# Ansys 16 Magnitude

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## Ansys 16 Magnitude

The phase delay and groupdelay of linear phase FIR filters are equal and constant over thefrequency band. For an order n linear phase FIRfilter, the group delay is n/2, and the filteredsignal is simply delayed by n/2 time steps (andthe magnitude of its Fourier transform is scaled by the filter's magnituderesponse). This property preserves the wave shape of signals in thepassband; that is, there is no phase distortion.

Kaiser Window Order Estimation. The kaiserord functionestimates the filter order, cutoff frequency, and Kaiser window betaparameter needed to meet a given set of specifications. Given a vectorof frequency band edges and a corresponding vector of magnitudes,as well as maximum allowable ripple, kaiserord returnsappropriate input parameters for the fir1 function.

return row vector b containing the n+1 coefficients of the order n FIR filter whose frequency-magnitude characteristics match those given by vectors f and m. f is a vector of frequency points ranging from 0 to 1, where 1 represents the Nyquist frequency. m is a vector containing the specified magnitude response at the points specified in f. (The IIR counterpart of this function is yulewalk, which also designs filters based on arbitrary piecewise linear magnitude responses. See IIR Filter Design for details.)

The Constrained Least Squares (CLS) FIR filter design functionsimplement a technique that enables you to design FIR filters withoutexplicitly defining the transition bands for the magnitude response.The ability to omit the specification of transition bands is usefulin several situations. For example, it may not be clear where a rigidlydefined transition band should appear if noise and signal informationappear together in the same frequency band. Similarly, it may makesense to omit the specification of transition bands if they appearonly to control the results of Gibbs phenomena that appear in thefilter's response. See Selesnick, Lang, and Burrus [2] for discussionof this method.

The key feature of the CLS method is that it enables you to define upper and lower thresholds that contain the maximum allowable ripple in the magnitude response. Given this constraint, the technique applies the least square error minimization technique over the frequency range of the filter's response, instead of over specific bands. The error minimization includes any areas of discontinuity in the ideal, "brick wall" response. An additional benefit is that the technique enables you to specify arbitrarily small peaks resulting from the Gibbs phenomenon.

fircls uses the same technique to design FIR filters with a specified piecewise constant magnitude response. In this case, you can specify a vector of band edges and a corresponding vector of band amplitudes. In addition, you can specify the maximum amount of ripple for each band.

Supporting the single-phase HEA approach, it is believed that solid solution strengthening is more effective in HEAs than in conventional alloys [3]. The problem is complex, and present analysis shows that solid solution hardening in HEAs can be as much as an order of magnitude higher than in binary alloys [4]. However, the potency of HEA solid solution strengthening has not been sufficiently studied, especially for extended loading times or at temperatures above Tm/2. There have been no studies to establish effectiveness of solid solution hardening in creep loading of HEAs.

Perhaps the most significant benefit of HEAs has little to do with the magnitude of configurational entropy. A major benefit of HEAs is that they stimulate the study of compositionally complex alloys not previously considered. This suggests an astronomical number of compositions, giving great potential for discoveries of scientific and practical benefit. Supporting this view, a wide array of HEA microstructures has been produced, including single phase, multiple phase, nanocrystalline and even amorphous alloys. A relatively small number of HEA systems currently receive a major portion of attention, and we propose the exploration of an expanded range of HEAs. To most effectively explore this vast alloy space, we define a palette of elements from which HEAs can be designed to meet a particular set of target properties (Section 3.2). This is coupled with aggressive use of high-throughput computational and experimental techniques (Section 3.5).

Here we are concerned more broadly with the competitiveness of a single-phase solid solution (which depends primarily on the magnitude of Î”Sconf), and less so with whether compounds form in a given alloy (which also depends on Î”Hf of all competing phases). Thus, both CoCrFeMnNi and TiCrFeMnNi equimolar alloys are considered HEAs in the present work, although the former is a disordered single-phase and the latter forms intermetallic compounds [8]. Both have the same Î”Sconf at high temperature and differ primarily in the magnitude of Î”Hf of the competing phases. The magnitude of Î”Sconf in an HEA does not guarantee suppression of intermetallic compounds, but it does increase the probability that this will occur (see Section 2.2). Even when Î”Sconf is insufficient to suppress compounds, it may nevertheless influence the temperature at which the intermetallic phase dissolves upon heating. The ability to influence the dissolution temperature of a second phase has profound importance via the particle strengthening mechanism. This will be developed in more detail in Section 2.2 and can be applied to the development of new HEAs (Section 3.3.2).

