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This paper is written to honor Raphael T. Haftka’s seminal contributions to multidisciplinary design optimization. We focus on those contributions that directly impacted our research, namely: the adjoint method for computing derivatives, wing aerostructural design optimization, and architectures for multidisciplinary design optimization. For each of these topics, we describe Haftka’s contributions, how they impacted our research, and examples of what they enabled us to do. The overarching theme of the contributions and developments described in this paper is the efficient computation of derivatives, which, together with gradient-based optimizers, enables the optimization with respect to large numbers of design variables, even when using costly high-fidelity models.

Background Accumulation of multiple pockets of fluid at the fovea, as a complication of poor blood glucose control in diabetes, causes impairment of central vision. A new ability to demonstrate a pre-clinical phase of this maculopathy could be valuable, enabling diabetic individuals to be alerted to the need to improve their glycaemic control. This study aimed to use swept-source optical coherence tomography (SS-OCT) to measure foveal thickness and macular volume in diabetic individuals without cystoid macular oedema, and in non-diabetic individuals, and relate these measures to participants’ glycaemic control. Methods Centre point thickness (CPT) and total macular volume (TMV) were measured using SS-OCT (DRI OCT Triton™, Topcon, Tokyo, Japan). Participants’ glycosylated haemoglobin (HbA1c) level was also assessed (A1cNow®+ System, PTS Diagnostics, Indianapolis, IN, USA). The diabetic (n = 27) and non-diabetic (n = 27) groups were matched for age (p = 0.100) and sex (p = 0.414), and HbA1c level differed between diabetic and non-diabetic groups (p n = 7) and type 2 (n = 20) diabetic individuals who were matched for duration of diabetes (p = 0.617) and whose glycaemic control was similar (p = 0.814). Results Diabetic individuals had significantly higher CPT (t(37) = 3.859, p 1c level (β = 0.501, t(21) = 3.139, p = 0.005): there was a 19-μm increase in CPT for each 1% increase in HbA1c level. This relationship was not present in the non-diabetic group (β = − 0.068, t(23) = − 0.373, p = 0.712). Conclusions SS-OCT is the only way to measure macular thickness in vivo. Diabetic individuals en bloc had higher CPT compared with non-diabetic individuals. Moreover, in the diabetic group, HbA1c level significantly predicted CPT. Our results suggest that, in diabetes, sub-clinical thickening may occur at the fovea before cystoid macular oedema becomes clinically evident. This could provide diabetic individuals with an early warning of disease progression and motivate them to improve control of their diabetes, with a view to avoiding the need of intra-vitreal injections with their attendant risks.

The adoption of conventional “black metal” composites in aircraft structures has lead to an improvement in performance over previous metallic designs. With the maturation of automated fiber placeme...

Conformal ablators are low-density composite materials comprising a flexible fibrous substrate and polymer matrix. Recent advancements have improved the efficiency of conformal ablator fabrication ...

Fiber substrate-based ablators such as Phenolic-Impregnated Carbon Ablator are composite materials comprising a fibrous substrate and a polymer matrix. This paper presents an approach for estimatin...

Introduction Diabetes is a global issue that currently affects 425 million people worldwide. One observable microvascular complication of this condition is a change in the foveal avascular zone (FAZ). In this study, we used optical coherence tomography angiography (OCT-A) to investigate the effect of diabetes on the FAZ. Materials and methods Eleven diabetic and eleven non-diabetic participants took part in this study. Participants in both groups were matched for age (p = 0.217) and sex (p = 0.338), and had no history of ocular disease. Macular OCT-A scans of participants' right and left eyes were taken. Glycosylated haemoglobin (HbA1c ) and blood glucose levels were also measured. The FAZ area was manually segmented at the levels of the superficial capillary plexus (FAZSCP ) and deep capillary plexus (FAZDCP ). Results There was a strong relationship between the FAZ area of participants' right and left eyes (p ≤ 0.001) in both diabetic and non-diabetic groups. In the diabetic group, the FAZSCP (p = 0.047) and FAZDCP (p = 0.011) areas was significantly larger than in the non-diabetic group. Moreover, multiple linear regression analysis predicted a 0.07-mm2 increase in diabetic individuals' FAZSCP and FAZDCP areas for every 1% increase in their HbA1c level. Conclusions Our findings indicate that there is enlargement of the FAZ in diabetic individuals compared with non-diabetic individuals. In the diabetic group, this enlargement appears to be correlated with HbA1c level. OCT-A imaging could, therefore, be a useful tool to monitor the FAZ and identify potential early microvasculopathy in diabetes.

