“Mixed” Meshless Time-Domain Adaptive Algorithm for Solving Elasto-Dynamics Equations
A time-domain adaptive algorithm was developed for solving elasto-dynamics problems through a mixed meshless local Petrov-Galerkin finite volume method (MLPG5). In this time-adaptive algorithm, each time-dependent variable is interpolated by a time series function of n-order, which is determined by...
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/10/1722 |
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| author | Maoxiong Liao Tao Zhang Jinggu Cao |
| author_facet | Maoxiong Liao Tao Zhang Jinggu Cao |
| author_sort | Maoxiong Liao |
| collection | DOAJ |
| description | A time-domain adaptive algorithm was developed for solving elasto-dynamics problems through a mixed meshless local Petrov-Galerkin finite volume method (MLPG5). In this time-adaptive algorithm, each time-dependent variable is interpolated by a time series function of n-order, which is determined by a criterion in each step. The high-order series of expanded variables bring high accuracy in the time domain, especially for the elasto-dynamic equations, which are second-order PDE in the time domain. In the present mixed MLPG5 dynamic formulation, the strains are interpolated independently, as are displacements in the local weak form, which eliminates the expensive differential of the shape function. In the traditional MLPG5, both shape function and its derivative for each node need to be calculated. By taking the Heaviside function as the test function, the local domain integration of stiffness matrix is avoided. Several numerical examples, including the comparison of our method, the MLPG5–Newmark method and FEM (ANSYS) are given to demonstrate the advantages of the presented method: (1) a large time step can be used in solving a elasto-dynamics problem; (2) computational efficiency and accuracy are improved in both space and time; (3) smaller support sizes can be used in the mixed MLPG5. |
| first_indexed | 2024-03-10T03:28:54Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:28:54Z |
| publishDate | 2022-05-01 |
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| series | Mathematics |
| spelling | doaj.art-5dfc0ae83ab34511a74d2502d9ce0c012023-11-23T12:01:28ZengMDPI AGMathematics2227-73902022-05-011010172210.3390/math10101722“Mixed” Meshless Time-Domain Adaptive Algorithm for Solving Elasto-Dynamics EquationsMaoxiong Liao0Tao Zhang1Jinggu Cao2School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, ChinaA time-domain adaptive algorithm was developed for solving elasto-dynamics problems through a mixed meshless local Petrov-Galerkin finite volume method (MLPG5). In this time-adaptive algorithm, each time-dependent variable is interpolated by a time series function of n-order, which is determined by a criterion in each step. The high-order series of expanded variables bring high accuracy in the time domain, especially for the elasto-dynamic equations, which are second-order PDE in the time domain. In the present mixed MLPG5 dynamic formulation, the strains are interpolated independently, as are displacements in the local weak form, which eliminates the expensive differential of the shape function. In the traditional MLPG5, both shape function and its derivative for each node need to be calculated. By taking the Heaviside function as the test function, the local domain integration of stiffness matrix is avoided. Several numerical examples, including the comparison of our method, the MLPG5–Newmark method and FEM (ANSYS) are given to demonstrate the advantages of the presented method: (1) a large time step can be used in solving a elasto-dynamics problem; (2) computational efficiency and accuracy are improved in both space and time; (3) smaller support sizes can be used in the mixed MLPG5.https://www.mdpi.com/2227-7390/10/10/1722meshless local Petrov-Galerkin approach (MLPG)finite volume methodsmixed methodsadaptive algorithmtime-domainmoving least squares (MLS) |
| spellingShingle | Maoxiong Liao Tao Zhang Jinggu Cao “Mixed” Meshless Time-Domain Adaptive Algorithm for Solving Elasto-Dynamics Equations Mathematics meshless local Petrov-Galerkin approach (MLPG) finite volume methods mixed methods adaptive algorithm time-domain moving least squares (MLS) |
| title | “Mixed” Meshless Time-Domain Adaptive Algorithm for Solving Elasto-Dynamics Equations |
| title_full | “Mixed” Meshless Time-Domain Adaptive Algorithm for Solving Elasto-Dynamics Equations |
| title_fullStr | “Mixed” Meshless Time-Domain Adaptive Algorithm for Solving Elasto-Dynamics Equations |
| title_full_unstemmed | “Mixed” Meshless Time-Domain Adaptive Algorithm for Solving Elasto-Dynamics Equations |
| title_short | “Mixed” Meshless Time-Domain Adaptive Algorithm for Solving Elasto-Dynamics Equations |
| title_sort | mixed meshless time domain adaptive algorithm for solving elasto dynamics equations |
| topic | meshless local Petrov-Galerkin approach (MLPG) finite volume methods mixed methods adaptive algorithm time-domain moving least squares (MLS) |
| url | https://www.mdpi.com/2227-7390/10/10/1722 |
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