Peter A. Fotiu

Transient electro-thermal simulation of microsystems with space-continuous thermal models in an analogue behavioural simulator

Abstract In many microsystems (MEMS), thermal effects have significant importance and system-level electro-thermal simulation is needed to shorten the product development cycle and to increase system reliability. The possibilities for space-continuous simulation of electro-thermal problems using an analogue simulator and an analogue hardware description language are described. In comparison to commercial finite element simulators, the relative error of thermal simulation is

Advances in Quadrilateral Shell Elements with Drilling Degrees of Freedom

A unique derivation of quadrilateral shell elements with six degrees of freedom at each node is presented. The theoretical and numerical formulation is based on the combination of a membrane element with drilling degrees of freedom and a shear deformable plate element. The predictive quality and the computational efficiency is improved by applying multifield variational principles in connection with suitable assumed strain fields. The resulting element formulation does not require any Gaussian quadrature since all parts of the stiffness matrix can be integrated analytically. Furthermore, the derivation is generalized to geometrical and physical nonlinearities according to a corotational updated Lagrangian description.

Analogue behavioural simulator as a tool for coupled electro-thermal analysis of microsystems

In many microsystems, thermal effects have significant importance and electro-thermal simulation is necessary to shorten the product development cycle. The possibilities for space-continuous simulation of electrothermal problems by using an analogue simulator and an analogue hardware description language have been described. In comparison to commercial finite element simulators, the relative error of thermal simulation is less than 0.08% for three-dimensional static analyses. Transient thermal problems with coupled electronic components have been simulated.

Electro-thermal simulation of microsystems with mixed abstraction modelling☆

Abstract Electro-thermal coupling is only one aspect of numerous interactions between physical domains in microsystems. Different physical effects govern the functionality of microsystems and the system-level modelling using standard electro-thermal tools is not easy. In order to predict potential failures in microsystem designs and reduce the costs of prototyping, it is important to involve the simulation of electro-thermal effects at the system level, early in the design process. Also, it is necessary to conduct a final verification of the complete system with all governing subsystems. This paper considers different issues of electro-thermal modelling for microsystems and proposes analogue simulators with hardware description languages as a tool for the system-level modelling. With increasing system complexity, the mixed abstraction modelling is the only way to achieve an optimal blend of the accuracy and the speed.

On Drilling Degrees of Freedom

In this paper the development of a new quadrilateral membrane finite element with drilling degrees of freedom is discussed. A variational principle employing an independent rotation field around the normal of a plane continuum element is derived. This potential is based on the Cosserat continuum theory where skew symmetric stress and strain tensors are introduced in connection with the rotation of a point. From this higher continuum theory a formulation that incorporates rotational degrees of freedom is extracted, while the stress tensor is symmetric in a weak form. The resulting potential is found to be similar to that obtained by the procedure of Hughes and Brezzi. However, Hughes and Brezzi derived their potential in terms of pure mathematical investigations of Reissner’s potential, while the present procedure is based on physical considerations. This framework can be enhanced in terms of assumed stress and strain interpolations, if the numerical model is based on a modified Hu-Washizu functional with symmetric and asymmetric terms. The resulting variational statement enables the development of a new finite element that is very efficient since all parts of the stiffness matrix can be obtained analytically even in terms of arbitrary element distortions. Without the addition of any internal degrees of freedom the element shows excellent performance in bending dominated problems for rectangular element configurations.