A localized MAPS using polynomial basis functions for the fourth-order complex-shape plate bending problems

Abstract

In this paper, the localized method of approximate particular solutions using polynomial basis functions is proposed to solve plate bending problems with complex domains. The closed-form particular solutions of fourth-order differential equations can be reduced to the linear combination of the particular solutions of Helmholtz and modified Helmholtz equations. To alleviate the difficulty of solving overdetermined fourth-order plate bending problems using the localized collocation method, additional ghost points outside the computational domain are introduced to improve the stability and accuracy. Three examples are illustrated to validate the feasibility of the proposed localized MAPS.

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Acknowledgements

The work described in this paper was supported by the National Science Funds of China (Grant Nos. 11772119), the Fundamental Research Funds for the Central Universities (Grant No. B200202124), Alexander von Humboldt Research Fellowship (ID: 1195938), the Six Talent Peaks Project in Jiangsu Province of China (Grant No. 2019-KTHY-009) and the Programme B18019 of Discipline Expertise to Universities MOE & MST. The third author acknowledges HPC at the University of Southern Mississippi supported by the National Science Foundation under the Major Research Instrumentation (MRI) program via Grant # ACI 1626217.

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Correspondence to Zhuo-Jia Fu.

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Tang, Z., Fu, Z. & Chen, C.S. A localized MAPS using polynomial basis functions for the fourth-order complex-shape plate bending problems. Arch Appl Mech (2020). https://doi.org/10.1007/s00419-020-01718-y

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Keywords

  • Localized
  • Method of approximate particular solutions (MAPS)
  • Helmholtz-type equations
  • Fourth-order plate bending problems