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| Evaluation of singular physical field near the vertex of piezoelectric material notch |
| Received:January 04, 2023 Revised:February 12, 2023 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20230104001 |
| KeyWord:piezoelectric material notch asymptotic expansion singular stress field singular electric displacement field |
| Author | Institution |
| 潘伟 |
合肥工业大学 土木与水利工程学院, 合肥 |
| 程长征 |
合肥工业大学 土木与水利工程学院, 合肥 |
| 王飞炀 |
合肥工业大学 土木与水利工程学院, 合肥 |
| 李腾岳 |
合肥工业大学 土木与水利工程学院, 合肥 |
| 牛忠荣 |
合肥工业大学 土木与水利工程学院, 合肥 |
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| Abstract: |
| The idea of combining the singularity characteristic analysis with the finite element method is used to calculate the singular physical fields near the vertex of a notch of a piezoelectric material.Firstly,based on the singular asymptotic expansion technique,the singular characteristic equation of the notch is established.The interpolating matrix method is then introduced to solve it.The singularity order,characteristic angular function and its derivative of the singular asymptotic expansion are obtained.The displacement and electric potential near the notch are calculated on a relatively sparse finite element mesh.These results are introduced into the asymptotic expansion to obtain the amplitude coefficients in the asymptotic expansion.According to the calculated amplitude coefficients,singularity order,characteristic angular function and its derivative,the singular physical field can be reconstructed,and then the stress and electric displacement intensity factors can be calculated.The proposed semi-analytical method is basing on the results from the finite element sparse grid.Thus,a small amount of calculation is needed and a higher-precision singular physical field can be obtained.The proposed method does not need to modify the interpolation function of the finite element method.It is suitable for embedding into the commercial finite element software. |
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