Analysis of natural frequency for bioinspired functional gradient plates

  • Chaohui Zhang
  • Peng Liu
  • Deju ZhuEmail author
  • Le Van Lich
  • Tinh Quoc BuiEmail author


Biological materials-fish scales exhibit ultra-flexibility due to its functionally graded materials. Inspired by the hierarchical gradient structure of fish scales, a new flexible gradient model that can adequately describe the characteristics of the bioinspired hierarchical structures is proposed in this work. To assess the flexibility of the proposed gradient model, a combination of extended finite element method (XFEM) and stabilized discrete shear gap (DSG) is established to analyze the vibration of bioinspired gradient plates with/without cracks. The DSG technique is employed to eliminate the shear locking phenomenon, while the XFEM is used for a mesh-independent modelling of crack. The combined approach is applicable to both moderately thick and thin plates, and is insensitive to mesh distortion. Functionally gradient plates take two types: power law function (Type I) and bioinspired hierarchical mode (Type II). For Type I, the natural frequencies decrease by increasing the gradient factor, i.e., the exponent of the power law. When the gradient factor is larger than one, the improvement of the plate stiffness by material gradient is restricted. For Type II, the natural frequencies are mostly independent of the step smoothing factor, yet quite sensitive to the number of step layers, providing an additional degree of freedom in tailoring the material properties. In addition, the natural frequencies of the bioinspired gradient plate are lower than that of the homogeneous ceramic plate. By using Type II, the stiffness of the plate can be reduced effectively, making the plate prone to deformation, which coincides with the flexible scale design. Therefore, the present study provides an incisive method and instructive guideline for a new era of artificially designed flexible materials inspired by natural (or biological) materials and structures.


Biological materials Flexible structure Bio-inspired hierarchical gradient plate XFEM DSG 



Funding was provided by National Defense Science and Technology Innovation District Program (Grant No. 19-H863-03-ZT-003-026-01), High-level Talent Gathering Project in Hunan Province (Grant No. 2018RS3057), Key Technology Research and Development Program of Shandong (Grant No. 2017GK2130), Natural Science Foundation of Hunan Province (Grant No. 2019JJ50063), China Postdocral Science Fundation (2018M632957) and Hunan Provincial Innovation Foundation for Postgraduate (Grant No. 541109080163).


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Key Laboratory for Green and Advanced Civil Engineering Materials and Application Technology of Hunan Province, College of Civil EngineeringHunan UniversityChangshaPeople’s Republic of China
  2. 2.International Science Innovation Collaboration Base for Green and Advanced Civil Engineering Materials of Hunan ProvinceHunan UniversityChangshaPeople’s Republic of China
  3. 3.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaPeople’s Republic of China
  4. 4.School of Materials Science and TechnologyHanoi University of Science and TechnologyHanoiVietnam
  5. 5.Institute for Research and DevelopmentDuy Tan UniversityDa Nang CityVietnam
  6. 6.Department of Civil and Environmental EngineeringTokyo Institute of TechnologyTokyoJapan

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