Accurate FE-simulation of three-dimensional microstructures

This thesis presents the development and the application of a software tool ADAPTREF with which to automatically control the accuracy of simulation results obtained by finite element (FE) computations. It is especially designed to meet the requirements that are present when simulating micro-electro-mechanical systems (MEMS). The software tool aims to improve the solution accuracy of the computed fields from the coupled electrical, thermal and mechanical domains. <br>The fields obey (non-linear) partial differential equations and are derived by a thermodynamic formalism. Besides a FE-formulation for thermal problems we give a <br>more general presentation also comprising coupled <br>thermo-electro-mechanical multi-layered plate problems which for MEMS make <br>great demands on the computational resources. <br>Therefore, dealing <br>economically with the computational resources we are bound to choose <br>the number of computational nodes as small as possible. The tool ADAPTREF adaptively introduces new nodes into the computational mesh which describes the device geometry. The adaptivity is carried out according to the requirement to reduce the error of the computed solution. The main tool in doing so is error estimation with which we can localize the magnitude of the errors introduced by the discretization of the physical problem and which, for multi-physically active thin structures, is derived on the basis of a functional analytical framework. In addition, a refinement strategy and a geometrical split pattern are required in order to be able to implement a reliable and stable software tool with which to control the accuracy of the solution fields. <br>By choosing an Object-Oriented architecture and implementation (C++), we assure a flexible extensibility of the software ADAPTREF into a great range of directions. By providing a proper interface it can be used with virtually any FE-tool. <br>The power of the ADAPTREF is illustrated by simulations of a selected set of microsystems.

Author dc:creator

• Müller, Jens

Contributors dc:contributor

• Korvink, Jan G.

• Dünnschicht
• Fehleradaptivität
• Thermomechanik
• Piezoelektromechanik, CAD
• Mesh adaptivity
• MEMS CAD
• Slender Structures
• Finite Elements
• Plate theory

Repository record source_url

https://freidok.uni-freiburg.de/data/251

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:251