W.G. Dettmer

An analysis of the time integration algorithms for the finite element solutions of incompressible Navier–Stokes equations based on a stabilised formulation

Abstract This work is concerned with the analysis of time integration procedures for the stabilised finite element formulation of unsteady incompressible fluid flows governed by the Navier–Stokes equations. The stabilisation technique is combined with several different implicit time integration procedures including both finite difference and finite element schemes. Particular attention is given to the generalised-α method and the linear discontinuous in time finite element scheme. The time integration schemes are first applied to two model problems, represented by a first order differential equation in time and the one dimensional advection–diffusion equation, and subjected to a detailed mathematical analysis based on the Fourier series expansion. In order to establish the accuracy and efficiency of the time integration schemes for the Navier–Stokes equations, a detailed computational study is performed of two standard numerical examples: unsteady flow around a cylinder and flow across a backward facing step. It is concluded that the semi-discrete generalised-α method provides a viable alternative to the more sophisticated and expensive space–time methods for simulations of unsteady flows of incompressible fluids governed by the Navier–Stokes equations.

A computational model for generalized inelastic materials at finite strains combining elastic, viscoelastic and plastic material behaviour

This work is concerned with the computational modelling of non‐linear solid material behaviour in the finite strain regime. Based on the recent computational formulations for modelling of inelastic material behaviour, a generalized material model is presented for inelastic materials incorporating classical elastic, viscoelastic, plastic and viscoplastic material description, all operating in the finite strain regime. The underlying rheological model corresponds to the combined action of several rheological components, such as Hooke, Maxwell and Prandtl elements, arranged in parallel. This work summarizes the theoretical basis of the material model and presents the computational treatment in the framework of a finite element solution procedure. Numerical examples are provided to illustrate the scope of the described computational strategy.

Quantum Corrections Based on the 2-D Schrödinger Equation for 3-D Finite Element Monte Carlo Simulations of Nanoscaled FinFETs

Solutions of the 2-D Schrödinger equation across the channel using a finite element method have been implemented into a 3-D finite element (FE) ensemble Monte Carlo (MC) device simulation toolbox as quantum corrections. The 2-D FE Schrödinger equation-based quantum corrections are entirely calibration free and can accurately describe quantum confinement effects in arbitrary device cross sections. The 3-D FE quantum corrected MC simulation is based on the tetrahedral decomposition of the simulation domain and the 2-D Schrödinger equation is solved at prescribed transverse planes of the 3-D mesh in the transport direction. We apply the method to study output characteristics of a nonplanar nanoscaled MOSFET, a{10.7}-nm gate length silicon-on-insulator FinFET, investigating 〈100〉 and 〈110〉 channel orientations. The results are then compared with those obtained from 3-D FE MC simulations with quantum corrections via the density gradient method showing very similar I-V characteristics but very different density distributions.

Conceptual Modeling of an Adaptive Torsion Wing Structure

This paper presents the conceptual analysis of a novel Active Aeroelastic Structure (AAS) device, which allows tailored twist deformations of wing structures to be achieved. The Adaptive Torsion Wing (ATW) concept is a thin-walled closed section two-spar wing-box whose torsional stiffness can be adjusted by changing the area enclosed between the front and rear spar webs. This is done by translating the spar webs in the chord-wise direction inward and towards each other using internal actuators. As the webs move closer to each other, the torsional stiffness of the structure reduces, while its bending stiffness in the span-wise direction is unaffected. The reduction in torsional stiffness allows external aerodynamic loads to induce twist on the structure and to maintain its deformed shape. These twist deformations can be controlled by changing the relative position of the webs as a function of the flight conditions to obtain an optimal or targeted level of performance. A Quasistatic Aeroelastic Suite has been developed in MATLAB TM to model the ATW concept and to study its behavior with respect to different web shifting strategies. Finally, the variation of structural figures of merit such as torsion constant, tip twist, shear centre position, and minimum actuation energy are evaluated and discussed.

3-D Finite Element Monte Carlo Simulations of Scaled Si SOI FinFET With Different Cross Sections

Nanoscaled Si SOI FinFETs with gate lengths of 12.8 and 10.7 nm are simulated using 3-D finite element Monte Carlo (MC) simulations with 2-D Schrodinger-based quantum corrections. These nonplanar transistors are studied for two cross sections: rectangular-like and triangular-like, and for two channel orientations: (100) and (110). The 10.7-nm gate length rectangular-like FinFET is also simulated using the 3-D nonequilibrium Greens functions (NEGF) technique and the results are compared with MC simulations. The 12.8 and 10.7 nm gate length rectangular-like FinFETs give larger drive currents per perimeter by about 33- 37% than the triangular-like shaped but are outperformed by the triangular-like ones when normalised by channel area. The devices with a (100) channel orientation deliver a larger drive current by about 11% more than their counterparts with a (110) channel when scaled to 12.8 nm and to 10.7 nm gate lengths. ID - VG characteristics obtained from the 3-D NEGF simulations show a remarkable agreement with the MC results at low drain bias. At a high drain bias, the NEGF overestimates the on-current from about VG - VT = 0.3 V because the NEGF simulations do not include the scattering with interface roughness and ionized impurities.

