A New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils

This paper derives an original finite element for the static bending analysis of a transversely cracked uniform beam resting on a two-parametric elastic foundation. In the simplified computational model based on the Euler–Bernoulli theory of small displacements, the crack is represented by a linear...

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Autores principales:	Matjaž Skrinar, Mojmir Uranjek, Iztok Peruš, Denis Imamović
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	static bending analysis two-parametric elastic soil uniform cracked beam finite element method stiffness matrix of medium Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/5d725446158d4a53b3740e15f2f5e231
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spelling	oai:doaj.org-article:5d725446158d4a53b3740e15f2f5e2312021-11-25T16:41:31ZA New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils10.3390/app1122109392076-3417https://doaj.org/article/5d725446158d4a53b3740e15f2f5e2312021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/22/10939https://doaj.org/toc/2076-3417This paper derives an original finite element for the static bending analysis of a transversely cracked uniform beam resting on a two-parametric elastic foundation. In the simplified computational model based on the Euler–Bernoulli theory of small displacements, the crack is represented by a linear rotational spring connecting two elastic members. The derivations of approximate transverse displacement functions, stiffness matrix coefficients, and the load vector for a linearly distributed load along the entire beam element are based on novel cubic polynomial interpolation functions, including the second soil parameter. Moreover, all derived expressions are obtained in closed forms, which allow easy implementation in existing finite element software. Two numerical examples are presented in order to substantiate the discussed approach. They cover both possible analytical solution forms that may occur (depending on the problem parameters) from the same governing differential equation of the considered problem. Therefore, several response parameters are studied for each example (with additional emphasis on their convergence) and compared with the corresponding analytical solution, thus proving the quality of the obtained finite element.Matjaž SkrinarMojmir UranjekIztok PerušDenis ImamovićMDPI AGarticlestatic bending analysistwo-parametric elastic soiluniform cracked beamfinite element methodstiffness matrix of mediumTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10939, p 10939 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	static bending analysis two-parametric elastic soil uniform cracked beam finite element method stiffness matrix of medium Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	static bending analysis two-parametric elastic soil uniform cracked beam finite element method stiffness matrix of medium Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Matjaž Skrinar Mojmir Uranjek Iztok Peruš Denis Imamović A New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils
description	This paper derives an original finite element for the static bending analysis of a transversely cracked uniform beam resting on a two-parametric elastic foundation. In the simplified computational model based on the Euler–Bernoulli theory of small displacements, the crack is represented by a linear rotational spring connecting two elastic members. The derivations of approximate transverse displacement functions, stiffness matrix coefficients, and the load vector for a linearly distributed load along the entire beam element are based on novel cubic polynomial interpolation functions, including the second soil parameter. Moreover, all derived expressions are obtained in closed forms, which allow easy implementation in existing finite element software. Two numerical examples are presented in order to substantiate the discussed approach. They cover both possible analytical solution forms that may occur (depending on the problem parameters) from the same governing differential equation of the considered problem. Therefore, several response parameters are studied for each example (with additional emphasis on their convergence) and compared with the corresponding analytical solution, thus proving the quality of the obtained finite element.
format	article
author	Matjaž Skrinar Mojmir Uranjek Iztok Peruš Denis Imamović
author_facet	Matjaž Skrinar Mojmir Uranjek Iztok Peruš Denis Imamović
author_sort	Matjaž Skrinar
title	A New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils
title_short	A New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils
title_full	A New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils
title_fullStr	A New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils
title_full_unstemmed	A New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils
title_sort	new beam finite element for static bending analysis of slender transversely cracked beams on two-parametric soils
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/5d725446158d4a53b3740e15f2f5e231
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A New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils

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