Generalized Functions And Calculus Operators Of Mathematica Applied To Evaluation Of Influence Lines And Envelopes Of Statically Indeterminate Beams
The paper presents an analytical method of finding functions of influence lines of statically indeterminate beams. There are presented solutions of a fourth order equation with a right hand side with second and third derivative of Dirac delta. There is shown that their solution are influence lines o...
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| Format: | Article |
| Language: | English |
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VŠB-Technical University of Ostrava, Faculty of Civil Engineering
2015-12-01
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| Series: | Transactions of the VŠB: Technical University of Ostrava, Civil Engineering Series |
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| Online Access: | http://www.degruyter.com/view/j/tvsb.2015.15.issue-2/tvsb-2015-0025/tvsb-2015-0025.xml?format=INT |
| _version_ | 1797817252514365440 |
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| author | Walentyński Ryszard |
| author_facet | Walentyński Ryszard |
| author_sort | Walentyński Ryszard |
| collection | DOAJ |
| description | The paper presents an analytical method of finding functions of influence lines of statically indeterminate beams. There are presented solutions of a fourth order equation with a right hand side with second and third derivative of Dirac delta. There is shown that their solution are influence lines of moments and transverse forces. Moreover, thanks to Mathematica, analytical form of envelopes functions can be evaluated. |
| first_indexed | 2024-03-13T08:50:37Z |
| format | Article |
| id | doaj.art-dfcd90b0dbfc4bbbb41ce79216645877 |
| institution | Directory Open Access Journal |
| issn | 1804-4824 |
| language | English |
| last_indexed | 2024-03-13T08:50:37Z |
| publishDate | 2015-12-01 |
| publisher | VŠB-Technical University of Ostrava, Faculty of Civil Engineering |
| record_format | Article |
| series | Transactions of the VŠB: Technical University of Ostrava, Civil Engineering Series |
| spelling | doaj.art-dfcd90b0dbfc4bbbb41ce792166458772023-05-29T13:15:28ZengVŠB-Technical University of Ostrava, Faculty of Civil EngineeringTransactions of the VŠB: Technical University of Ostrava, Civil Engineering Series1804-48242015-12-0115210.1515/tvsb-2015-0025tvsb-2015-0025Generalized Functions And Calculus Operators Of Mathematica Applied To Evaluation Of Influence Lines And Envelopes Of Statically Indeterminate BeamsWalentyński Ryszard0 Prof. (assoc.) Ryszard Walentyński M.Sc. C.Eng. Ph.D. D.Sc., Chair of Building Structures Theory, Faculty of Civil Engineering, Silesian University of Technology, ul. Akademicka 5, 44-100 Gliwice, Poland, phone: (+48) 32 237 21 18The paper presents an analytical method of finding functions of influence lines of statically indeterminate beams. There are presented solutions of a fourth order equation with a right hand side with second and third derivative of Dirac delta. There is shown that their solution are influence lines of moments and transverse forces. Moreover, thanks to Mathematica, analytical form of envelopes functions can be evaluated.http://www.degruyter.com/view/j/tvsb.2015.15.issue-2/tvsb-2015-0025/tvsb-2015-0025.xml?format=INTInfluence linesfundamental solutiongeneralized functionsDirac deltaHeaviside step functionstructural mechanicsdifferential equationsenvelopesMathematica |
| spellingShingle | Walentyński Ryszard Generalized Functions And Calculus Operators Of Mathematica Applied To Evaluation Of Influence Lines And Envelopes Of Statically Indeterminate Beams Transactions of the VŠB: Technical University of Ostrava, Civil Engineering Series Influence lines fundamental solution generalized functions Dirac delta Heaviside step function structural mechanics differential equations envelopes Mathematica |
| title | Generalized Functions And Calculus Operators Of Mathematica Applied To Evaluation Of Influence Lines And Envelopes Of Statically Indeterminate Beams |
| title_full | Generalized Functions And Calculus Operators Of Mathematica Applied To Evaluation Of Influence Lines And Envelopes Of Statically Indeterminate Beams |
| title_fullStr | Generalized Functions And Calculus Operators Of Mathematica Applied To Evaluation Of Influence Lines And Envelopes Of Statically Indeterminate Beams |
| title_full_unstemmed | Generalized Functions And Calculus Operators Of Mathematica Applied To Evaluation Of Influence Lines And Envelopes Of Statically Indeterminate Beams |
| title_short | Generalized Functions And Calculus Operators Of Mathematica Applied To Evaluation Of Influence Lines And Envelopes Of Statically Indeterminate Beams |
| title_sort | generalized functions and calculus operators of mathematica applied to evaluation of influence lines and envelopes of statically indeterminate beams |
| topic | Influence lines fundamental solution generalized functions Dirac delta Heaviside step function structural mechanics differential equations envelopes Mathematica |
| url | http://www.degruyter.com/view/j/tvsb.2015.15.issue-2/tvsb-2015-0025/tvsb-2015-0025.xml?format=INT |
| work_keys_str_mv | AT walentynskiryszard generalizedfunctionsandcalculusoperatorsofmathematicaappliedtoevaluationofinfluencelinesandenvelopesofstaticallyindeterminatebeams |