Truss topology optimization with simultaneous analysis and design

Sankaranarayanan, S.; Haftka, Raphael T.; Kapania, Rakesh K.

doi:10.2514/3.12000

Cited by 25 publications

(6 citation statements)

References 7 publications

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“…Although he proposed this in the context of a single discipline, demonstrating it in a structural optimization problem, the approach can be generalized for MDO problems. SAND combines the solution of the governing equations with the optimality conditions, and has been shown to be more efficient than the conventional approach not only for structural optimization [75,76], but for aerodynamic optimization [77,78] and MDO problems as well [20]. In a benchmarking study of various monolithic and distributed MDO architectures, Tedford and Martins [20] found that monolithic architectures vastly outperform distributed ones in terms of convergence time.…”

Section: Mdo Methodologiesmentioning

confidence: 99%

Enabling Large-scale Multidisciplinary Design Optimization through Adjoint Sensitivity Analysis

Martins

Kennedy

2019

AIAA Scitech 2019 Forum

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This paper is written to honor Rafael T. Haftka's seminal contributions to the field of multidisciplinary design optimization. We focus on those contributions that had a direct impact on 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 gradientbased optimizers enables the optimization with respect to large numbers of design variables, even when using costly high-fidelity models.

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Section: Mdo Methodologiesmentioning

confidence: 99%

Enabling Large-scale Multidisciplinary Design Optimization through Adjoint Sensitivity Analysis

Martins

Kennedy

2019

AIAA Scitech 2019 Forum

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“…By including the deflection constraints and statically indeterminate solutions, the discussed truss problem becomes a non-linear one. Numerous topology optimization problems of trusses, solved by the non-linear programming (NLP) approach, were therefore subsequently presented [6][7][8][9][10][11]. Using continuous optimization methods, i.e., the LP or the NLP, the truss topology optimizations were performed by either allowing zero values or by defining a small lower bound of the cross-section areas of bars.…”

Section: Topology Optimizationmentioning

confidence: 99%

“…An extra binary variable y is associated with each truss element, indicating whether this particular element is included in (y = 1) or excluded from (y = 0) the current topology. By means of discrete optimization, numerous authors optimize the truss topology applying the genetic algorithm (GA) [12][13][14][15][16], the penalty function method [10] and the simulated annealing [17][18][19].…”

Section: Topology Optimizationmentioning

confidence: 99%

The MINLP Approach to Topology, Shape and Discrete Sizing Optimization of Trusses

Šilih

Kravanja

2022

Applied Sciences

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The paper presents the Mixed-Integer Non-linear Programming (MINLP) approach to the synthesis of trusses. The solution of continuous/discrete non-convex and non-linear optimization problems is discussed with respect to the simultaneous topology, shape and discrete sizing optimization of trusses. A truss MINLP superstructure of different topology and design alternatives has been generated, and a special MINLP model formulation for trusses has been developed. In the optimization model, a mass objective function of the structure has been defined and subjected to design, load and dimensioning constraints. The MINLP problems are solved using the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm. Multi-level MINLP strategies are introduced to accelerate the convergence of the algorithm. The Modified Two-Phase and the Sequential Two-Phase MINLP strategies are proposed in order to solve highly combinatorial topology, shape and discrete sizing optimization problems. The importance of local buckling constraints on topology optimization is also discussed. Some simple numerical examples are shown at the end of the paper to demonstrate the suitability and efficiency of the proposed method.

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“…The second disadvantage was addressed through various types of topology optimization, which have algorithmic differences (Bendsøe and Kikuchi 1988;Bendsøe 1989;Zhou and Rozvany 1991;Sankaranarayanan et al 1994;Diaz and Sigmund 1995;Sigmund 1997;Bendsøe and Sigmund 1999;Wang et al 2003;Allaire et al 2004;Sigmund 2007) in the mathematical process. However, the improved algorithms, with iterative finite element method (FEM) calculations, still had common flaws that required significant computational effort to determine the optimum structures.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization with advanced CNN using mapped physics-based data

Seo

Kapania

2023

Struct Multidisc Optim

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This research proposes a new framework to develop an accurate machine-learning-based surrogate model to predict the optimum topological structures using an advanced encoder–decoder network, Unet, and Unet++. The trained surrogate model predicts the optimum structural layout as output by inputting the results from the initial static analysis without any iterative optimization calculations. Input and output data are generated using the commercial finite element analysis package, Abaqus/Standard, and an optimization package, Abaqus/Tosca. We applied the data augmentation technique to increase the amount of data without actual calculations. Primarily, this research focused on overcoming the weaknesses of previous studies that the trained network is only applicable to limited geometry variations and requires an organized grid rectangular mesh. Therefore, this study suggests a mapping process to convert the analysis data on any type of mesh element to a tensor form, which enables training and employing the network. Also, to increase the prediction accuracy, we trained the network with the labeled optimum material data using a binary segmented output, representing the structure and void regions in the domain. Finally, the trained networks are evaluated using the intersection over union (IoU) scores representing the classification accuracy. The best-performing network provides highly accurate results, and this model provided the IoU scores for average, maximum, and standard deviation as 90.0%, 99.8%, and 7.1%, respectively. Also, we apply it to solve local-global structural optimization problems, and the overall calculation time is reduced by 98%.

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Truss topology optimization with simultaneous analysis and design

Cited by 25 publications

References 7 publications

Enabling Large-scale Multidisciplinary Design Optimization through Adjoint Sensitivity Analysis

Enabling Large-scale Multidisciplinary Design Optimization through Adjoint Sensitivity Analysis

The MINLP Approach to Topology, Shape and Discrete Sizing Optimization of Trusses

Topology optimization with advanced CNN using mapped physics-based data

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