A parallel finite element framework for high-fidelity structural dynamic analysis and gradient evaluation using the discrete adjoint method is presented. The framework is intended to be used for gr...

Topology optimization tools offer the potential to design novel aerospace structures that are subject to demanding strength and natural frequency requirements. However, algorithms for stress- and f...

Over the past several decades, composites have increasingly become the material of choice in modern aircraft structural design. This is primarily due to the high stiffness- and strength-to-weight ratios offered by conventional composites when compared to metals. Unconventional composite designs, such as tow-steered composites, have demonstrated potential for further expanding these advantages. Unlike their conventional composite counterparts, tow-steered composites feature layers with spatially varying fiber orientations. When applied to wing design, tow-steered composites offer an increase in design freedom at the cost of higher design complexity, making them ideal candidates for design optimization. We develop a methodology for the aerostructural design optimization of tow-steered composite wings using high-fidelity physics models. We also quantify the benefits of this new technology by performing a fuel burn minimization for both a tow-steered and a conventional composite wing design. This assessment is done for the undeflected Common Research Model, which is representative of a twin-aisle transport aircraft. We find improvements of up to 2.4% in fuel burn and 24% in wing weight relative to the optimized conventional composite design. We show that this improvement is due to a combination of improved passive aeroelastic tailoring and local strength tailoring in high-stress regions in the tow-steered structure. For a higher-aspect-ratio (13.5) wing design, we find improvements of up to 1.5% and 14% in fuel savings and wing weight, respectively. To better understand the effect of aspect ratio on tow-steered wing design, we perform an optimization study where the aspect ratio is varied between 7.5 and 13.5. We found that there are diminishing returns in the benefit of tow steering as the aspect ratio is increased because less passive load alleviation is possible.

As engineers increasingly pursue air vehicle designs with slender, lightweight aerostructures, it has become necessary to model nonlinear aeroelastic effects earlier in the design process. As a result, high-fidelity analysis tools are required that can efficiently identify flutter within the flight envelope, and find design modifications to alleviate adverse aeroelastic behavior. To address these requirements, we have systematically evaluated automated methods to identify the damping of an aeroelastic system from a time-domain simulation. The techniques evaluated include the log decrement method, envelope function methods that use the Hilbert transformation, the half-power bandwidth method, and the matrix pencil method. The optimal approach was determined to be the matrix pencil method due to its robustness to noise and its ability to handle multi-component signals over short time simulations. Identification of the flutter boundary of the AGARD-445.6 wing is demonstrated with an automated method based on the adjoint sensitivities and the matrix pencil method. While the matrix pencil method is robust, identification of the flutter boundary using gradient-based optimization is shown to be sensitive to the initial dynamic pressure guess.

This paper presents a sequential convex optimization method for minimum compliance design of multimaterial problems. The proposed method uses a multimaterial parametrization based on SIMP or RAMP penalization. At each iteration of the algorithm, a convex subproblem is constructed by forming a nonlinear, convex approximation of the penalized compliance based on a linearization of the stiffness matrix. Subsequent solutions of the convex subproblems form a non-increasing sequence of compliance values. The subproblems are solved using a tailored inexact Newton–Krylov interior point method that leverages relatively inexpensive Hessian-vector products. The algorithm is demonstrated on a series of isotropic and orthotropic multimaterial plane stress design problems.

