### 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 language | English |
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Title of host publication | Computational Science and Its Applications – ICCSA 2019 - 19th International Conference, 2019, Proceedings |

Editors | Sanjay Misra, Elena Stankova, Vladimir Korkhov, Carmelo Torre, Eufemia Tarantino, Ana Maria A.C. Rocha, David Taniar, Osvaldo Gervasi, Bernady O. Apduhan, Beniamino Murgante |

Publisher | Springer |

Pages | 37-51 |

Number of pages | 15 |

ISBN (Print) | 9783030242886 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

Event | 19th International Conference on Computational Science and Its Applications, ICCSA 2019 - Saint Petersburg Duration: 1 Jul 2019 → 4 Jul 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11619 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 19th International Conference on Computational Science and Its Applications, ICCSA 2019 |
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Country | Russian Federation |

City | Saint Petersburg |

Period | 1/07/19 → 4/07/19 |

### Fingerprint

### Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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

}

*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.

Research output

TY - GEN

T1 - Computational Peculiarities of the Method of Initial Functions

AU - Matrosov, Alexander V.

PY - 2019/1/1

Y1 - 2019/1/1

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.

KW - Computational instability

KW - Method of initial functions

KW - Orthotropic solid

UR - http://www.scopus.com/inward/record.url?scp=85069219114&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-24289-3_4

DO - 10.1007/978-3-030-24289-3_4

M3 - Conference contribution

AN - SCOPUS:85069219114

SN - 9783030242886

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 37

EP - 51

BT - Computational Science and Its Applications – ICCSA 2019 - 19th International Conference, 2019, Proceedings

A2 - Misra, Sanjay

A2 - Stankova, Elena

A2 - Korkhov, Vladimir

A2 - Torre, Carmelo

A2 - Tarantino, Eufemia

A2 - Rocha, Ana Maria A.C.

A2 - Taniar, David

A2 - Gervasi, Osvaldo

A2 - Apduhan, Bernady O.

A2 - Murgante, Beniamino

PB - Springer

ER -