Using the ERFI Function in the Problem of the Shape Optimization of the Compressed Rod
The shape of the optimal rod determined in the work meets the condition of mass conservation in relation to the reference rod. At the same time, this rod shows a significant increase in resistance to axial force. In the examples presented, this increase was 80 % and 117 %, respectively, for rods w...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2020-06-01
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| Series: | International Journal of Applied Mechanics and Engineering |
| Subjects: | |
| Online Access: | https://www.ijame-poland.com/Using-the-ERFI-Function-in-the-Problem-of-the-Shape-Optimization-of-the-Compressed,166855,0,2.html |
| _version_ | 1797750512127311872 |
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| author | J. Marcinowski M. Sadowski |
| author_facet | J. Marcinowski M. Sadowski |
| author_sort | J. Marcinowski |
| collection | DOAJ |
| description | The shape of the optimal rod determined in the work meets the condition of mass conservation in relation to the reference rod. At the same time, this rod shows a significant increase in resistance to axial force. In the examples presented, this increase was 80 % and 117 %, respectively, for rods with slenderness of 125 and 175. A practical benefit from the use of compression rods of the proposed shapes is clearly visible.
The example presented in this publication shows how great the utility in the structural mechanics can be, resulting from the applications of complex analysis (complex numbers). This approach to many problems can find its solutions, while they are lacking in the real numbers domains. What is more, although these are operations on complex numbers, these solutions have often their real representations, as the numerical example shows.
There are too few applications of complex numbers in the technique and science, therefore it is obvious that the use of complex analysis should have an increasing range.
One of the first people to use complex numbers was Girolamo Cardano. Cardano, using complex numbers, was solving cubic equations, unsolvable to his times – as the famous Franciscan and professor of mathematics Luca Pacioli put it in his paper Summa de arithmetica, geometria, proportioni et proportionalita (1494). It is worth mentioning that history has given Cardano priority in the use of complex numbers, but most probably they were discovered by another professor of mathematics – Scipione del Ferro (cf. [1]).
We can see, that already then, they were definitely important (complex numbers). |
| first_indexed | 2024-03-12T16:33:48Z |
| format | Article |
| id | doaj.art-bde3efc8002d4709bf4d0bfa94d4f50d |
| institution | Directory Open Access Journal |
| issn | 1734-4492 2353-9003 |
| language | English |
| last_indexed | 2024-03-12T16:33:48Z |
| publishDate | 2020-06-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | International Journal of Applied Mechanics and Engineering |
| spelling | doaj.art-bde3efc8002d4709bf4d0bfa94d4f50d2023-08-08T15:02:50ZengUniversity of Zielona GóraInternational Journal of Applied Mechanics and Engineering1734-44922353-90032020-06-01252758710.2478/ijame-2020-0021166855Using the ERFI Function in the Problem of the Shape Optimization of the Compressed RodJ. Marcinowski0M. Sadowski1Chair of Building Constructions, Institute of Civil Engineering, University of Zielona Góra, Szafrana 1, 65 – 516Zielona Góra, PolandChair of Building Constructions, Institute of Civil Engineering, University of Zielona Góra, Szafrana 1, 65 – 516Zielona Góra, PolandThe shape of the optimal rod determined in the work meets the condition of mass conservation in relation to the reference rod. At the same time, this rod shows a significant increase in resistance to axial force. In the examples presented, this increase was 80 % and 117 %, respectively, for rods with slenderness of 125 and 175. A practical benefit from the use of compression rods of the proposed shapes is clearly visible. The example presented in this publication shows how great the utility in the structural mechanics can be, resulting from the applications of complex analysis (complex numbers). This approach to many problems can find its solutions, while they are lacking in the real numbers domains. What is more, although these are operations on complex numbers, these solutions have often their real representations, as the numerical example shows. There are too few applications of complex numbers in the technique and science, therefore it is obvious that the use of complex analysis should have an increasing range. One of the first people to use complex numbers was Girolamo Cardano. Cardano, using complex numbers, was solving cubic equations, unsolvable to his times – as the famous Franciscan and professor of mathematics Luca Pacioli put it in his paper Summa de arithmetica, geometria, proportioni et proportionalita (1494). It is worth mentioning that history has given Cardano priority in the use of complex numbers, but most probably they were discovered by another professor of mathematics – Scipione del Ferro (cf. [1]). We can see, that already then, they were definitely important (complex numbers).https://www.ijame-poland.com/Using-the-ERFI-Function-in-the-Problem-of-the-Shape-Optimization-of-the-Compressed,166855,0,2.htmlcompressed rodhollow rodshape optimizationbuckling criterionanalytical approacherfi functionprogram mathematicatm |
| spellingShingle | J. Marcinowski M. Sadowski Using the ERFI Function in the Problem of the Shape Optimization of the Compressed Rod International Journal of Applied Mechanics and Engineering compressed rod hollow rod shape optimization buckling criterion analytical approach erfi function program mathematicatm |
| title | Using the ERFI Function in the Problem of the Shape Optimization of the Compressed Rod |
| title_full | Using the ERFI Function in the Problem of the Shape Optimization of the Compressed Rod |
| title_fullStr | Using the ERFI Function in the Problem of the Shape Optimization of the Compressed Rod |
| title_full_unstemmed | Using the ERFI Function in the Problem of the Shape Optimization of the Compressed Rod |
| title_short | Using the ERFI Function in the Problem of the Shape Optimization of the Compressed Rod |
| title_sort | using the erfi function in the problem of the shape optimization of the compressed rod |
| topic | compressed rod hollow rod shape optimization buckling criterion analytical approach erfi function program mathematicatm |
| url | https://www.ijame-poland.com/Using-the-ERFI-Function-in-the-Problem-of-the-Shape-Optimization-of-the-Compressed,166855,0,2.html |
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