This paper describes a new efficient method for the construction of an approximately balanced aerodynamic Reduced Order Model (ROM) via the frequency domain using Computational Fluid Dynamics data. Time domain ROM construction requires CFD data, which is obtained from the DLR TAU RANS or Euler Linearised Frequency Domain (LFD) solver. The ROMs produced with this approach, using a small number of frequency simulations, are shown to exhibit a strong ability to reconstruct the system response for inviscid flow about the NLR7301 aerofoil and the FFAST wing; and viscous flow about the NASA Common Research Model. The latter demonstrates that the reduced order model approach can reconstruct the full order frequency response of a viscous aircraft configuration with excellent accuracy using a strip wise approach. The time domain models are built using the frequency domain, but also give promising results when applied to reconstruct non-periodic motions. Results are compared to time domain simulations, showing good agreement even with small ROM sizes, but with a substantial reduction in calculation time. The main advantage of the current model order reduction approach is that the method does not require the formation and storage of large matrices, such as in POD approaches.

A Doyle–Fuller–Newman (DFN) model for the charge and discharge of nano-structured lithium iron phosphate (LFP) cathodes is formulated on the basis that lithium transport within the nanoscale LFP electrode particles is much faster than cell discharge, and is therefore not rate limiting. We present some numerical solutions to the model and show that for relevant parameter values, and a variety of C-rates, it is possible for sharp discharge fronts to form and intrude into the electrode from its outer edge(s). These discharge fronts separate regions of fully utilised LFP electrode particles from those that are not. Motivated by this observation an asymptotic solution to the model is sought. The results of the asymptotic analysis of the DFN model lead to a reduced order model, which we term the reaction front model (or RFM). Favourable agreement is shown between solutions to the RFM and the full DFN model in appropriate parameter regimes. The RFM is significantly cheaper to solve than the DFN model, and therefore has the potential to be used in scenarios where computational costs are prohibitive, e.g. in optimisation and parameter estimation problems or in engineering control systems.

We present a hybrid, semi-analytical approach to perform an eigenvalue-based flutter analysis of an Unmanned Aerial Vehicle (UAV) wing. The wing has a modern design that integrates metal and composite structures. The stiffness and natural frequency of the wing are calculated using a Finite Element (FE) model. The modal parameters are extracted by applying a recursive technique to the Lanczos method in the FE model. Subsequently, the modal parameters are used to evaluate the flutter boundaries in an analytical model based on the p-method. Two-degree-of-freedom bending and torsional flutter equations derived using Lagrange’s principle are transformed into an eigenvalue problem. The eigenvalue framework is used to evaluate the stability characteristics of the wing under various flight conditions. An extension of this eigenvalue framework is applied to determine the stability boundaries and corresponding critical flutter parameters at a range of altitudes. The stability characteristics and critical flutter speeds are also evaluated through computational analysis of a reduced-order model of the wing in NX Nastran using the k- and pk-methods. The results of the analytical and computational methods are found to show good agreement with each other. A parametric study is also carried out to analyse the effects of the structural member thickness on the wing flutter speeds. The results suggest that changing the spar thickness contributes most significantly to the flutter speeds, whereas increasing the rib thickness decreases the flutter speed at high thickness values.

A rigid body dynamical model and control architecture are developed for the closed chain motion of two structurally dissimilar manipulators holding a rigid object in a three-dimensional workspace. The model is first developed in the joint space and then transformed to obtain reduced order equations of motion and a separate set of equations describing the behavior of the generalized contact forces. The problem of solving the joint space and reduced order models for the unknown variables is discussed. A new control architecture consisting of the sum of the outputs of a primary and secondary controller is suggested which, according to the model, decouples the force and position-controlled degrees of freedom during motion of the system. The proposed composite controller enables the designer to develop independent, non-interacting control laws for the force and position control of the complex closed chain system.

The reduced basis element method is a new approach for approximating the solution of problems described by partial differential equations. The method takes its roots in domain decomposition methods and reduced basis discretizations. The basic idea is to first decomposethe computational domain into a series of subdomains that are deformationsof a few reference domains (or generic computational parts). Associated with each reference domain are precomputed solutions corresponding to the same governing partial differential equation,but solved for different choices of deformations of the referencesubdomains and mapped onto the reference shape.The approximation corresponding to a new shape is then taken to be a linear combination of the precomputed solutions, mappedfrom the generic computational part to the actual computational part.We extend earlier work in this direction to solve incompressible fluid flow problems governed by the steady Stokes equations. Particular focus is given to satisfying the inf-sup condition,to a posteriori error estimation, and to “gluing” the local solutions together in the multidomain case.