A fourth-order multi-scale computational method and its convergence analysis for composite Kirchhoff plates with microscopic periodic configurations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914190017429504 |
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| author | Dong, Hao Cao, Liqun |
| author_facet | Dong, Hao Cao, Liqun |
| contents | The Kirchhoff plate model plays a vital role in modeling, computing and analyzing the mechanical behaviors of thin plate structures. This study propose a novel fourth-order multi-scale (FOMS) computational method for high-accuracy and efficient simulation of composite Kirchhoff plates with highly periodic heterogeneities. At first, two-scale asymptotic expansion theory is employed to establish the high-accuracy fourth-order multi-scale computation model with novel fourth-order correctors for composite Kirchhoff plates, which are governed by fourth-order partial differential equation (PDE) with periodically oscillatory and highly discontinuous coefficients. Then, the locally point-wise error analysis is derived to theoretically illustrate the local balance preserving of fourth-order multi-scale model enabling high-accuracy multi-scale computation. Furthermore, a global error estimation with an explicit order for fourth-order multi-scale solutions is first demonstrated under appropriate assumptions. In contrast to the second- and third-order multi-scale solutions, only the fourth-order one is capable of providing an explicit error order estimate. Additionally, an efficient numerical algorithm is developed to conduct high-accuracy simulation for heterogeneous plate structures. Extensive numerical examples are provided to confirm the theoretical results for the computational convergence and accuracy of the proposed method. This work offers a higher-order (fourth-order) multi-scale computational framework that enables robust simulation and high-accuracy analysis to composite Kirchhoff plates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08597 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A fourth-order multi-scale computational method and its convergence analysis for composite Kirchhoff plates with microscopic periodic configurations Dong, Hao Cao, Liqun Numerical Analysis The Kirchhoff plate model plays a vital role in modeling, computing and analyzing the mechanical behaviors of thin plate structures. This study propose a novel fourth-order multi-scale (FOMS) computational method for high-accuracy and efficient simulation of composite Kirchhoff plates with highly periodic heterogeneities. At first, two-scale asymptotic expansion theory is employed to establish the high-accuracy fourth-order multi-scale computation model with novel fourth-order correctors for composite Kirchhoff plates, which are governed by fourth-order partial differential equation (PDE) with periodically oscillatory and highly discontinuous coefficients. Then, the locally point-wise error analysis is derived to theoretically illustrate the local balance preserving of fourth-order multi-scale model enabling high-accuracy multi-scale computation. Furthermore, a global error estimation with an explicit order for fourth-order multi-scale solutions is first demonstrated under appropriate assumptions. In contrast to the second- and third-order multi-scale solutions, only the fourth-order one is capable of providing an explicit error order estimate. Additionally, an efficient numerical algorithm is developed to conduct high-accuracy simulation for heterogeneous plate structures. Extensive numerical examples are provided to confirm the theoretical results for the computational convergence and accuracy of the proposed method. This work offers a higher-order (fourth-order) multi-scale computational framework that enables robust simulation and high-accuracy analysis to composite Kirchhoff plates. |
| title | A fourth-order multi-scale computational method and its convergence analysis for composite Kirchhoff plates with microscopic periodic configurations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.08597 |