David J. Munk

Topology optimisation of micro fluidic mixers considering fluid-structure interactions with a coupled Lattice Boltzmann algorithm

Abstract Recently, the study of micro fluidic devices has gained much interest in various fields from biology to engineering. In the constant development cycle, the need to optimise the topology of the interior of these devices, where there are two or more optimality criteria, is always present. In this work, twin physical situations, whereby optimal fluid mixing in the form of vorticity maximisation is accompanied by the requirement that the casing in which the mixing takes place has the best structural performance in terms of the greatest specific stiffness, are considered. In the steady state of mixing this also means that the stresses in the casing are as uniform as possible, thus giving a desired operating life with minimum weight. The ultimate aim of this research is to couple two key disciplines, fluids and structures, into a topology optimisation framework, which shows fast convergence for multidisciplinary optimisation problems. This is achieved by developing a bi-directional evolutionary structural optimisation algorithm that is directly coupled to the Lattice Boltzmann method, used for simulating the flow in the micro fluidic device, for the objectives of minimum compliance and maximum vorticity. The needs for the exploration of larger design spaces and to produce innovative designs make meta-heuristic algorithms, such as genetic algorithms, particle swarms and Tabu Searches, less efficient for this task. The multidisciplinary topology optimisation framework presented in this article is shown to increase the stiffness of the structure from the datum case and produce physically acceptable designs. Furthermore, the topology optimisation method outperforms a Tabu Search algorithm in designing the baffle to maximise the mixing of the two fluids.

Experimental Validation of Polynomial Chaos Theory on an Aircraft T-Tail

Uncertainty quantification (UQ) is a notion which has received much interest over the past decade. It involves the extraction of statistical information from a problem with inherent variability, where this variability may stem from a lack of model knowledge or through observational uncertainty. Traditionally, UQ has been a challenging pursuit owing to the lack of efficient methods available. The archetypal UQ method is Monte Carlo theory, however this method possesses a slow convergence rate and is therefore a computational burden. In contrast to Monte Carlo theory, polynomial chaos theory aims to spectrally expand the modelled uncertainty via polynomials of random variables which have deterministic coefficients. Once the spectral expansion has been fully defined, it is possible to obtain statistical properties using simple integration procedures. Although literature has proven polynomial chaos theory to be more efficient than Monte Carlo theory in several contexts, there has been very little effort to experimentally validate polynomial chaos theory. Hence, it is the aim of this paper to perform an experimental validation on an in-house physical T-Tail structure by analysing the first six vibrational modes of this structure, and comparing these against the predicted uncertainty bounds of polynomial chaos theory.

Novel Moving Isosurface Threshold Technique for Optimization of Structures Under Dynamic Loading

The optimum design of structures with frequency constraints is of great importance in the aeronautical industry. To avoid severe vibration, it is necessary to shift the fundamental frequency of the...

A Hypersonic Aircraft Optimization Tool with Strong Aerothermoelastic Coupling

The design and optimization of hypersonic aircraft is severely impacted by the high temperatures encountered during flight as they can lead to high thermal stresses and a significant reduction in material strength and stiffness. This reduction in rigidity of the structure requires innovative structural concepts and a stronger focus on aerothermoelastic deformations in the early design and optimization phase of the design cycle. This imposes the need for a closer coupling of the aerodynamic, thermal and structural design tools than is currently in practice. The paper presents a multi-disciplinary, closely coupled optimization suite that is suitable for preliminary design in the hypersonic regime. The time varying temperature distribution is applied through an equilibrium analysis, and is coupled to the aerodynamics through the Tranair® solver. An analysis of the effect that the aerothermodynamic coupling has on the sizing of the aircraft is given, along with the effect of skin buckling. It is shown that the coupling of the aerothermodynamics drives the sizing of the structure and therefore must be considered for hypersonic applications.

Development of a Hypersonic Aircraft Design Optimization Tool

The design and optimization of hypersonic aircraft is severely impacted by the high temperatures encountered during flight as they can lead to high thermal stresses and a significant reduction in material strength and stiffness. This reduction in rigidity of the structure requires innovative structural concepts and a stronger focus on aeroelastic deformations in the early design and optimisation of the aircraft structure. This imposes the need for a closer coupling of the aerodynamic and structural design tools than is current practice. The paper presents the development of a multi-disciplinary, closely coupled optimisation suite for hypersonic aircraft. An overview of the setup and structure of the optimization suite is given and the integration between the Tranair solver, used to determine the aerodynamic loads and temperatures, and MSC/NASTRAN, used for the structural sizing and design, will be given.

A Generalized SNC-BESO Method for Multi-objective Topology Optimization

Multi-objective optimization has become an invaluable tool in engineering design. One class of solutions to the multi-objective optimization problem is known as the Pareto frontier. The Pareto frontier is made up of a group of solutions known as Pareto optimal solutions. These solutions are optimal in the sense that any improvement in one design objective must come with the worsening of at least one other. Therefore, the Pareto frontier plays a vital role in engineering design, since it defines the trade-offs between conflicting objectives. Methods exist that can automatically generate a set of Pareto solutions from which the final design can be chosen. For such an approach to be successful, the generated set must truly be representative of the complete design space. This paper offers a new phase in the development of the smart normal constraint bi-directional evolutionary optimization method, which is a recently developed approach that allows the efficient and effective generation of smart Pareto sets to multi-objective topology optimization problems. Currently, only bi-objective topology optimization problems can be solved with this method. Therefore, in this paper the method is generalized to solve topology optimization problems with any number of objectives. This is demonstrated on an example having three objectives.

