A modified crack closure integral method for calculating stress intensity factors for cracked plates subject to bending loads

A method is developed to calculate strain energy release rates, G, or stress intensity factors, K, using only nodal forces and displacements from a standard finite element analysis code. The method is an extension of the modified crack closure integral (MCCI) approach to the bending of plates with through cracks. An examination of bending of plates with through cracks based on shear deformation theories has shown that the bending K depends strongly on the ratio of plate thickness, h, and half crack length, a. Hence, the need to examine the effect of h/a on the accuracy of G and K obtained by the MCCI approach is examined. The accuracy of the MCCI method is verified by analyzing a square plate with a central crack subjected to a uniform edge moment and comparing the results with those reported in the literature

Finite element analysis of plates with through cracks from higher order plate theory

A special crack tip element for plate bending is developed using general crack tip solutions derived from a continuum analysis through Reissnerls theory. It is demonstrated that using this in combination with a conventional shear flexible element, accurate results for bending stress intensity factor can be obtained over a wide range of a plate thickness parameter

Exact and Asymptotic Conditions on Traveling Wave Solutions of the Navier-Stokes Equations

We derive necessary conditions that traveling wave solutions of the Navier-Stokes equations must satisfy in the pipe, Couette, and channel flow geometries. Some conditions are exact and must hold for any traveling wave solution irrespective of the Reynolds number ($Re$). Other conditions are asymptotic in the limit $Re\to\infty$. The exact conditions are likely to be useful tools in the study of transitional structures. For the pipe flow geometry, we give computations up to $Re=100000$ showing the connection of our asymptotic conditions to critical layers that accompany vortex structures at high $Re$

The Recursion Method Applied to the T=0 Dynamics of the 1D s=1/2 Heisenberg and XY Models

The frequency‐dependent spin autocorrelation functions for the 1D s=1/2 Heisenberg and XY models at zero temperature are determined by the recursion method. These applications further demonstrate the efficacy of a new calculational scheme developed for the termination of continued fractions. A special feature of the recursion method highlighted here is its capability to predict the exponent of the infrared singularities in spectral densities

Dynamical Properties of Quantum Spin Systems in Magnetically Ordered Product Ground States

The one‐dimensional spin‐s XYZmodel in a magnetic field of particular strength has a ferro‐ or antiferromagnetically ordered product ground state. The recursion method is employed to determine T=0 dynamic structure factors for systems with s=1/2, 1, 3/2. The line shapes and peak positions differ significantly from the corresponding spin‐wave results, but their development for increasing values of s suggests a smooth extrapolation to the spin‐wave picture