University of Toronto Institute for Aerospace Studies (UTIAS)

Permanent URI for this collectionhttps://hdl.handle.net/1807/69353

UTIAS is a graduate studies and research institute, forming part of the Faculty of Applied Science and Engineering at the University of Toronto . The continuing involvement of the University of Toronto in the aerospace sciences since World War I eventually led to the establishment of this institute in 1949. Originally called the Institute of Aerophysics, it is now known as the Institute for Aerospace Studies.

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Optimizing sandwich beams for strength and stiffness
(SAGE, 2012-09) Steeves, Craig A
This paper presents a method for minimising structural mass by optimising the geometry and core density of sandwich beams comprising composite face sheets and polymer foam cores, loaded in three-point bending. The optimisation is constrained by both strength and stiffness requirements. All possible locations in design space which might be global minima of mass are identified, and it is shown that, for a global minimum mass, at least two constraints must be simultaneously active. Calculations for a typical set of material properties are performed with the result that, for a wide range of typical materials, a minimum-mass sandwich beam satisfying both strength and stiffness requirements utilises low density foam and is constrained by stiffness and indentation strength.
Material selection in sandwich beam construction
(Elsevier, 2004-05) Steeves, Craig A; Fleck, Norman A
A systematic procedure is presented for comparing the relative performance of sandwich beams with various combinations of materials in three-point bending. Operative failure mechanisms are identified and failure maps are constructed. The geometry of sandwich beams is optimized to minimize the mass for a required load bearing capacity in three point bending.
In-plane properties of composite laminates with through-thickness pin reinforcement
(Elsevier, 2006-05) Steeves, Craig A; Fleck, Norman A
Laminated fibre reinforced composites can be reinforced by through-thickness pins to reduce their susceptibility to delamination. However, the presence of the pins creates resin pockets and disrupts the alignment of the fibres, and may thereby lead to a degradation of the in-plane strength of the composite. Experiments and numerical simulations show that the presence of through-thickness reinforcing pins decreases the tensile strength of the composite by 27%, and the compressive strength of the composite by at least 30%. It is also shown that the pattern in which the pins are inserted has a strong influence on the compressive strength. A pin pattern is identified in order to minimise fibre alignment disruption and thereby maximise the compressive strength.
Concepts for structurally robust materials that combine low thermal expansion with high stiffness
(Elsevier, 2007-09) Steeves, Craig A; dos Santos e Lucato, Sergio L; He, Ming; Antinucci, Emilio; Hutchinson, John W; Evans, Anthony G
A family of robust stretch-dominated bimaterial lattices is introduced which combines low (or zero) thermal expansion with high stiffness, structural robustness over wide temperature ranges and manufacturing facility. This combination of properties is unavailable through any other material solution. The concept uses two constituents configured as adjoining sub-lattices. It accommodates the thermal expansion through rotation of the members of one sub-lattice. Moreover, the lattice exhibits large stiffness to weight because it is fully triangulated and does not rely on rotational resistance at the joints for structural rigidity. A wide range of constituents can be used to build the new lattices enabling many desirable properties to be incorporated, especially high strength and toughness. Examples of both planar and volumetric lattices are presented, and their thermo-mechanical properties derived. The results are verified by conducting experiments and finite element simulations on a lattice fabricated using aluminium and titanium alloy constituents.
