Piecewise exact solution of nonlinear momentum conservation equation with unconditional stability for time increment

Exact solution is adopted for computation of the inviscid Burgers equation on finite difference grid. Initial condition and following computed values of the independent variable are assumed to be piecewisely linear between fixed grid points, and local exact solution is used to find the value at the next time step at each grid point. Comparisons of Piecewise Exact Solution Method (PESM), existing upwind scheme, and the analytic solution show that the present method is more accurate than the upwind scheme. The unconditional stability is a strong merit of this method and is shown with a test result

Studying Initiation and Growth of Shear Cracks in Reinforced Concrete Beams Using Full-Field Digital Imaging

The mechanisms which lead to shear failure of longitudinally reinforced concrete beams are complex and often misunderstood. In this paper, a combination of a special closed loop test technique and machine vision are applied to tests on two reinforced concrete beams failing in shear: one made of normal strength concrete and the second of high strength concrete. To control the progression of the shear crack, a closed-loop test technique was devised and employed such that the crack propagation was stable even during the post peak. To locate the crack and to measure the crack displacements, machine vision, a nondestructive measuring technique, was employed which gives full-field displacements of a viewed area. The displacement measurements are obtained by first grabbing digital images of the observed area at different stages of loading during the test. By comparing discrete subsets of the reference and target images using normalized cross correlation matching, the displacement fields of the images are calculated. Shear crack initiation and progression are monitored for the two beams tested through complete failure, and differences in the shear failures between reinforced beams made of normal and high strength concretes are noted