Mechanic of Advanced and Smart Materials
Quarterly

Deflection analysis of composite micro-beam on elastic foundation by strain gradient theory

Document Type : Original Article

Authors

Saeed Jafari Mehrabadi 1
Alireza NezamAbadi 2
Ehsan Moayeedi 2

1 Department of Mechanical Engineering, Islamic Azad University, Arak branch, Arak, Iran

2 Faculty Engineering of Islamic Azad University, Arak Branch, Arak, Iran

https://doi.org/10.52547/masm.2.1.94
Abstract
In this article bending analysis of composite Euler-Bernoulli micro-beam made of functionally graded materials resting on elastic foundation by strain gradient theory has been studied. The material properties of structure have been assumed by Reddy’s power law model such as the bottom layer and top layer being ceramic and metal material respectively. At first, by using the assumptions of elasticity strain gradient theory and calculating the total potential energy of system after determining the work of external distributed load by using the Hamilton's principal the equations of motion have been derived. Note that the work down by the Winkler elastic foundation is considered. Because the solutions of mentioned equations are not possible by analytical method, the equations have been solved by generalized differential quadrature method in simply supported boundary conditions. By comparing the answers of problem with other published references, we confident form the obtained results. At the end, effect of material length scale and power law index coefficient of functionally graded materials and stiffness of elastic foundation on deflection of micro-beam has been studied.

Keywords

strain gradient theory
functionally graded material
micro-beam
elastic foundation
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Mechanic of Advanced and Smart Materials
Volume 2, Issue 1
Spring 2022
Pages 94-107

  • Receive Date 25 April 2022
  • Revise Date 16 May 2022
  • Accept Date 17 May 2022

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