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Finite element formulations for Kirchhoff-Love microplates

Kandaz, Murat
Micro- and nano-electromechanical systems (MEMS-NEMS) are integral parts of the modern world today and have gained importance since they were first introduced. There is still a huge demand for accurate electromechanical analyses of MEMS devices in order to reach even better design and manufacturing methods. It is vital that these devices are accurately modelled and analyzed based on the physical phenomena occurring within their inner structure as a result of the conditions they are subjected to. Classical continuum mechanics approaches are highly accurate for large scale structures where the structural length scale is several order of magnitudes higher than the microstructural length scale. However, they fail to describe the mechanical behavior of smaller parts, i.e. MEMS-NEMS devices, as the structural length scale becomes comparable to grain size. Hence, the effect of discontinuities in field variables at grain boundaries and other imperfections should be considered. This phenomenon is known as size effect or scale effect. To model such structures in the scale of microns, several techniques have been developed, the dominating and most well-proven being the modified gradient elasticity theories. Within this context, micron-scaled parts and materials are modelled using gradients, and in turn, higher order terms are introduced with relevant length scale parameters into the constitutive theory which take the size effects into account. In this study, sample microstructures and MEMS-NEMS devices are analyzed using finite element method (FEM) based on variational formulation of modified strain gradient theories. In this framework, new finite elements are developed and verified for Kirchhoff-Love plate theory, making it possible to model complex planar MEMSNEMS geometries. Structural behavior is elaborated using codes based on numerical analyses, that are also developed within this study. The results are then compared with experimental results and literature for verification. The convergence and validity of model results and the extent upto which they are applicable within the general continuum approach are also discussed. Length scale parameters for gold microstructures are proposed based on theoretical computational-experimental framework.