rational basis for the interpretation of seismic and aseismic anomalies and expedite efforts in forecasting the stability of plate boundary deformation. Special focus is placed on the three dimensional time dependent surface deformation due to localized slippage in a elastic layer coupled to a visco-elastic substrate. The numerical analysis is based on a 3-D boundary element technique. Extension to visco-elastic coupling demands the derivation of 3-D time dependent Green's function. This method was applied to analyze the viscoelastic surface displacements due to a dislocated embedded patch. Surface uplift as a function of time and position are obtained. Comparisons between surface uplift for long and short dislocated patches are made.
Li, Victor C.↗
An extended field method solution for a pulse loaded thin plate
This paper deals with a new extension of a weighted residual method of analysis called the extended field method. The extended field method is applied for the first time to the problem of the transient vibration of a uniformly thin elastic plate. Numerical results have been obtained which validate the analysis procedure and show better solution convergence than is obtainable by standard methods of analysis for the same number of degrees of freedom. Further studies are necessary to obtain still better convergence.
Donaldson, B. K.↗