Accumulation of multiple pockets of fluid at the fovea, as a complication of poor blood glucose control in diabetes, causes impairment of central vision. A new ability to demonstrate a pre-clinical phase of this maculopathy could be valuable, enabling diabetic individuals to be alerted to the need to improve their glycaemic control. This study aimed to use swept-source optical coherence tomography (SS-OCT) to measure foveal thickness and macular volume in diabetic individuals without cystoid macular oedema, and in non-diabetic individuals, and relate these measures to participants' glycaemic control.Centre point thickness (CPT) and total macular volume (TMV) were measured using SS-OCT (DRI OCT Triton™, Topcon, Tokyo, Japan). Participants' glycosylated haemoglobin (HbADiabetic individuals had significantly higher CPT (t(37) = 3.859, p 0.0005) than non-diabetic individuals. In the diabetic group, multiple linear regression analysis revealed a conspicuous relationship between CPT and HbASS-OCT is the only way to measure macular thickness in vivo. Diabetic individuals en bloc had higher CPT compared with non-diabetic individuals. Moreover, in the diabetic group, HbA

Aims Diabetes mellitus affects about 6% of the world’s population, and the chronic complications of the disease may result in macro- and micro-vascular changes. The purpose of the current study was to shed light on visual cortical oxygenation in diabetic individuals. We then aimed to compare the haemodynamic response (HDR) to visual stimulation with glycaemic control, given the likelihood of diabetic individuals suffering from such macro- and micro-vascular insult. Methodology Thirty participants took part in this explorative study, fifteen of whom had diabetes and fifteen of whom were non-diabetic controls. The HDR, measured as concentrations of oxyhaemoglobin [HbO] and deoxyhaemoglobin [HbR], to visual stimulation was recorded over the primary visual cortex (V1) using a dual-channel oximeter. The stimulus comprised a pattern-reversal checkerboard presented in a block design. Participants’ mean glycated haemoglobin (HbA1c) level (± SD) was 7.2 ± 0.6% in the diabetic group and 5.5 ± 0.4% in the non-diabetic group. Raw haemodynamic data were normalised to baseline, and the last 15 s of data from each ‘stimulus on’ and ‘stimulus off’ condition were averaged over seven duty cycles for each participant. Results There were statistically significant differences in ∆[HbO] and ∆[HbR] to visual stimulation between diabetic and non-diabetic groups (p

Constraint aggregation makes it feasible to solve large-scale stress-constrained mass minimization problems efficiently using gradient-based optimization where the gradients are computed using adjoint methods. However, it is not always clear which constraint aggregation method is more effective, and which values to use for the aggregation parameters. In this work, the accuracy and efficiency of several aggregation methods are compared for an aircraft wing design problem. The effect of the type of aggregation function, the number of constraints, and the value of the aggregation parameter are studied. Recommendations are provided for selecting a constraint aggregation scheme that balances computational effort with the accuracy of the computed optimal design. Using the recommended aggregation method and associated parameters, a mass of within 0.5 % of the true optimal design was obtained.

In this paper, we present a full-space barrier method designed for stress-constrained mass minimization problems with discrete material options. The advantages of the full-space barrier method are twofold. First, in the full-space the stress constraints are provably concave, which facilitates the construction of convex subproblems within the optimization algorithm. Second, by using the full-space, it is no longer necessary to employ stress constraint aggregation techniques to reduce adjoint-gradient evaluation costs. The proposed optimization algorithm uses a Newton method where an approximate linearization of the KKT conditions is solved inexactly at each iteration using a preconditioned Krylov subspace method. Sparse constraints that arise in the discrete material parametrization are treated using a null-space method. Results of the proposed algorithm are demonstrated on a series of three topology and multimaterial optimization problems with selection between isotropic and orthotropic materials, as well as discrete ply-angle selection.

Constraint-aggregation methods are used in engineering optimization problems to approximately impose a bound on a quantity of interest in a differentiable manner. In this paper, we present strategies to adaptively solve aggregation-constrained problems. These adaptive techniques achieve a tighter bound approximation while also reducing the computational cost of optimization. We focus on two aggregation techniques: Kreisselmeier-Steinhauser (KS) aggregation, and induced exponential aggregation. We demonstrate that the proposed adaptive technique achieves significant computational savings compared to fixed-aggregation methods for a series of stress-constrained mass-minimization problems.

