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Formulation for Mechanical Modelling of Small-Scale Micro- and Nano- Beams and Plates for Statical and Vibrational Analysis Based on the Second Strain Gradient Theory

Momeni, Alireza | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 50689 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen; Vatankhah, Ramin
  7. Abstract:
  8. In this thesis, the formulation of beams and plates in the micro- and nano scales is presented based on the second strain gradient theory (SSGT) introduced by Mindlin. The SSGT is a non-classical continuum theory that includes the second-order gradients of strain tensor in its formulation and this leads to more accurate modeling for mechanical behavior of materials than the strain gradient theory. On the other hand, due to the ever-increasing use of micro- and nano-electromechanical systems, analysis of the mechanical behavior of their deformable components for design and construction is of particular importance. For this purpose, analysis of Timoshenko beams and Euler-bernoulli beams made of functionally graded materials, as well as classical plates, have been studied and their formulation has been obtained utilizing the Hamilton principle. In the case of micro-plates an attempt has been made to provide a comprehensive and precise analysis of the corner conditions for the first time. The presented case studies which has been carried out utilizing available values of the additional material constants appeared in the SSGT formulation, indicate that the results of the SSGT is less than that of the SGT and classical continuum theory of beams and plates (for example,in case of beams made of Aluminium, up to 20% less than the classical theory and 8.5% less than the SGT predictions). On the other hand, vibrational analysis indicates that the natural frequencies obtained by the SSGT for beams and plates is greater than the corresponding values calculated by the SGT and classical theories (in case of plates made of Aluminium, the natural frequency is increased by 43% compared to the classical theory). In conclusion, based on the presented case studies, when the thickness of the elements are closer to the lattic parameter of the material, the difference between the results of this theory and the results of other theories is considerable and it is justifiable to utilize SSGT
  9. Keywords:
  10. Second Strain Gradient Theory ; Non-Classical Continum Mechanics Theories ; Nano/Micro Beams ; Static Analysis ; Vibrational Analysis ; Micro and Nanoplates

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