Collapse mechanisms of sandwich beams with composite faces and a foam core, loaded in three-point bending. Part II: experimental investigation and numerical modelling
(Elsevier, 2004-04) Steeves, Craig A; Fleck, Norman A
This study focuses on the competing collapse mechanisms for simply supported sandwich beams with composite faces and a PVC foam core subjected to three point bending. The faces comprise Hexcel Fibredux 7781-914G woven glass fibre-epoxy prepreg, while the core comprises closed cell Divinycell PVC foam of relative density 6.6% and 13.3%. The mechanical properties of the face sheets and core are measured independently. Depending upon the geometry of the beam and the relative properties of the constituents, collapse is by core shear, face sheet microbuckling or by indentation beneath the middle loading roller. A systematic series of experiments and finite element simulations have been performed in order to assess the accuracy of simple analytic expressions for the strength. In general, the analytic expressions for peak load are adequate; however, simple beam theory becomes inappropriate and the analytic models are inaccurate for stubby beams with thick faces relative to the core thickness. A failure mechanism map is constructed to reveal the dependence of the dominant collapse mechanism upon the geometry of the beam.
Collapse mechanisms of sandwich beams with composite faces and a foam core, loaded in three-point bending. Part I: analytical models and minimum weight design
(Elsevier, 2004-04) Steeves, Craig A; Fleck, Norman A
Analytical predictions are made for the three-point bending collapse strength of sandwich beams with composite faces and polymer foam cores. Failure is by the competing modes of face sheet microbuckling, plastic shear of the core, and face sheet indentation beneath the loading rollers. Particular attention is paid to the development of an indentation model for elastic faces and an elastic-plastic core. Failure mechanism maps have been constructed to reveal the operative collapse mode as a function of geometry of sandwich beam, and minimum weight designs have been obtained as a function of an appropriate structural load index. It is shown that the optimal designs for composite-polymer foam sandwich beams are of comparable weight to sandwich beams with metallic faces and a metallic foam core.
Mixed-dimensional Modeling of Structures with Thin Coatings Using Rotation-free Elements
(Elsevier, 2020-04) Chung, Steven C; Steeves, Craig A
This paper describes a new mixed-dimensional finite element model for structures that consist of thick substrates with thin coatings. For such structures, the difference in length scale between the substrate and the coating often makes meshing problematic, leading to severe solution inefficiencies for conventional finite element techniques. In the new approach presented here, rotation-free beam elements are used to model the thin coating, and solid elements to model the substrate. The new model employs a unique transition element to couple the rotation-free beam elements to biquadratic quadrilateral elements without using additional constraint equations. The 10-node transition element is created by modifying the shape functions of a biquadratic quadrilateral element to ensure that the displacement field on the coated surface is consistent with the displacement field of an overlaid rotation-free beam element. Convergence studies of thin-coated structures with both straight and curved geometries show excellent accuracy while using orders of magnitude fewer degrees of freedom than a conventional finite element model using only solid elements. Hence the new model enables efficient analysis of complicated coated structures.
Random matrix theory for robust topology optimization with material uncertainty
(Springer Nature, 2023-11) Li, Linxi G; Steeves, Craig A
This paper presents an efficient computational method for optimal structural design in the presence of uncertain Young's modulus modeled using discretized random fields. To quantify and propagate the uncertainty, random matrix theory is employed to quantify uncertainty in the context of robust topology optimization (RTO) for the minimization of compliance. Random matrix theory employs statistical inference methods to model the matrix-variate probability distribution of the finite element stiffness matrix. This provides analytical expressions for the mean and the standard deviation of the compliance, a combination of which is minimized in RTO. The novel random matrix theory-based RTO is computationally efficient due to the intrusive nature of the method, and is flexible as its computational performance and robustness remain consistent regardless of the correlation lengths or the variance of the random field, as demonstrated through numerical cases. The random matrix RTO method is applied to several two-dimensional numerical problems where the random fields of the modulus are assigned with ranges of correlation lengths and variances to illustrate the versatility of the method. The performance of random matrix RTO is compared with Monte Carlo RTO and stochastic collocation RTO to explore the efficiency and accuracy of the method.
