Grid deformation

Figure 2.59 Grid deformation following a wave propagating from right to left on a liquid surface.

Indications concerning the nature of the flow of the powder was obtained by disposing in grid pattern small (0.5 mm) lead balls in some of the beds tested. Grid deformation could be monitored by taking X ray pictures at different points along the slider course (fig.12). Clearly, the scale of the contact is multiplied as the thickness of the bed is of the order of the centimeter and the inclined plane is 20 cm long. 

In numerical analysis, both functions of normal surface deformation and pressure distribution have to be discretized in a space domain over U grid points for a line load, or grid points for two-dimensional distributed load. As an example, the deformation for line loading can be rewritten in discrete form as follows ... 

Comparisons of the accuracy and efficiency for three numerical procedures, the direct summation, DC-FFT-based method and MLMI, are made in this section. The three methods were applied to calculating normal surface deformations at different levels of grids, under the load of a uniform pressure on a rectangle area 2a X 2fo, or a Hertzian pressure on a circle area in radius a. The calculations were performed on the same personal computer, the computational domain was set as -1.5a=Sx 1.5a and -1.5a=Sy 1.5a, and covered... 

Fig. 5—A comparison of deformation profiies at =0 on 256 X256 grid for a uniform pressure on a rectangie area 2aX2b, obtained from the three methods.

A major message carried in this section is that the FFT-based method is faster and easier to implement but with similar accuracy in comparison to the MLMI, so it is expected to be a powerful numerical approach suitable for the deformation computations, especially when a larger number of grid nodes are involved. 

Upon the reconstruction of the full 3D velocity field, the deformation of the Cartesian grid is recreated on selected slices (Figure 4.4.6(c)) in order to verify that the algorithm is properly implemented. 

Most of the relevant features of the charge density distribution can be elegantly elucidated by means of the topological analysis of the total electron density [43] nevertheless, electron density deformation maps are still a very effective tool in charge density studies. This is especially true for all densities that are not specified via a multipole model and whose topological analysis has to be performed from numerical values on a grid. 

Figure 17. Diametral compression test. Deformations are followed by compression gages, cross head travel, and grid markings on the sample surface...

An Instron Testing System (Model 1122), fitted with a 10 cm six-wire grid (Ottawa Texture measuring system, OTMS cell) was used to determine rheological properties. A loading rate of 50 mm/min and a chart speed of 500 mm/min resulted in a well defined force-deformation curve. Force at the bioyield point and the area under the curve were calculated. These values were then converted into maximum stress, work and specific work values ... 

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