Elastic Crack Propagation Along a Pressurized Pipe

1976 ◽  
Vol 98 (1) ◽  
pp. 2-7 ◽  
Author(s):  
A. F. Emery ◽  
W. J. Love ◽  
A. S. Kobayashi
Keyword(s):  
Finite Difference ◽  
Transverse Shear ◽  
Critical Stress ◽  
Maximum Stress ◽  
Terminal Velocity ◽  
Rotatory Inertia ◽  
Stress Criterion ◽  
Short Cracks ◽  
Elastic Crack ◽  
Pressurized Cylinder

A finite difference shell code which considers transverse shear and rotatory inertia is used to calculate the dynamic behavior of axially running cracks. Short cracks were instantaneously introduced into a static pressurized cylinder and their tips advanced according to a maximum stress criterion. Calculations were made for a range of the critical stress and the terminal velocity of the crack tip was found to be linearly related to the value of the critical stress. Calculations were also made for rapid and slow depressurization of the cylinder to observe the nature of the arrest. In all cases where arrest occurred it did so abruptly.

scholarly journals Dynamic faulting studied by a finite difference method

1982 ◽  
Vol 72 (2) ◽  
pp. 345-369
Author(s):  
Jean Virieux ◽  
Raul Madariaga
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Maximum Stress ◽  
Numerical Solutions ◽  
Shear Crack ◽  
Numerical Results ◽  
Three Dimensions ◽  
Shear Cracks ◽  
Stress Criterion

Abstract We have developed a finite difference method that is especially adapted to the study of dynamic shear cracks. We studied a number of simple earthquake source models in two and three dimensions with special emphasis on the modeling of the stress field. We compared our numerical results for semi-infinite and self-similar shear cracks with the few exact solutions that are available in the literature. We then studied spontaneous rupture propagation with the help of a maximum stress criterion. From dimensional arguments and a few simple examples, we showed that the maximum stress criterion depended on the physical dimensions of the fault. For a given maximum stress intensity, the finer the numerical mesh, the higher the maximum stress that had to be adopted. A study of in-plane cracks showed that at high rupture velocities, the numerical results did not resolve the stress concentration due to the rupture front from the stress peak associated with the shear wave propagating in front of the crack. We suggest that this is the reason why transonic rupture velocities are found in the numerical solutions of in-plane faulting when the rupture resistance is rather low. Finally, we studied the spontaneous propagation of an initially circular rupture. Two distinct modes of nucleation of the rupture were studied. In the first, a plane circular shear crack was formed instantaneously in a uniformly prestressed medium. After a while, once stress concentrations had developed around the crack edge, the rupture started to grow. In the second type of nucleation, a preexisting circular crack became unstable at time t = 0 and started to grow. The latter model appeared to us as a more realistic simulation of earthquake triggering. In this case, the initial stress was nonuniform and was the static field of the preexisting fault.

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

The Influence of Rotatory Inertia and Transverse Shear on the Dynamic Plastic Behavior of Beams

1979 ◽  
Vol 46 (2) ◽  
pp. 303-310 ◽  
Author(s):  
Norman Jones ◽  
J. Gomes de Oliveira
Keyword(s):  
Transverse Shear ◽  
Shear Force ◽  
Yield Criterion ◽  
Yield Condition ◽  
Bending Moment ◽  
Plastic Behavior ◽  
Plastic Response ◽  
Rotatory Inertia ◽  
Perfectly Plastic ◽  
Theoretical Procedure

The theoretical procedure presented herein examines the influence of retaining the transverse shear force in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Exact theoretical rigid perfectly plastic solutions are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively. It transpires that rotatory inertia might play a small, but not negligible, role on the response of these beams. The results in the various figures indicate that the greatest departure from an analysis which neglects rotatory inertia but retains the influence of the bending moment and transverse shear force in the yield condition is approximately 11 percent for the particular range of parameters considered.

Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress

1985 ◽  
Vol 52 (3) ◽  
pp. 536-542 ◽  
Author(s):  
K. S. Sivakumaran ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Orientation Angle ◽  
Nonlinear Frequency ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Transverse Normal Stress

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.

Symmetric Flexural Vibrations of a Clamped Circular Disk

1956 ◽  
Vol 23 (2) ◽  
pp. 319
Author(s):  
H. Deresiewicz
Keyword(s):  
Shear Deformation ◽  
Frequency Spectrum ◽  
Transverse Shear ◽  
Circular Disk ◽  
Transverse Shear Deformation ◽  
Axially Symmetric ◽  
Rotatory Inertia ◽  
Flexural Vibrations ◽  
Clamped Edges

Abstract The frequency spectrum is computed for the case of free, axially symmetric vibrations of a circular disk with clamped edges, using a theory which includes the effects of rotatory inertia and transverse shear deformation.

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