@inproceedings{6af284a614a840549aca871f35e9fa25,

title = "Computational Peculiarities of the Method of Initial Functions",

abstract = "The paper investigates the computational features of the method of initial functions. Its idea is to express the components of the stress and strain state of an elastic body through initial functions defined on the initial line (a 2D problem) or surface (a 3D problem). A solution by the method of initial functions for a linear-elastic orthotropic rectangle under plane deformation is constructed. Its implementation when initial functions are represented by trigonometric functions is given. The influence of the value of a load harmonic on stable computations is studied on the example of bending of a free-supported rectangle of average thickness under the normal load specified on its upper boundary face. The causes of computational instability of the algorithm of the method of initial functions are found out. A modified algorithm is presented to increase twice the limit value of the “stable” harmonic. It is noted that calculations with a long mantissa should be cardinally performed to solve the problem of unstable computations. The results of computational experiments to determine the maximum harmonics for stable calculations of orthotropic rectangle depending on its relative thickness and mantissa length are presented. Implementation of the algorithm of the initial function method and calculations are performed using the system of analytical calculations Maple.",

keywords = "Computational instability, Method of initial functions, Orthotropic solid",

author = "Matrosov, {Alexander V.}",

note = "Matrosov A.V. (2019) Computational Peculiarities of the Method of Initial Functions. In: Misra S. et al. (eds) Computational Science and Its Applications – ICCSA 2019. ICCSA 2019. Lecture Notes in Computer Science, vol 11619. Springer, Cham; 19th International Conference on Computational Science and Its Applications, ICCSA 2019 ; Conference date: 01-07-2019 Through 04-07-2019",

year = "2019",

doi = "10.1007/978-3-030-24289-3_4",

language = "English",

isbn = "9783030242886",

series = "Lecture Notes in Computer Science ",

publisher = "Springer Nature",

pages = "37--51",

editor = "Sanjay Misra and Osvaldo Gervasi and Beniamino Murgante and {et al.}",

booktitle = "Computational Science and Its Applications – ICCSA 2019",

address = "Germany",

}