Feasibility of Metallic Structural Heat Pipes as Sharp Leading Edges for Hypersonic Vehicles
(American Society of Mechanical Engineers, 2009) Steeves, Craig A; He, Ming Y; Kaen, Scott D; Valdevit, Lorenzo; Wadley, Haydn N G; Evans, Anthony G
Hypersonic flight with hydrocarbon-fueled airbreathing propulsion requires sharp leading edges. This generates high temperatures at the leading edge surface which cannot be sustained by most materials. By integrating a planar heat pipe into the structure of the leading edge, the heat can be conducted to large flat surfaces from which it can be radiated out to the environment, significantly reducing the temperatures at the leading edge and making metals feasible materials. This paper describes a method by which the leading edge thermal boundary conditions can be ascertained from standard hypersonic correlations, and then uses these boundary conditions along with a set of analytical approximations to predict the behaviour of a planar leading edge heat pipe. The analytical predictions of the thermostructural performance are verified by finite element calculations. Given the results of the analysis, possible heat pipe fluid systems are assessed, and their applicability to the relevant conditions determined. The results indicate that the niobium alloy Cb-752, with lithium as the working fluid, is a feasible combination for Mach 6 to 8 flight with a 3 mm leading edge radius.
Experimental Investigation of the Thermal Properties of Tailored Expansion Lattices
(Springer Nature, 2009-05) Steeves, Craig A; Mercer, Chris; Antinucci, Emilio; He, Ming Y; Evans, Anthony G
Composite bimaterial lattice structures which possess both low, tailorable thermal expansion and nearly optimal stiffness have been proposed for applications which require high structural stiffness in environments which include large temperature fluctuations, such as the surfaces of high-speed aerospace vehicles. An experimental validation of the thermal properties of these lattices when they are constructed of practical materials with easily manufactured bonded joints is contained herein. Bonded lattices, comprising aluminum and titanium alloys, have been manufactured with press-fit dovetail joints and tested in a variety of thermal environments. Results for equilibrium heating, rapid transient heating and thermal cycling leading to shakedown are presented and shown to be consistent with theoretically and numerically attained results.
Supplementary Material for "Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion"
(2018-11-16) Giamou, Matthew; Ma, Ziye; Peretroukhin, Valentin; Kelly, Jonathan
This document contains theorems and proofs that supplement the Robotics and Automation Letters paper titled "Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion".
Monolithic homotopy continuation with predictor based on higher derivatives
(Elsevier, 2019-01-15) Brown, David A.; Zingg, David W.
The predictor component of a monolithic homotopy continuation algorithm is augmented with higher derivative information for use as an efficient, robust, and scalable continuation algorithm suitable for application to large sparse systems of nonlinear algebraic equations. Convergence of the algorithm is established analytically, and efficiency studies are performed by applying the method to a practical computational aerodynamics problem.
Multifidelity Optimization of Hybrid Wing–Body Aircraft with Stability and Control Requirements
(American Institute of Aeronautics and Astronautics, 2018-12-03) Reist, Thomas A.; Zingg, David W.; Rakowitz, Mark; Potter, Graham; Banerjee, Sid
Methods of satisfying the stability and control (S&C) requirements for hybrid wing–body (HWB) aircraft are investigated using a multifidelity multidisciplinary optimization framework. A Reynolds-averaged Navier–Stokes solver is used for aerodynamic prediction, together with conceptual-level weight and balance models. These are coupled with a gradient-based optimizer to form a multidisciplinary optimization tool. Two HWB configurations are investigated. The first uses winglets with winglet-mounted rudders for lateral control, whereas the second uses centerbody-mounted fins with rudders. Longitudinal control is achieved with one centerbody elevator and six wing-mounted elevons. The designs are optimized for a combination of minimum/maximum takeoff weight and cruise drag. The ability of the designs to maintain lateral trim with one engine inoperative at a specified minimum control speed and to achieve a given rotational acceleration at a specified rotation speed forms the off-design S&C constraints. Additional constraints at cruise ensure trim and a required static margin. In addition to a classical HWB shape, a narrower cabin layout is also considered, which provides an improved performance. The required S&C requirements are found to be attainable using both configurations, with the fin-based control having a small performance advantage. The narrow-centerbody configuration is found to provide superior performance over the classical configuration.
