Finite element formulations for Kirchhoff-Love microplates

Download

index.pdf

Date

2020

Author

Kandaz, Murat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

308
views

272
downloads

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.

Subject Keywords

Finite element method., Size effect, higher order finite element method, modified strain gradient theory, length scale parameter, microplates, MEMS, higher order elasticity, higher order Kirchhoff-Love plate theory.

URI

http://etd.lib.metu.edu.tr/upload/12625529/index.pdf
https://hdl.handle.net/11511/45748

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Analysis of Gold Microbeams with Higher Order Continuum Theories Kandaz, Murat; Dal, Hüsnü; Ünlü, Mehmet (null; 2017-03-10) Microbeams are building blocks for many micro and nanostructures as well as microelectromechanical systems (MEMS) and cannot accurately be modelled by classical continuum theories due to size effects due to their micro-scale. These size effects can be taken into account by the so-called higher order continuum theories. Modified Strain Gradient Theory (MSGT) and Modified Couple Stress Theory (MCST) are two commonly used theories, which extend the classical local continuum theories of grade one with the intro...
Discrete Optimization of Truss Structure using Probability Collectives Kulkarni, Anand J.; Kale, I. R.; Tai, K.; Azad, S. Kazemzadeh (2012-12-07) Traditionally, complex systems were treated using centralized approaches; however, recent trends highlighted that the growing complexity can be best dealt by decomposing the entire system into subsystems and further treat them in a distributed way. The approach of Probability Collectives (PC) in Collective Intelligence (COIN) framework decomposes the entire system into a Multi-Agent System (MAS) or a collection of rational and self interested agents and further optimizes them in a distributed and decentrali...
Finite element modeling of micro particle separation using ultrasonic standing waves Süleyman, Büyükkoçak; Çetin, Barbaros; Özer, Mehmet Bülent (2014-08-07) Acoustophoresis which means separation of particles and cells using acoustic waves is becoming an intensive research subject. The method is based on inducing an ultrasonic compression standing wave inside a microchannel. A finite element approach is used to model the acoustic and electro-mechanical behavior of the piezoelectric material, the micro-channel geometry as well as the fluid inside the channel. The choices of silicon and PDMS materials are investigated as the chip materials for the resonator. A se...
Space-bandwidth-efficient realizations of linear systems KUTAY, MA; ERDEN, MF; OZAKTAS, HM; ARIKAN, O; GULERYUZ, O; Candan, Çağatay (The Optical Society, 1998-07-15) One can obtain either exact realizations or useful approximations of linear systems or matrix-vector products that arise in many different applications by implementing them in the form of multistage or multichannel fractional Fourier-domain filters, resulting in space-bandwidth-efficient systems with acceptable decreases in accuracy. Varying the number and the configuration of filters enables one to trade off between accuracy and efficiency in a flexible manner. The proposed scheme constitutes a systematic ...
Analysis of gold micro-beams with modified strain gradient theory Dal, Hüsnü (2017-07-01) Micro-beams are building blocks for many micro- and nano-electro-mechanical systems (MEMS/NEMS) and cannot accurately be modeled by classical continuum theories due to significant size effects at the length scales associated with these structures. Size effects can be taken into account by the so-called higher-order continuum theories. In this study, Euler-Bernoulli microbeams are analyzed with the Modified Strain Gradient Theory (MSGT), which extends the classical local continuum theories of grade one with ...

Citation Formats

M. Kandaz, “Finite element formulations for Kirchhoff-Love microplates,” Thesis (Ph.D.) -- Graduate School of Natural and Applied Sciences. Mechanical Engineering., Middle East Technical University, 2020.