HEAs offer an exceptional testing ground to develop and implement high-throughput test and evaluation methods described here. As stated in the Introduction, perhaps the most important contribution of the HEA concept is to motivate the systematic exploration of a vast and unexplored composition space, regardless of the magnitude of configurational entropy or its influence on the stability of competing phases. While HEAs represent a truly astronomical number of compositions, they are still only a subset of the full space of compositionally complex alloys that may or may not meet the definitions used to bound HEAs. The strategy outlined here applies to any large number of structural materials, and is by no means limited to HEAs.

Displacements : a) Displacement x (dx) Elementary Theory for an Axially-loaded Member Predictions: To determine the displacement of the neutral axis, we can use the concept of strain. The definition of Strain is elongation per unit length, which is expressed by : e = d/L , where e is strain, d is elongation or stretching of the the material, and L is the length from the origin. Since L is known, and strain is also known from the previous analysis, we can use this expression to find the displacement. And since we first consider the displacement in x direction, the value of strain used in the calculation is Axial Strain (Strain xx). Calculate the elongation at different points along the length of the bar, for example at L = 0, 2, 4 inches. L=0; dx = 0* 6.667E-4 = 0.00 in. L=2; dx = 2* 6.667E-4 = 0.0013334 in. L=4; dx = 4* 6.667E-4 = 0.0026668 in. ANSYS Predictions: Figure 13 and 14 show the ANSYS results for the displacement x. Both the 4 element model and 16 element model give pretty much the same values for displacement at the same locations, that is L=2; dx = 0.001333 in. L=2; dx = 0.001333 in. The results at L=0 for both cases are slightly different. For 4 element model dx = 0.271E-17 in., but for 16 element model dx = 0.412E-17 in. However, both numbers are quite small and essentially zero. Note: The red circle marks the maximum displacement in x direction. Figure 13 (Query Displacement x for 4 element model) Figure 14 (Query Displacement x for 16 element model) b) Displacement y (dy) Elementary Theory for an Axially-loaded Member Predictions: Use the same equation e = d/L to determine the displacement in y direction, but this time the value of Lateral Strain is used for e. Also use different values of L along the height of the bar to locate the points of interest. For example, L = -1, 0, 1 L=-1; dx = -1* -2.0001E-4 = 2.0001E-4 in. L=0; dx = 0* -2.0001E-4 = 0.00 in. L=1; dx = 1* -2.0001E-4 = -2.0001E-4 in. ANSYS Predictions: Figure 15 and 16 show ANSYS results for displacement y. It is shown that 4 element model and 16 element model give the same results. Displacement at the points along the x-axis are zero (-.325E-18 and .240E-17 are very small and essentially zero) The maximum displacement in y direction is at 1 inch above and below the x-axis and has magnitude of 2.00E-3 in.The negative and positive signs indicate the direction of the displacement. Thus, negative value at the position 1 in. above the x-axis and positive value at 1 in. below the x-axis imply that the plate is shortening in y direction. Figure 15 (Query Displacement y for 4 element model) Figure 16 (Query Displacement y for 16 element model) Interpretation of the Results: Usually we know by inspection that when the bar is in tension, it is stretched in x direction, and as a result, it is shortened in the y direction. According to the analysis above and the figures shown, the results are as we expected. Note : We also can define the displacement using another equation combining the basic relationship between stress and strain : d = PL/EA This equation shows that the elongation of a prismatic bar is directly proportional to the load P, the length L, and inversely proportional to the modulus of elasticity E and the cross-sectional area A. For this equation, the sign convention is important. The elongation is usually taken as positive and shortening as negative. Overall, we have seen that mesh resolution is not an issue for this problem. For some simple loading geometries, it is possible for ANSYS to give exact answers for a small number of elements. This is one of those cases. In fact, you would have obtained the same stress and strain results if you had modeled the plate with a signle 4-noded rectangular element. This type of behavior is not typical, however. In more complex engineering analysis, finite element results will approach exact values only in the limit as a large number of elements are used. Use of mesh resolution that yields sufficient accuracy. Without consuming large amounts of computing and user time is a critical issue in finite element modeling. A Note on Linearity: The ANSYS model you have constructed assumes linear elastic behavior. Because of this, the stresses, strains and displacements scale with the applied load. As a result, if you need to obtain the stresses, strains and displacements for a different applied load, you can simply re-scale the results you already have. A new ANSYS run is not needed. For instance, if the applied load were 10,000 lb, the stresses, strains and displacements would be one-half of those obtained for 20,000 lb.