Empirical Approaches

In this approach, an initially designed part is fabricated and tested for its suitability in the application. If it does not serve the purpose fully, it is redesigned, refabricated, and retested. This kind of cycle is repeated until it 

As an alternative to the above-mentioned residual-stress based approach is a method based on multi-variable regression technique. For example, Walsh (1993) proposed expressions for the parallel shrinkage and the perpendicular shrinkage as follows  

The coefficients and bj k — 1. 5) are assumed to depend on material only. After obtained the coefficients with the associated material, they are input to filling and packing analyses to calculate the parallel and perpendicular shrinkages. The parallel and perpendicular shrinkages are then treated as the thermal strains (or converted to initial stresses) and passed to the structural analysis to calculate the shrinkage and warpage. 

Another approach described by Kennedy and Zheng (2002) is to introduce some correction factors to the residual-stress based model, and use the experimental shrinkage data to determine the correction factors. The semi-empirical method is known as the CRIMS (Corrected Residual In-Mold Stress) approach. 

As mentioned earlier, it is not feasible to generate test data for all possible combinations of load variations. However, there have been a number of experimental investigations of the problem and these have resulted in some very 

For a linear viscoelastic material in which the strain recovery may be regarded as the reversal of creep then the material behaviour may be represented by Fig. 2.49. Thus the time-dependent residual strain, Sr(t), may be expressed as 

Since there can be an infinite number of combinations of creep and recovery periods it has been found convenient to express this behaviour in terms of two dimensionless variables. The first is called the Fractional Recovery, defined as 

The second dimensionless variable is called the Reduced Time, tg, defined as 

Extensive tests have shown that if the final creep strain is not large then a graph of Fractional Recovery against Reduced Time is a master curve which 

Several equations have been formulated by various authors as presented in Table 8.8 for curves of S /cf versus consistency limits for remolded clays. For stable clays, ( ) varies between 20° and 35°. Stable loose silts and sands typically have values of ( ) between 28° and 34°. In addition, a correlation between and plasticity index has been given by Bjerrum and Simons (1960). 

When a fully saturated soil is sheared under undrained conditions and the results are interpreted in terms of total stresses, the material behaves as though it is purely cohesive. This holds for saturated sand as well as for clays (Bishop and Eldin, 1950). 

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The above expressions are empirical approaches, with m and D. as parameters, for including an anliamionic correction in the RRKM rate constant. The utility of these equations is that they provide an analytic fomi for the anliamionic correction. Clearly, other analytic fomis are possible and may be more appropriate. For example, classical sums of states for Fl-C-C, F1-C=C, and F1-C=C hydrocarbon fragments with Morse stretching and bend-stretch coupling anhamionicity [M ] are fit accurately by the exponential... 

Mark, A. E., Xu, Y., Liu, H., van Gunsteren, W. F. Rapid non-empirical approaches for estimating relative binding free energies. Acta Biochim. Polonica 42 (1995) 525-536... 

In principle, two different classes of structure generators can be distinguished, namely empirical approaches,. such as fragment-based or rule- and data-based... 

I 7,1 Empirical Approaches to the Calculation of Properties 7.1.2.1 Hybridization States... 

Several empirical approaches for NMR spectra prediction are based on the availability of large NMR spectral databases. By using special methods for encoding substructures that correspond to particular parts of the NMR spectrum, the correlation of substructures and partial spectra can be modeled. Substructures can be encoded by using the additive model greatly developed by Pretsch [11] and Clerc [12]. The authors represented skeleton structures and substituents by individual codes and calculation rules. A more general additive model was introduced... 

Inc, [34], is an example of a software package that can calculate 3D geometries, chemical shifts, and coupling constants using semi-empirical approaches (Figure 10.2-2). 

In this second empirical approach, which has also been used for C NMR spectra, predictions are based on tabulated chemical shifts for classes of structures, and corrected with additive contributions from neighboring functional groups or substructures. Several tables have been compiled for different types of protons. Increment rules can be found in nearly any textbook on NMR spectroscopy. 

Tersoff J 1988. New Empirical Approach for the Structure and Energy of Covalent Systems. Physical Review 837 6991-7000. 

Unlike the Hiickel and extended Hiickel methods, the semi-empirical approaches that explicitly treat electron-electron interactions give rise to Fock matrix element... 

In chemistry, there was clearly a great need to move ahead and bridge the gap between the earlier, entirely empirical approach of teaching and research and that incorporating the new trends of chem-... 

The pricing of a new chemical that will compete against other chemicals does involve the usual cost elements that set the price. However, it has been shown that an empirical approach may be of value. One empirical approach is the exclusion chart (7,8) developed in 1979 and modified several times over the years. The chart indicates the approximate volume that existing chemicals used for the same function have achieved at their price. There are exceptions where the new chemical can command a higher price and achieve comparable volume because it possesses a unique property. 

There are two approaches to estimation of AG fThe first is an empirical approach (36) based on dynamics of fluorescence quenching of aromatic hydrocarbons ia acetonitrile solution. Accordingly,... 

Ultrasonic Spectroscopy. Information on size distribution maybe obtained from the attenuation of sound waves traveling through a particle dispersion. Two distinct approaches are being used to extract particle size data from the attenuation spectmm an empirical approach based on the Bouguer-Lambert-Beerlaw (63) and a more fundamental or first-principle approach (64—66). The first-principle approach implies that no caHbration is required, but certain physical constants of both phases, ie, speed of sound, density, thermal coefficient of expansion, heat capacity, thermal conductivity. 

The metastable limit can provide an empirical approach to modeling primary nucleation. This limit, which was first observed in 1951 (6), must be determined through experimentation, and nucleation rate is correlated with the following equation... 

An empirical approach can also be used to relate growth kinetics to supersaturation with a power-law function of the form... 

Belt selection depends on power and development of the required tensile strength. Knowing drive-shaft power, belt tension can be calculated and a belt selected. However, since various combinations of width and ply thickness will develop the required strength, final selection is influenced by lump size, troughability of the belt, and abihty of the belt to support the load between idlers. Thus it is necessaiy to use an empirical approach to arrive at a belt selection which meets all requirements. 

Over 20 different methods have been proposed for predictions of secondary stmcture they can be categorized in two broad classes. The empirical statistical methods use parameters obtained from analyses of known sequences and tertiary stmctures. All such methods are based on the assumption that the local sequence in a short region of the polypeptide chain determines local stmcture as we have seen, this is not a universally valid assumption. The second group of methods is based on stereochemical criteria, such as compactness of form with a tightly packed hydrophobic core and a polar surface. Three frequently used methods are the empirical approaches of P.Y. Chou and G.D. Fasman and of J. Gamier, D.J. Osguthorpe and B. Robson (the GOR method), and third, the stereochemical method of V.l. him. 

It is perhaps not too fanciful to compare the stormy history of liquid crystals to that of colour centres in ionic crystals resolute empiricism followed by fierce strife between rival theoretical schools, until at last a systematic theoretical approach led to understanding and then to widespread practical application. In neither of these domains would it be true to say that the empirical approach sufficed to generate practical uses such uses in fact had to await the advent of good theory. 

You will find a very fundamental and in part, empirical approach to this subject. My experience has been for the majority of water treatment assignments over the... 

Example 3.5 Calculate the transverse modulus of the PEEK/carbon fibre composite referred to in Example 3.2, using both the simplified solid mechanics approach and the empirical approach. For PEEK = 0.36. 

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