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  • The results presented see Table and Fig prove

    2018-11-14

    The results presented (see Table 2 and Fig. 2) prove that the convergence of the obtained solution holds with an increase in the number of terms in somatostatin agonist (40). However, comparing the deflection and the moment curves to similar ones obtained by superposition of correcting functions [3] indicates that using this method for searching for the coefficients of homogenous solutions yields conservative values of bending moments in the clamped cross-section, although the behavior of the curves is similar. The obtained absolute deflection values were also lower than the corresponding ones determined by the superposition method. The numbers 2–5 and 7 of curves correspond to the n value (see Table 2), straight lines 9 to the cylindrical bending; curves 0 and 1 correspond to the solutions of Refs. [10] and [3], respectively The authors of Refs. [10,15] pointed out that numerical results produced a divergent solution with an increase in the number of terms in the expression for the deflection function (more than two or three), which is a series in terms of initial [10] or homogenous [15] functions (the results were obtained in these studies). The authors linked the decrease in accuracy with the increase of the modules of the eigenvalues , which leads to the convergence of the hyperbolic sine and cosine functions that contain these values. Agarev [10] states that an increase in the number of the terms held in the solution must be also accompanied by an increase in the number of significant digits in the roots , as well as in all the calculations. All calculations, including the calculations of the eigenvalues , were performed in this paper with better accuracy than in Refs. [10,15]. Therefore, the construction of the solution generating a minimum for functional (43) exhibited a convergent process in its behavior, as parasympathetic system should be. However, comparing these results with the ones obtained by superposition of correcting functions leads us to conclude that the calculations by the method of homogenous solutions that we have performed can hardly be deemed fully satisfactory as well. For example, the numerical results for plates with the aspect ratios of 0.5 and 1.0 are even less consistent with the known and more reliable data [3,16,17] obtained by other methods. In all likelihood, improved results can be achieved if all calculations are performed with an increased mantissa (for example, in the Maple system). Matrosov [18] notes the computational instability of the algorithm of initial functions (an equivalent of the method of homogenous solutions) for plane elasticity problems in a rectangular area when using trigonometric series for the higher harmonics. The author of Ref. [18] links this instability both to the fact that errors accumulate in calculating numerical coefficients in the series, and to the behavior of the convergence of the series themselves, resulting in a great loss of correct digits in the obtained sum of these series. These sums are in turn used as the coefficients of a resolving system which becomes ill-conditioned with an increase in the harmonic number. The author of [18] sees the solution to this problem in extending the size of the mantissa for calculations in the Maple computer algebra system and carries out the corresponding computational experiments. However, this study does not explain why other approximate methods do not have this drawback.
    Conclusion