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Post-Buckling Analysis of Microplates based on the Strain Gradient Elasticity Theory

Maboudi, Ghazale | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50508 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen
  7. Abstract:
  8. In recent years, the world has seen a great progress in micro electro-mechanical systems (MEMS). Small size, low weight, high accuracy and low energy consumption have made these devices applicable in a variety of usages. In MEMS devices, mechanical components are used for specific purposes among which one of the most widely used are micro plates. Microplates are used in the structure of many devices such as microswitchs and atomic force microscopes. Therefore, studying of static and dynamic behavior of microplates is important. As the object gets smaller (to the scale of micro and nano meters), the classic theory of mechanics of continuous media cannot predict the behavior due to its independence from the structural length scale. As a result, nonclassical theories are used for investigating behavior of microplates. In the present study, post buckling behavior of micro plates is investigated based on the strain gradient theory and nonlinear Von Karman geometrical relations. First, due to the small thickness of the plate, displacement field is obtained using Kirchhoff plate theory assumptions. Governing equations and corresponding boundary conditions are derived by using the principle of minimum potential energy and considering only one length scale parameter which determines the dependence of the behavior to the size. Next, the equations are discretized by the generalized differential quadrature method and solved by the Newton method. The effects of length scale parameter, length to thickness ratio, and boundary conditions on the post buckling responses of micro plates under uniaxial and biaxial loading are investigated. Results indicate that the length scale parameter is the most effective factor on postbuckling behavior. By increasing thickness of the plate, buckling load adjacents to the result of classic theory
  9. Keywords:
  10. Differential Quadrature (DQ) ; Size Effect ; Strain Gradient Theory ; Post-Buckling Behavior ; Kirchhoff Rectangular Plate

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