Least-squares Smoothed Shape Functions for Constructing Field-Consistent Timoshenko Beam Elements
This paper presents an approach for constructing field-consistent Timoshenko beam elements using least-squares smoothed (LSS) shape functions. The variational basis for shear strain redistribution is thoroughly explained, leading to the derivation of LSS shape functions for linear, quadratic, and c...
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| Format: | Article |
| Language: | English |
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Petra Christian University
2025-03-01
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| Series: | Civil Engineering Dimension |
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| Online Access: | https://ced.petra.ac.id/index.php/civ/article/view/30421 |
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| author | Foek Tjong Wong Henokh G. Tjahyono Sugiyono Hartono Timothy A. Setiabudi |
| author_facet | Foek Tjong Wong Henokh G. Tjahyono Sugiyono Hartono Timothy A. Setiabudi |
| author_sort | Foek Tjong Wong |
| collection | DOAJ |
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This paper presents an approach for constructing field-consistent Timoshenko beam elements using least-squares smoothed (LSS) shape functions. The variational basis for shear strain redistribution is thoroughly explained, leading to the derivation of LSS shape functions for linear, quadratic, and cubic Timoshenko beam elements. These elements are then applied to linear static analysis, bifurcation buckling analysis, and free vibration analysis of prismatic and tapered beams. Numerical tests demonstrate that the LSS-based beam elements effectively eliminate shear locking and provide accurate, reliable results. Their performance is comparable to the discrete shear gap technique but with a simpler implementation procedure. The LSS shape function approach offers a practical and efficient alternative for achieving field consistency in Timoshenko beam elements, with potential applications in enhanced finite element methods (FEMs) such as isogeometric FEM and Kriging-based FEM.
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| format | Article |
| id | doaj-art-7f99a0bf7d0548fbabc107570615718a |
| institution | Kabale University |
| issn | 1410-9530 1979-570X |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Petra Christian University |
| record_format | Article |
| series | Civil Engineering Dimension |
| spelling | doaj-art-7f99a0bf7d0548fbabc107570615718a2025-08-20T03:40:21ZengPetra Christian UniversityCivil Engineering Dimension1410-95301979-570X2025-03-0127110.9744/ced.27.1.22-32Least-squares Smoothed Shape Functions for Constructing Field-Consistent Timoshenko Beam ElementsFoek Tjong Wong0Henokh G. Tjahyono1Sugiyono Hartono2Timothy A. Setiabudi3Petra Christian UniversityAlumnus Petra Christian UniversityAlumnus Petra Christian UniversityAlumnus Petra Christian University This paper presents an approach for constructing field-consistent Timoshenko beam elements using least-squares smoothed (LSS) shape functions. The variational basis for shear strain redistribution is thoroughly explained, leading to the derivation of LSS shape functions for linear, quadratic, and cubic Timoshenko beam elements. These elements are then applied to linear static analysis, bifurcation buckling analysis, and free vibration analysis of prismatic and tapered beams. Numerical tests demonstrate that the LSS-based beam elements effectively eliminate shear locking and provide accurate, reliable results. Their performance is comparable to the discrete shear gap technique but with a simpler implementation procedure. The LSS shape function approach offers a practical and efficient alternative for achieving field consistency in Timoshenko beam elements, with potential applications in enhanced finite element methods (FEMs) such as isogeometric FEM and Kriging-based FEM. https://ced.petra.ac.id/index.php/civ/article/view/30421Timoshenko beam elementfield consistencyleast-squares smoothed shape functionshear lockingbifurcation bucklingfree vibration |
| spellingShingle | Foek Tjong Wong Henokh G. Tjahyono Sugiyono Hartono Timothy A. Setiabudi Least-squares Smoothed Shape Functions for Constructing Field-Consistent Timoshenko Beam Elements Civil Engineering Dimension Timoshenko beam element field consistency least-squares smoothed shape function shear locking bifurcation buckling free vibration |
| title | Least-squares Smoothed Shape Functions for Constructing Field-Consistent Timoshenko Beam Elements |
| title_full | Least-squares Smoothed Shape Functions for Constructing Field-Consistent Timoshenko Beam Elements |
| title_fullStr | Least-squares Smoothed Shape Functions for Constructing Field-Consistent Timoshenko Beam Elements |
| title_full_unstemmed | Least-squares Smoothed Shape Functions for Constructing Field-Consistent Timoshenko Beam Elements |
| title_short | Least-squares Smoothed Shape Functions for Constructing Field-Consistent Timoshenko Beam Elements |
| title_sort | least squares smoothed shape functions for constructing field consistent timoshenko beam elements |
| topic | Timoshenko beam element field consistency least-squares smoothed shape function shear locking bifurcation buckling free vibration |
| url | https://ced.petra.ac.id/index.php/civ/article/view/30421 |
| work_keys_str_mv | AT foektjongwong leastsquaressmoothedshapefunctionsforconstructingfieldconsistenttimoshenkobeamelements AT henokhgtjahyono leastsquaressmoothedshapefunctionsforconstructingfieldconsistenttimoshenkobeamelements AT sugiyonohartono leastsquaressmoothedshapefunctionsforconstructingfieldconsistenttimoshenkobeamelements AT timothyasetiabudi leastsquaressmoothedshapefunctionsforconstructingfieldconsistenttimoshenkobeamelements |