Numerical Analysis of Structures of Revolution using Universal Matrices Approach
Stress and displacement analysis of structures of revolution under axisymmetric loading is of considerable interest in engineering. Many practical problems can be idealized as an axisymmetric case, which simplifies the analysis and reduces the computational work. The axisymmetric triangular element...
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| Format: | Article |
| Language: | English |
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Faculty of Engineering and Technology
2019-03-01
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| Series: | Nigerian Journal of Technological Development |
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| Online Access: | https://journal.njtd.com.ng/index.php/njtd/article/view/274 |
| _version_ | 1818006725522882560 |
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| author | Hamza Sulayman Abdullahi |
| author_facet | Hamza Sulayman Abdullahi |
| author_sort | Hamza Sulayman Abdullahi |
| collection | DOAJ |
| description |
Stress and displacement analysis of structures of revolution under axisymmetric loading is of considerable interest in engineering. Many practical problems can be idealized as an axisymmetric case, which simplifies the analysis and reduces the computational work. The axisymmetric triangular element is commonly used for modeling these cases. This paper proposes a method of generating stiffness matrix for the axisymmetric triangular element using universal matrices instead of numerical integration. The computation time of the proposed method was compared against the Gaussian numerical integration. The CPU time ratio for the 3-node element was 1:1.56, 1:1.79, and 1:1.89 for the proposed method against 1-point, 3-points, and 4-points Gaussian numerical integration respectively. The accuracy of the proposed method was 0.012% against the exact integration method. The 1-point, 3-points, and 4-points Gaussian numerical integration have an error of 0.059%, 0.001%, and 0.0006% respectively. Nodal displacements from this method were compared against the results of some commercially available finite element packages. The proposed method has a deviation of 0.44% from the theoretical values, while ABAQUS, ANSYS, and Optistruct has a deviation of 1.26%, 1.29%, and 1.44% respectively using the default number of integration points provided by the packages.
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| first_indexed | 2024-04-14T05:05:17Z |
| format | Article |
| id | doaj.art-3450307569324f23a33552f9cd114c0e |
| institution | Directory Open Access Journal |
| issn | 2437-2110 |
| language | English |
| last_indexed | 2024-04-14T05:05:17Z |
| publishDate | 2019-03-01 |
| publisher | Faculty of Engineering and Technology |
| record_format | Article |
| series | Nigerian Journal of Technological Development |
| spelling | doaj.art-3450307569324f23a33552f9cd114c0e2022-12-22T02:10:43ZengFaculty of Engineering and TechnologyNigerian Journal of Technological Development2437-21102019-03-01162Numerical Analysis of Structures of Revolution using Universal Matrices ApproachHamza Sulayman Abdullahi0Bayero University, Kano Stress and displacement analysis of structures of revolution under axisymmetric loading is of considerable interest in engineering. Many practical problems can be idealized as an axisymmetric case, which simplifies the analysis and reduces the computational work. The axisymmetric triangular element is commonly used for modeling these cases. This paper proposes a method of generating stiffness matrix for the axisymmetric triangular element using universal matrices instead of numerical integration. The computation time of the proposed method was compared against the Gaussian numerical integration. The CPU time ratio for the 3-node element was 1:1.56, 1:1.79, and 1:1.89 for the proposed method against 1-point, 3-points, and 4-points Gaussian numerical integration respectively. The accuracy of the proposed method was 0.012% against the exact integration method. The 1-point, 3-points, and 4-points Gaussian numerical integration have an error of 0.059%, 0.001%, and 0.0006% respectively. Nodal displacements from this method were compared against the results of some commercially available finite element packages. The proposed method has a deviation of 0.44% from the theoretical values, while ABAQUS, ANSYS, and Optistruct has a deviation of 1.26%, 1.29%, and 1.44% respectively using the default number of integration points provided by the packages. https://journal.njtd.com.ng/index.php/njtd/article/view/274Stiffness matrixexplicit formulationclosed-formuniversal matrixaxisymmetric triangular elements |
| spellingShingle | Hamza Sulayman Abdullahi Numerical Analysis of Structures of Revolution using Universal Matrices Approach Nigerian Journal of Technological Development Stiffness matrix explicit formulation closed-form universal matrix axisymmetric triangular elements |
| title | Numerical Analysis of Structures of Revolution using Universal Matrices Approach |
| title_full | Numerical Analysis of Structures of Revolution using Universal Matrices Approach |
| title_fullStr | Numerical Analysis of Structures of Revolution using Universal Matrices Approach |
| title_full_unstemmed | Numerical Analysis of Structures of Revolution using Universal Matrices Approach |
| title_short | Numerical Analysis of Structures of Revolution using Universal Matrices Approach |
| title_sort | numerical analysis of structures of revolution using universal matrices approach |
| topic | Stiffness matrix explicit formulation closed-form universal matrix axisymmetric triangular elements |
| url | https://journal.njtd.com.ng/index.php/njtd/article/view/274 |
| work_keys_str_mv | AT hamzasulaymanabdullahi numericalanalysisofstructuresofrevolutionusinguniversalmatricesapproach |