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| Differential cubature solution of Kirchhoff plates with generalized staggered mesh pattern |
| Received:April 17, 2022 Revised:October 01, 2022 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20220417001 |
| KeyWord:differential cubature method well-posedness of interpolation base functions of multivariable interpolation generalized staggered-grid scheme weighting coefficient matrix |
| Author | Institution |
| 李鸿晶 |
南京工业大学 工程力学研究所, 南京 |
| 徐强 |
南京工业大学 工程力学研究所, 南京 |
| 孙广俊 |
南京工业大学 工程力学研究所, 南京 |
| 梅雨辰 |
南京工业大学 工程力学研究所, 南京 |
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| Abstract: |
| The differential cubature(DC) method was developed for solving numerically multi-dimensional differential equations.We focus on the well-posedness of multivariate polynomial interpolation and research the fundamental conditions that the appropriate node group of interpolation polynomial and the interpolation space should meet when applying the DC method.Furthermore,the specific operation for selecting the grid points in the solution domain and constructing the well-posed test functions is explored carefully,and a generalized staggered-grid scheme in which different numbers of grid points may be permitted along each coordinate direction is proposed.The interpolation space as well as test functions corresponding to this generalized staggered-grid DC scheme are also researched and presented.Finally,the reliability and potential of the generalized staggered grid-based DC method are examined in solving actual problems of structural mechanics by the deformation analysis of the rectangular elastic thin plate.The results show that the proposed DC method has stronger applicability and flexibility than the traditional staggered grid DC method,and similar accuracy could be achieved by means of a much smaller number of grid points.The proposed method appears characteristics of high precision solution without more computational efforts. |