Multi‑physics bi‑directional evolutionary topology optimization on GPU‑architecture

Topology optimization has proven to be viable for use in the preliminary phases of real world design problems. Ultimately, the restricting factor is the computational expense since a multitude of designs need to be considered. This is especially imperative in such fields as aerospace, automotive and biomedical, where the problems involve multiple physical models, typically fluids and structures, requiring excessive computational calculations. One possible solution to this is to implement codes on massively parallel computer architectures, such as graphics processing units (GPUs). The present work investigates the feasibility of a GPU-implemented lattice Boltzmann method for multi-physics topology optimization for the first time. Noticeable differences between the GPU implementation and a central processing unit (CPU) version of the code are observed and the challenges associated with finding feasible solutions in a computational efficient manner are discussed and solved here, for the first time on a multi-physics topology optimization problem. The main goal of this paper is to speed up the topology optimization process for multi-physics problems without restricting the design domain, or sacrificing considerable performance in the objectives. Examples are compared with both standard CPU and various levels of numerical precision GPU codes to better illustrate the advantages and disadvantages of this implementation. A structural and fluid objective topology optimization problem is solved to vary the dependence of the algorithm on the GPU, extending on the previous literature that has only considered structural objectives of non-design dependent load problems. The results of this work indicate some discrepancies between GPU and CPU implementations that have not been seen before in the literature and are imperative to the speed-up of multi-physics topology optimization algorithms using GPUs.

Frequency Response Characteristics of 2D Wings in Uncertain Environments: A Random Matrix Theory Approach

Whilst structural design processes in engineering have been extensively developed, the additional consideration of uncertainty quantification (UQ) provides a more holistic forecast on its long term sustainability. UQ methods such as Polynomial Chaos Theory have received attention in numerous fields within engineering for its ability to approximate statistical moments with good accuracy and with low computational expense. This study explores a probabilistic approach to analyze frequency response in 2D wings facilitated by Random Matrix Theory (RMT). This UQ method has not been explored thoroughly within the aerospace sector. Uncertainties are enforced on the length, width and Young’s modulus of two wings varying in geometry and the natural vibration mode characteristics are determined via finite element modeling. Baseline characteristics are compared to an approximation derived from RMT and the worst case scenarios. It was found that RMT provided a good estimate of both the frequency and magnitude shifts of the vibrational modes under the enforced uncertainty. The more complex geometry was found to be more robust to the imposed variations, and RMT was able to capture this behavior effectively.

Producing Smart Pareto Sets for Multi-objective Topology Optimisation Problems

To date the design of structures via topology optimisation methods has mainly focused on single-objective problems. However, real-world design problems usually involve several different objectives, most of which counteract each other. Therefore, designers typically seek a set of Pareto optimal solutions, a solution for which no other solution is better in all objectives, which capture the trade-off between these objectives. This set is known as a smart Pareto set. Currently, only the weighted sums method has been used for generating Pareto fronts with topology optimisation methods. However, the weighted sums method is unable to produce evenly distributed smart Pareto sets. Furthermore, evenly distributed weights have been shown to not produce evenly spaced solutions. Therefore, the weighted sums method is not suitable for generating smart Pareto sets. Recently, the smart normal constraints method has been shown to be capable of directly generating smart Pareto sets. This work presents an updated smart normal constraint method, which is combined with a bi-directional evolutionary structural optimisation algorithm for multi-objective topology optimisation. The smart normal constraints method has been modified by further restricting the feasible design space for each optimisation run such that dominant and redundant points are not found. The algorithm is tested on several different structural optimisation problems. A number of different structural objectives are analysed, namely compliance, dynamic and buckling objectives. Therefore, the method is shown to be capable of solving various types of multi-objective structural optimisation problems. The goal of this work is to show that smart Pareto sets can be produced for complex topology optimisation problems. Furthermore, this research hopes to highlight the gap in the literature of topology optimisation for multi-objective problems.

SIMP for Complex Structures

Designing structures with frequency constraints is an important task in aerospace engineering. Aerodynamic loading, gust loading, and engine vibrations all impart dynamic loads upon an airframe. To avoid structural resonance and excessive vibration, the natural frequencies of the structure must be shifted away from the frequency range of any dynamic loads. Care must also be taken to ensure that the modal frequencies of a structure do not coalesce, which can lead to dramatic structural failure. So far in industry, no aircraft lifting surfaces are designed from the ground up with frequency optimisation as the primary goal. This paper will explore computational methods for achieving this task.This paper will present a topology optimisation algorithm employing the Solid Isotropic Microstructure with Penalisation (SIMP) method for the design of an optimal aircraft wing structure for rejection of frequency excitation.