Nonlinear behavior of micro-mechanical systems is an interesting and little explored area of research. Although, micro-system technologies is new and fast developing area, there is little work carried out on modeling and simulation of MEMS devices which concerns their non-linear behavior. Nonlinear modeling of MEMS devices is based on observations related to the micro-systems performance which is often far away from linearity in MEMS devices.
There are two types of components that are extensively used in MEMS design: micro-beams (cantilever type) and micro-plates. Manufacturing as well as usage of these components are advantageous to MEMS applications. The main applications of such structures include micro-sensors and micro-actuators. 
Large deflection of micro-cantilever beams under electrostatic force is studied. Pull in voltage as a phenomenon was widely studied in conjunction with MEMS. Large deflection of micro-cantilever beams under electrostatic field with the application of a voltage very close to pull in voltage is studied in this thesis and it is shown that pull in voltage provided by the nonlinear analysis is different from the one yielded by the linear analysis and more accurate when compared to the experimental values.
Large deflection of curved micro-cantilever beams sometimes encountered as AFM probes was studied to investigate the variation of sensitivity under large deflection of originally curved micro-cantilever beams. Results show that curved or straight beams experience same sensitivity which decreases with the increase of deflection. 
Micro-plate pressure sensors are widely used in industrial applications. Deposition of several different layers creates residual stress in those layers. The residual stress is measured indirectly by Stoney equation. It is shown that Stoney equation yields under normal circumstances up to 40% error in the value of the predicted stress and the experimental results do not match any numerical analysis. An extraction method was developed to calculate the stress distribution in each layer based on the experimentally measured deflection.   
  In summary, the work proves on few general configurations that the non-linear analysis of microstructures yields results that are closer to the results of the experimental investigations when compared to the ones yielded by the linear analyses.  Analytical solutions of the differential equations were sought using Lie symmetry method.