Optimization of high-order diagonally-implicit Runge–Kutta methods
(Elsevier, 2018-05-15) Boom, Pieter D.; Zingg, David W.
This article presents constrained numerical optimization of high-order linearly and algebraically stable diagonally-implicit Runge–Kutta methods. After satisfying the desired order conditions, undetermined coefficients are optimized with respect to objective functions which consider accuracy, stability, and computational cost. Constraints are applied during the optimization to enforce stability properties, to ensure a well-conditioned method, and to limit the domain of the abscissa. Two promising third-order methods are derived using this approach, labelled SDIRK[3,(1,2,2)](3)L_14 and SDIRK[3,1](4)L_SA_5. Both optimized schemes have a good balance of properties. The relative error norm of the latter, the L2-norm scaled by a function of the number of implicit stages, is a factor of two smaller than comparable methods found in the literature. Variations on these methods are discussed relative to trade-offs in their accuracy and stability properties. A novel fifth-order scheme SDIRK[5,1](5)L_02 is derived with a significantly lower relative error norm than the comparable fifth-order A-stable reference method. In addition, the optimized scheme is L-stable. The accuracy and relative efficiency of the Runge–Kutta methods are verified through numerical simulation of van der Pol’s equation, as well as numerical simulation of vortex shedding in the laminar wake of a circular cylinder, and in the turbulent wake of a NACA 0012 airfoil. These results demonstrate the value of numerical optimization for selecting undetermined coefficients in the construction of high-order Runge–Kutta methods with a balance between competing objectives.
Airfoil Optimization Using Practical Aerodynamic Design Requirements
(American Institute of Aeronautics and Astronautics, 2010-09-01) Buckley, Howard P.; Zhou, Beckett Y.; Zingg, David W.
Practical aerodynamic design problems must balance the goal of performance optimization over a range of on-design operating conditions with the need to meet design constraints at various off-design operating conditions. Such design problems can be cast as multipoint optimization problems where the on-design and off-design operating conditions are represented as design points with corresponding objective/constraint functions. Two methods are presented for obtaining optimal airfoil designs that satisfy all design objectives and constraints. The first method uses an unconstrained optimization algorithm where the optimal design is achieved by minimizing a weighted sum of the objective functions at each of the operating conditions. To address the competing design objectives between on-design and off-design operating conditions, an automated procedure is used to efficiently weight the off-design objective functions so as to limit their influence on the overall optimization while satisfying the design constraints. The second method uses the constrained optimization algorithm SNOPT, which allows the aerodynamic constraints imposed at the off-design operating conditions to be treated explicitly. Both methods are applied to the design of an airfoil for a hypothetical aircraft where the problem is formulated as an 18-point multipoint optimization.
Mesh Movement for a Discrete-Adjoint Newton-Krylov Algorithm for Aerodynamic Optimization
(American Institute of Aeronautics and Astronautics, 2008-07-01) Truong, A. H.; Oldfield, C. A.; Zingg, D. W.
A grid movement algorithm based on the linear elasticity method with multiple increments is presented. The method is relatively computationally expensive but is exceptionally robust, producing high-quality elements even for large shape changes. It is integrated with an aerodynamic shape optimization algorithm that uses an augmented adjoint approach for gradient calculation. The discrete-adjoint equations are augmented to explicitly include the sensitivities of the mesh movement, resulting in an increase in efficiency and numerical accuracy. This gradient computation method requires less computational time than a function evaluation and leads to significant computational savings as dimensionality is increased. The results of the application of these techniques to several large deformation and optimization cases are presented.
Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements
(Elsevier, 2017-12-17) Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.
We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor–product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.
Relative continuous-time SLAM
(Sage Publishing, 2015-08-21) Anderson, Sean; MacTavish, Kirk; Barfoot, Timothy D.
