Computational Peculiarities of the Method of Initial Functions

Research output

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.

Original languageEnglish
Title of host publicationComputational Science and Its Applications – ICCSA 2019 - 19th International Conference, 2019, Proceedings
EditorsSanjay Misra, Elena Stankova, Vladimir Korkhov, Carmelo Torre, Eufemia Tarantino, Ana Maria A.C. Rocha, David Taniar, Osvaldo Gervasi, Bernady O. Apduhan, Beniamino Murgante
PublisherSpringer
Pages37-51
Number of pages15
ISBN (Print)9783030242886
DOIs
Publication statusPublished - 1 Jan 2019
Event19th International Conference on Computational Science and Its Applications, ICCSA 2019 - Saint Petersburg
Duration: 1 Jul 20194 Jul 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11619 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th International Conference on Computational Science and Its Applications, ICCSA 2019
CountryRussian Federation
CitySaint Petersburg
Period1/07/194/07/19

Fingerprint

Mantissa
Rectangle
Harmonic
Circular function
Maple
Elastic body
Computational Experiments
Express
Unstable
Face
Line
Experiments

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Matrosov, A. V. (2019). Computational Peculiarities of the Method of Initial Functions. In S. Misra, E. Stankova, V. Korkhov, C. Torre, E. Tarantino, A. M. A. C. Rocha, D. Taniar, O. Gervasi, B. O. Apduhan, ... B. Murgante (Eds.), Computational Science and Its Applications – ICCSA 2019 - 19th International Conference, 2019, Proceedings (pp. 37-51). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11619 LNCS). Springer. https://doi.org/10.1007/978-3-030-24289-3_4
Matrosov, Alexander V. / Computational Peculiarities of the Method of Initial Functions. Computational Science and Its Applications – ICCSA 2019 - 19th International Conference, 2019, Proceedings. editor / Sanjay Misra ; Elena Stankova ; Vladimir Korkhov ; Carmelo Torre ; Eufemia Tarantino ; Ana Maria A.C. Rocha ; David Taniar ; Osvaldo Gervasi ; Bernady O. Apduhan ; Beniamino Murgante. Springer, 2019. pp. 37-51 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Matrosov, AV 2019, Computational Peculiarities of the Method of Initial Functions. in S Misra, E Stankova, V Korkhov, C Torre, E Tarantino, AMAC Rocha, D Taniar, O Gervasi, BO Apduhan & B Murgante (eds), Computational Science and Its Applications – ICCSA 2019 - 19th International Conference, 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11619 LNCS, Springer, pp. 37-51, Saint Petersburg, 1/07/19. https://doi.org/10.1007/978-3-030-24289-3_4

Computational Peculiarities of the Method of Initial Functions. / Matrosov, Alexander V.

Computational Science and Its Applications – ICCSA 2019 - 19th International Conference, 2019, Proceedings. ed. / Sanjay Misra; Elena Stankova; Vladimir Korkhov; Carmelo Torre; Eufemia Tarantino; Ana Maria A.C. Rocha; David Taniar; Osvaldo Gervasi; Bernady O. Apduhan; Beniamino Murgante. Springer, 2019. p. 37-51 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11619 LNCS).

Research output

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N2 - 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.

AB - 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.

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Matrosov AV. Computational Peculiarities of the Method of Initial Functions. In Misra S, Stankova E, Korkhov V, Torre C, Tarantino E, Rocha AMAC, Taniar D, Gervasi O, Apduhan BO, Murgante B, editors, Computational Science and Its Applications – ICCSA 2019 - 19th International Conference, 2019, Proceedings. Springer. 2019. p. 37-51. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-24289-3_4