Many constraints in design-optimization problems take the form of bounds on a physical quantity over a domain. These infinite-dimensional constraints are often addressed through aggregation methods that approximate the bound in a differentiable manner. However, the most common constraint-aggregation methods exhibit mesh dependence; as the mesh spacing decreases, the aggregation function diverges. In addition, there are no established methods to assess the impact of constraint aggregation on the optimized design. To address these deficiencies, we propose a new class of constraint-aggregation method that we call induced aggregates. We examine the properties of these aggregation methods, describe their numerical implementation, and test their numerical accuracy on a pressure-loaded circular cylinder test case. Furthermore, we propose a post-optimality estimation technique to assess the impact of the constraint-aggregation method on the design. We use this method to examine the optimized mass obtained from two stress-constrained mass minimization problems: a variable-thickness sheet problem and a wingbox design problem.

Structural engineers are often constrained by cost or manufacturing considerations to select member thicknesses from a discrete set of values. Conventional, gradient-free techniques to solve these discrete problems cannot handle large problem sizes, while discrete material optimization (DMO) techniques may encounter difficulties, especially for bending-dominated problems. To resolve these issues, we propose an efficient gradient-based technique to obtain engineering solutions to the discrete thickness selection problem. The proposed technique uses a series of constraints to enforce an effective stiffness-to-mass and strength-to-mass penalty on intermediate designs. In conjunction with these constraints, we apply an exact penalty function which drives the solution towards a discrete design. We utilize a continuation approach to obtain approximate solutions to the discrete thickness selection problem by solving a sequence of relaxed continuous problems with increasing penalization. We also show how this approach can be applied to combined discrete thickness selection and topology optimization design problems. To demonstrate the effectiveness of the proposed technique, we present both compliance and stress-constrained results for in-plane and bending-dominated problems.

Structural optimization using gradient-based methods is a powerful design technique that is well suited for the design of high-performance structures. However, the ever-increasing complexity of finite-element models and design formulations results in a bottleneck in the computation of the gradients required for the design optimization. Furthermore, in light of current high-performance computing trends, any methods intended to address this bottleneck must efficiently utilize parallel computing resources. Therefore, there is a need for solution and gradient evaluation methods that scale well with the number of design variables, constraints, and processors. We address this need by developing an integrated parallel finite-element analysis tool for gradient-based design optimization that is designed to use specialized parallel solution methods to solve large-scale high-fidelity structural optimization problems with thousands of design variables, millions of state variables, and hundreds of load cases. We describe the most relevant details of the parallel algorithms used within the tool. We present consistent constraint formulations and aggregation techniques for both material failure and buckling constraints. To demonstrate both the solution and functional accuracy, we compare our results to an exact solution of a pressure-loaded cylinder made with either isotropic or orthotropic material. To demonstrate the parallel solution and gradient evaluation performance, we perform a structural analysis and gradient evaluation for a large transport aircraft wing with over 5.44 million unknowns. The results show near-ideal scalability of the structural solution and gradient computation with the number of design variables, constraints, and processors, which makes this framework well suited for large-scale high-fidelity structural design optimization.

Preliminary aircraft design studies use structural weight models that are calibrated with data from existing aircraft. Computing weights with these models is a fast procedure that provides reliable weight estimates when the candidate designs lie within the domain of the data used for calibration. However, this limitation is too restrictive when we wish to assess the relative benefits of new structural technologies and new aircraft configurations early in the design process. To address this limitation, we present a computationally efficient aerostructural design framework for initial aircraft design studies that uses a full finite-element model of key structural components to better assess the potential benefits of new technologies. We use a three-dimensional panel method to predict the aerodynamic forces and couple the lifting surface deflections to compute the deformed aerodynamic flying shape. To be used early in the design cycle, the aerostructural computations must be fast, robust, and allow for significant design flexibility. To address these requirements, we develop a geometry parametrization technique that enables large geometric modifications, we implement a parallel Newton---Krylov approach that is robust and computationally efficient to solve the aeroelastic system, and we develop an adjoint-based derivative evaluation method to compute the derivatives of functions of interest for design optimization. To demonstrate the capabilities of the framework, we present a design optimization of a large transport aircraft wing that includes a detailed structural design parametrization. The results demonstrate that the proposed framework can be used to make detailed structural design decisions to meet overall aircraft mission requirements.