Appearance-based techniques for simultaneous localization and mapping (SLAM) have been highly successful in assisting robot-motion estimation; however, these vision-based technologies have long assumed the use of imaging sensors with a global shutter, which are well suited to the traditional, discrete-time formulation of visual problems. In order to adapt these technologies to use scanning sensors, we propose novel methods for both outlier rejection and batch nonlinear estimation. Traditionally, the SLAM problem has been formulated in a single-privileged coordinate frame, which can become computationally expensive over long distances, particularly when a loop closure requires the adjustment of many pose variables. Recent discrete-time estimators have shown that a completely relative coordinate framework can be used to incrementally find a close approximation of the full maximum-likelihood solution in constant time. In order to use scanning sensors, we propose moving the relative coordinate formulation of SLAM into continuous time by estimating the velocity profile of the robot. We derive the relative formulation of the continuous-time robot trajectory and formulate an estimator using temporal basis functions. A motion-compensated outlier rejection scheme is proposed by using a constant-velocity model for the random sample consensus algorithm. Our experimental results use intensity imagery from a two-axis scanning lidar; due to the sensors’ scanning nature, it behaves similarly to a slow rolling-shutter camera. Both algorithms are validated using a sequence of 6880 lidar frames acquired over a 1.1 km traversal.
Learning-based Nonlinear Model Predictive Control to Improve Vision-based Mobile Robot Path Tracking
(Wiley, 2015-06-15) Ostafew, Chris J.; Schoellig, Angela P.; Barfoot, Timothy D.; Collier, Jack
This paper presents a Learning-based Nonlinear Model Predictive Control (LB-NMPC) algorithm to achieve high-performance path tracking in challenging off-road terrain through learning. The LB-NMPC algorithm uses a simple a priori vehicle model and a learned disturbance model. Disturbances are modeled as a Gaussian process (GP) as a function of system state, input, and other relevant variables. The GP is updated based on experience collected during previous trials. Localization for the controller is provided by an onboard, vision-based mapping and navigation system enabling operation in large-scale, GPS-denied environments. The paper presents experimental results including over 3 km of travel by three significantly different robot platforms with masses ranging from 50 to 600 kg and at speeds ranging from 0.35 to 1.2 m/s (associated video at http://tiny.cc/RoverLearnsDisturbances). Planned speeds are generated by a novel experience-based speed scheduler that balances overall travel time, path-tracking errors, and localization reliability. The results show that the controller can start from a generic a priori vehicle model and subsequently learn to reduce vehicle- and trajectory-specific path-tracking errors based on experience.
Relationship between local reaction rate and flame structure in turbulent premixed flames from simultaneous 10 kHz TPIV, OH PLIF, and CH 2 O PLIF
(Elsevier, 2017) Osborne, Jeffrey R.; Ramji, Sarah A.; Carter, Campbell D.; Steinberg, Adam M.
This work experimentally quantifies the relationship between metrics of the local reaction rate and flame thickness for turbulent premixed flames in the corrugated flamelet and thickened preheat zone/thin reaction zones regime using data from simultaneous 10 kHz tomographic particle image velocimetry (TPIV), hydroxyl planar laser induced fluorescence (OH PLIF), and formaldehyde (CH2O) PLIF. Two reaction rate metrics are presented, which are based on tracking fluid elements in a Lagrangian manner as they traverse from the flame leading edge to the reaction zone. This yields both a fluid residence time in the flame (τc) and a metric of the flame speed (S). τc in the thickened preheat zone regime was reduced by nearly 40% compared with the corrugated flamelet despite the flame being broader, indicating a substantial increase in the local reaction rate. The joint PDFs of S and local flame thickness showed a positive linear correlation between these quantities, which can be explained by turbulent diffusivity arguments. These data provide guidelines for reaction rate models, as well as a quantitative means of comparing local behavior between experiments and simulations.

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