Cargando…
Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method
New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by the means of the Homotopy Analysis Method (HAM). The method provides a closed-form series solution for the problem described by a non-homogeneous system...
Autores principales: | , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Vienna
2021
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8549990/ https://www.ncbi.nlm.nih.gov/pubmed/34720109 http://dx.doi.org/10.1007/s00707-021-03043-z |
_version_ | 1784590869296316416 |
---|---|
author | Doeva, Olga Masjedi, Pedram Khaneh Weaver, Paul M. |
author_facet | Doeva, Olga Masjedi, Pedram Khaneh Weaver, Paul M. |
author_sort | Doeva, Olga |
collection | PubMed |
description | New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by the means of the Homotopy Analysis Method (HAM). The method provides a closed-form series solution for the problem described by a non-homogeneous system of coupled ordinary differential equations with constant coefficients and one variable coefficient reflecting variable stiffness elastic foundation. Analytical solutions are obtained based on two different algorithms, namely conventional HAM and iterative HAM (iHAM). To investigate the computational efficiency and convergence of HAM solutions, the preliminary studies are performed for a composite beam without elastic foundation under the action of transverse uniformly distributed loads considering three different types of stacking sequence which provide different levels and types of anisotropy. It is shown that applying the iterative approach results in better convergence of the solution compared with conventional HAM for the same level of accuracy. Then, analytical solutions are developed for composite beams on elastic foundations. New analytical results based on HAM are presented for the static deflection of composite beams resting on variable stiffness elastic foundations. Results are compared to those reported in the literature and those obtained by the Chebyshev Collocation Method in order to verify the validity and accuracy of the method. Numerical experiments reveal the accuracy and efficiency of the Homotopy Analysis Method in static beam problems. |
format | Online Article Text |
id | pubmed-8549990 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Springer Vienna |
record_format | MEDLINE/PubMed |
spelling | pubmed-85499902021-10-29 Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method Doeva, Olga Masjedi, Pedram Khaneh Weaver, Paul M. Acta Mech Original Paper New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by the means of the Homotopy Analysis Method (HAM). The method provides a closed-form series solution for the problem described by a non-homogeneous system of coupled ordinary differential equations with constant coefficients and one variable coefficient reflecting variable stiffness elastic foundation. Analytical solutions are obtained based on two different algorithms, namely conventional HAM and iterative HAM (iHAM). To investigate the computational efficiency and convergence of HAM solutions, the preliminary studies are performed for a composite beam without elastic foundation under the action of transverse uniformly distributed loads considering three different types of stacking sequence which provide different levels and types of anisotropy. It is shown that applying the iterative approach results in better convergence of the solution compared with conventional HAM for the same level of accuracy. Then, analytical solutions are developed for composite beams on elastic foundations. New analytical results based on HAM are presented for the static deflection of composite beams resting on variable stiffness elastic foundations. Results are compared to those reported in the literature and those obtained by the Chebyshev Collocation Method in order to verify the validity and accuracy of the method. Numerical experiments reveal the accuracy and efficiency of the Homotopy Analysis Method in static beam problems. Springer Vienna 2021-08-13 2021 /pmc/articles/PMC8549990/ /pubmed/34720109 http://dx.doi.org/10.1007/s00707-021-03043-z Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Original Paper Doeva, Olga Masjedi, Pedram Khaneh Weaver, Paul M. Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method |
title | Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method |
title_full | Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method |
title_fullStr | Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method |
title_full_unstemmed | Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method |
title_short | Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method |
title_sort | static analysis of composite beams on variable stiffness elastic foundations by the homotopy analysis method |
topic | Original Paper |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8549990/ https://www.ncbi.nlm.nih.gov/pubmed/34720109 http://dx.doi.org/10.1007/s00707-021-03043-z |
work_keys_str_mv | AT doevaolga staticanalysisofcompositebeamsonvariablestiffnesselasticfoundationsbythehomotopyanalysismethod AT masjedipedramkhaneh staticanalysisofcompositebeamsonvariablestiffnesselasticfoundationsbythehomotopyanalysismethod AT weaverpaulm staticanalysisofcompositebeamsonvariablestiffnesselasticfoundationsbythehomotopyanalysismethod |