Anisotropic Quantum Corrections for 3-D Finite-Element Monte Carlo Simulations of Nanoscale Multigate Transistors

Anisotropic 2-D Schrödinger equation-based quantum corrections dependent on valley orientation are incorporated into a 3-D finite-element Monte Carlo simulation toolbox. The new toolbox is then applied to simulate nanoscale Si Siliconon-Insulator FinFETs with a gate length of 8.1 nm to study the contributions of conduction valleys to the drive current in various FinFET architectures and channel orientations. The 8.1 nm gate length FinFETs are studied for two cross sections: rectangular-like and triangular-like, and for two channel orientations: 〈100〉 and 〈110〉. We have found that quantum anisotropy effects play the strongest role in the triangular-like 〈100〉 channel device increasing the drain current by ~13% and slightly decreasing the current by 2% in the rectangular-like 〈100〉 channel device. The quantum anisotropy has a negligible effect in any device with the 〈110〉 channel orientation.

Performance and control optimisations using the adaptive torsion wing

This paper presents the Adaptive Torsion Wing (ATW) concept and performs two multidisciplinary design optimisation (MDO) studies by employing this novel concept across the wing of a representative UAV. The ATW concept varies the torsional stiffness of a two-spar wingbox by changing the enclosed area through the relative chordwise positions of the front and rear spar webs. The first study investigates the use of the ATW concept to improve the aerodynamic efficiency (lift-to-drag ratio) of the UAV. In contrast, the second study investigates the use of the concept to replace conventional ailerons and provide roll control. In both studies, the semi-span of the wing is split into five equal partitions and the concept is employed in each of them. The partitions are connected through thick ribs that allow the spar webs of each partition to translate independently of the webs of adjacent partitions and maintain a continuous load path across the wing span. An MDO suite consisting of a Genetic Algorithm (GA) optimiser coupled with a high-end low-fidelity aero-structural model was developed and employed in this paper.

Dynamic modelling and actuation of the adaptive torsion wing

This article presents the dynamical modelling of a novel active aeroelastic structure. The adaptive torsion wing concept is a thin-wall, two-spar wingbox whose torsional stiffness can be adjusted by translating the spar webs in the chordwise direction inward and towards each other using internal actuators. The reduction in torsional stiffness allows external aerodynamic loads to induce twist on the structure and maintain its deformed shape. Here, the adaptive torsion wing system is considered as integrated within the wing of a representative unmanned aerial vehicle to replace conventional ailerons and provide roll control. The adaptive torsion wing is modelled as a two-dimensional equivalent aerofoil using bending and torsion shape functions to express the equations of motion in terms of the twist angle and plunge displacement at the wingtip. The full equations of motion for the adaptive torsion wing equivalent aerofoil were derived using Lagrangian mechanics. The aerodynamic lift and moment acting on the aerofoil were modelled using Theodorsen’s unsteady aerodynamic theory. A low-dimensional, state-space representation of an empirical Theodorsen’s transfer function was adopted to allow time-domain analyses. Four actuation strategies were investigated. Figures of merit, including plunge displacement, twist angle, actuation forces and actuation powers, were quantified and discussed for each of the scenarios. This study allows the conceptual design and sizing of the internal actuators that are required to drive the webs.

A multi-scale computational assessment of channel gating assumptions within the Meissner corpuscle ☆

From the macroscopic mechanical deformation of skin to the feeling of touch is a chain of complex events whereby information is converted from one form to another between different scales. An important link in this chain is receptor activation, which requires incorporation of microanatomical, cellular and ion channel transduction models. Of particular interest is the deformations at the axon membrane bi-layer, which are believed to be involved in mechanoelectrical signal transduction by activation of ion channels. We present a fully coupled multi-scale finite element analysis of the finger pad during tactile exploration, whereby the Meissner corpuscle, which is modeled as a single representative volume element (RVE) at the microscopic level, interacts with the macroscopic finger model. Maximum values of local stretching and compression occurring at the bi-layer are monitored for finger models with and without fingerprints, the presence of which generates a remarkable amplification of the signal. The contours of the surface being explored are well represented by the maximal peaks observed within the membrane.

Roll control of a MALE UAV using the adaptive torsion wing

This paper assesses the feasibility of the Adaptive Torsion Wing (ATW) concept to replace conventional control surfaces and enhance the manoeuvrability of a UAV. The ATW concept is a thin-walled closed section two-spar wingbox whose torsional stiffness can be adjusted through the chord-wise position of the front and rear spar webs. The reduction in torsional stiffness allows external aerodynamic loads to induce aeroelastic twist that can be used as a function of the flight conditions to obtain a desired roll control authority. Modelling of the concept was performed using a low fidelity quasi-static aeroelastic suite developed in MATLAB. The variation of structural figures of merit are evaluated and discussed. Finally, an MDO study was performed to have in-depth assessments of the potential benefits of the ATW in replacing ailerons and providing sufficient roll control.