Date of Award


Degree Name

Master of Science


Mechanical and Aerospace Engineering

First Advisor

Jinseok Kim, Ph.D.

Second Advisor

Peter A. Gustafson, Ph.D.

Third Advisor

Judah Ari-Gur, Ph.D.


Composite materials, couple stress theory, finite element method, functionally graded materials, plate theory

Access Setting

Masters Thesis-Open Access


A nonlinear finite element model for micro circular/annular plates under thermal and mechanical loading is developed using a third order shear deformation theory. In the kinematic assumptions, the change of plate thickness is allowed and no transverse shear strains are considered on the top and bottom surfaces. A power-law distribution is utilized to account for variations of two constituents through the thickness of the plate. Three different types of porosity distributions are considered. The strain gradient effect in micro scale structures is considered using the modified couple stress theory. The dynamic version of the principle of virtual displacements is used to obtain the equations of motion, and conforming plate elements with 28 degrees of freedom per node are used in the development of the finite element model. The developed finite element model is verified against available literature, and analytical solutions. The effects of the material and porosity distributions, microstructure-dependency, the geometric non-linearity, and various boundary conditions on the bending response of functionally graded porous circular/annular micro-plates are studied using the developed nonlinear finite element model.