Bending and Vibration of Microstructure-Dependent Kirchhoff Microplates and Finite Element Implementations with R

  • Khameel B. Mustapha
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


In Chaps.  2 and  3, our concern was on structures for which only one of the geometric dimensions dominates. This resulted in the approximations of such three-dimensional (3D) structures as one-dimensional beams. However, for 3D structures having two dominating planar geometric dimensions, a more appropriate approximation demands the move from the use of beam theories to advance structural models. This chapter deals with the most elementary of such theories, the so-called classical plate theory following the Kirchhoff’s hypothesis. Our interest being on the microstructured-dependent behaviour, the theoretical treatment is again approached from the perspectives of the modified couple stress theory to establish the appropriate size-dependent model of a microscale plate for static and free vibration analyses. Attention is given to the implementation of the finite element solutions for these analyses in the R programming language. Although the developed finite element model is a non-conforming rectangular element, it provides a straightforward way to demonstrate the influence of material length-scale parameters on the bending and dynamic behaviour of plates with various boundary conditions.


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Copyright information

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Khameel B. Mustapha
    • 1
  1. 1.Department of Mechanical, Materials and Manufacturing EngineeringUniversity of Nottingham Malaysia CampusSemenyihMalaysia

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