Aeroelastic systems achieve the best performance when the aerodynamic shape and structural sizing are optimized concurrently, but such an optimization is challenging when high-fidelity aerodynamic and structural models are required. This paper addresses this challenge through several significant improvements. Fully coupled Newton–Krylov methods are presented for the solution of aerostructural systems and for the corresponding adjoint systems. The coupled adjoint method presented can compute gradients with respect to thousands of multidisciplinary design variables accurately and efficiently. This is enabled by several improvements in the computation of the multidisciplinary terms in the coupled adjoint. The parallel scalability of the methods is demonstrated for a full aircraft configuration using an Euler computational fluid dynamics model with more than 8×106 state variables and a detailed structural finite element model of the wing with more than 1×106 degrees of freedom. The coupled Newton–Krylov metho...

This paper presents a novel multidisciplinary framework for performing shape and topology optimization of a flexible wing structure. The topology optimization is integrated into a multidisciplinary algorithm in which both the aerodynamic shape and the structural topology are optimized concurrently using gradient-based optimization. The optimization results were compared with the results of a sequential procedure in which the aerodynamic shape was optimized separately and then used as a fixed design feature in a subsequent structural optimization. The results show that the concurrent approach offers a significant advantage, as this design achieved 42% less drag than the sequentially optimized wing.

Advancements in multimaterial additive manufacturing have the potential to enable the creation of topology optimized structures with both shape and material tailoring. However, multimaterial topology optimization methods that use Discrete Material Optimization (DMO) face three technical challenges for large-scale high-resolution problems: 1) the large-scale design space, since selection variables must be added for each additional candidate material; 2) the treatment of numerous sparse partition of unity constraints required in some DMO parametrizations; and 3) the multimaterial design space that has more local minima than an equivalent single material design space. This paper addresses these issues by presenting a parallel, scalable analysis and design optimization framework for multimaterial topology optimization that optionally uses local mesh refinement using semi-structured octree meshes. The advantages of this framework are demonstrated by showcasing its solution and design scalability and by efficiently solving large 3D multimaterial compliance-minimization problems with both isotropic and orthotropic material options on meshes with up to 329 million elements. For the largest case, the adaptive strategy is shown to achieve a compliance objective within 1.86% with roughly 1/4 the mesh size.

In this paper we present a novel laminate parametrization technique for layered composite structures that can handle problems in which the ply angles are limited to a discrete set. In the proposed technique, the classical laminate stiffnesses are expressed as a linear combination of the discrete options and design-variable weights. An exact $\ell _{1}$ penalty function is employed to drive the solution toward discrete 0---1 designs. The proposed technique can be used as either an alternative or an enhancement to SIMP-type methods such as discrete material optimization (DMO). Unlike mixed-integer approaches, our laminate parametrization technique is well suited for gradient-based design optimization. The proposed laminate parametrization is demonstrated on the compliance design of laminated plates and the buckling design of a laminated stiffened panel. The results demonstrate that the approach is an effective alternative to DMO methods.

Next-generation additive manufacturing technologies will enable novel, low-weight, highperformance aircraft structures. Topology optimization techniques can be used to obtain unconventional internal aircraft wing structures that can be manufactured using additive methods which depart significantly from conventional rib-spar wing constructions. However, there are significant issues that must be overcome when applying traditional topology optimization techniques to the design of aerospace structures. These challenges include efficiently solving large-scale design problems, and applying buckling criteria within a topology optimization design formulation. In this paper, we seek to address these issues by applying a scalable topology optimization method to the undeformed Common Research Model (uCRM) wing with buckling constraints applied to the skins of the wingbox. The proposed approach uses a multigrid-preconditioned Krylov method to solve the large-scale finite element analysis problem, coupled with a parallel interior-point optimizer to solve the largescale constrained design optimization problem. This proposed method is applied to two different optimization problems: mass-constrained compliance minimization, and mass-constrained bucklingload maximization. In addition, we apply a segment-wise topology optimization design strategy to the uCRM wingbox.