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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Evaluation of Topology Optimization to Achieve Energy Savings at the Urban District Level: Preprint

Advanced district thermal energy systems have the potential to achieve significant energy savings and facilitate the integration of renewable thermal resources and waste heat, contributing to reductions in carbon emissions. Such systems, also known as fifth generation district heating and cooling (5GDHC) systems, circulate water at temperatures close to ambient, and leverage electrically-driven water-source heat pumps located at connected buildings to further temper the water. However, barriers exist to the adoption of 5GDHC systems, including the factorial growth in potential network configurations as a function of the number of considered buildings. Topology optimization, which seeks to answer the questions, “Which is the best subset of buildings, if any, to connect to a district thermal energy system, and by what network should they be connected, to minimize life cycle cost?” can accelerate the adoption of 5GDHC systems. This study is part of an effort to develop a topology optimization framework for district thermal energy systems. In this study, a heuristic for one aspect of the topology optimization problem---the use of the minimal spanning tree network to connect a given set of buildings at the least life cycle cost---is validated.

28 EE - Advanced Manufacturing Office (EE-5A)↗
DOE OSTI2021

Structural stability and artificial buckling modes in topology optimization

Abstract This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.

Dalklint, Anna (ORCID:0000000346195205)↗
NASA NTRS2014

Preliminary Structural Design Using Topology Optimization with a Comparison of Results from Gradient and Genetic Algorithm Methods

In this paper, genetic algorithm based and gradient-based topology optimization is presented in application to a real hardware design problem. Preliminary design of a planetary lander mockup structure is accomplished using these methods that prove to provide major weight savings by addressing the structural efficiency during the design cycle. This paper presents two alternative formulations of the topology optimization problem. The first is the widely-used gradient-based implementation using commercially available algorithms. The second is formulated using genetic algorithms and internally developed capabilities. These two approaches are applied to a practical design problem for hardware that has been built, tested and proven to be functional. Both formulations converged on similar solutions and therefore were proven to be equally valid implementations of the process. This paper discusses both of these formulations at a high level.

Burt, Adam O.↗
NASA NTRSDate not supplied

Voxel Based Three-Dimensional Topology Optimization of Heat Exchanger Fins

Increasing interest in novel aircraft propulsion systems and potential for unwanted heat generation, or capture and reuse of waste heat, may require increasingly lightweight and high performing heat exchangers. Advances in manufacturing technologies have shown potential to create complex designs, but design tools need more flexibility. This study utilizes genetic algorithm-driven topology optimization to develop high performance heat exchanger fins for critical applications such as aerospace. The solid domain is generated using voxel representation where a voxel value of 1 indicates the solid domain and a voxel value of 0 refers to the fluid domain. The use of voxel representation somewhat matches the digitization of a model that is required to fabricate using additive manufacturing, and also allows for a highly unconstrained geometry. To test the topology optimization approach, a three-dimensional(3D)baseline offset strip fin geometry in steady laminar flow(Reynolds number = 215)with conjugate heat transfer(simultaneous solution of solid and fluid temperature fields)is optimized. New designs are generated using the genetic algorithm (GA) and sent to evaluation by the CFD software OpenFOAM; then the GA sorts and selects the reproduction pool for the following generation. This process is repeated for 60 generations. The study also investigates the effect off in material on the performance of the GA and the resulting designs. The results show that the optimal designs have overall performance improvement of 18% relative to the baseline. Additionally, a fin constructed of a lower conductivity material (such as an Inconel super alloy that might be necessary for waste heat recovery applications)results in lower overall performance improvement (11%)and optimal designs with higher pressure drop relative to their baseline, and relative to optimal designs produced using higher conductivity materials.

3D Optimization↗
DOE OSTI2023

Influence of topology optimization parameters on the mechanical response of an additively manufactured test structure

Topology Optimization (TO) determines a material distribution within a domain under given conditions and design constraints, and generally generates complex geometries as a result. Complementary to TO, Additive Manufacturing (AM) offers the ability to fabricate complex geometries which may be difficult to manufacture using traditional techniques such as milling. AM has been used in multiple industries including the medical devices area. Hence, TO may be used to create patient-matched devices where the mechanical response is catered to a particular patient. Furthermore, during a medical device regulatory 510(k) pathway, demonstrating that worst-cases are known and tested is critical to the review process. Using TO and AM to predict worst-case designs for subsequent performance testing may be challenging and does not appear to have been thoroughly explored. Investigating the effects of TO input parameters when AM is employed may be the first step in determining the feasibility of predicting these worst-cases.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Multi-physics Topology OPtimization and Additive Manufacturing for High-temperature Heat Exchangers

This research significantly advances the understanding of high-temperature heat exchanger design through an integrated approach that combines topology optimization (TO), triply periodic minimal surface (TPMS) structures, additive manufacturing (AM) and thermohydraulic testing. Each of these components contributes uniquely to a unified, high-performance design, fabrication and testing workflow. Topology optimization serves as the foundation of the design methodology by providing a systematic way to determine the most effective material layout for separating hot and cold fluids while maximizing thermal performance. The researchers introduced a novel three-material optimization framework using two density fields to represent hot fluid, cold fluid, and solid domains. This approach enables automated discovery of optimal shapes and flow paths that cannot be intuitively designed, especially under constraints imposed by manufacturing technologies. Furthermore, constraints such as minimal wall thickness and overhang angles were embedded into the optimization process, ensuring that resulting designs are not only thermally efficient but also manufacturable using modern additive techniques. In parallel, the study delves into the use of Gyroid-based TPMS geometries for constructing the core of the heat exchanger. TPMS structures are known for their high surface area, excellent fluid mixing capabilities, and minimal pressure drop characteristics. The researchers applied a data-driven modeling framework using Heteroscedastic Sparse Gaussian Process Regression (HSGPR) combined with genetic algorithms. This allowed for the rapid evaluation and optimization of key geometric parameters such as frequency, iso-value, and phase shift. The result was a set of Gyroid structures tailored for high heat transfer and low flow resistance, demonstrating clear improvements over conventional straight-channel designs. After the designing process, additive manufacturing played a critical role by turning these highly complex, optimized geometries into physical components. Utilizing Laser Powder Bed Fusion (LPBF) with Haynes 282, the study demonstrated the feasibility of fabricating these heat exchangers at high precision. Post-processing methods, including dilation-erosion operations, were applied to ensure local features adhered to self-supporting constraints. The fabricated structures were then subjected to thermohydraulic testing under conditions representative of supercritical CO 2 Brayton cycles, validating the predicted performance and confirming the viability of the full design-to-fabrication pipeline. Finally, thermohydraulic testing across the above studies served as a crucial experimental validation of advanced heat exchanger. Under consistent high-temperature and high-pressure conditions using supercritical CO 2 , the testing demonstrated that both TO and Gyroid-based TPMS designs significantly outperformed conventional straight-channel HXs. The TO design achieved a 115% increase in UA and NTU and a 27.6% boost in gravimetric power density, while the data-driven optimized Gyroid design delivered a 166% increase in UA and NTU and improved effectiveness from 68.7% to 86.1%. These results validate the simulation models, confirm the manufacturability of complex geometries under AM constraints, and provide key insights into design-performance trade-offs, thereby advancing the development of high-efficiency, compact heat exchangers for extreme environments.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

42 ENGINEERING↗
DOE OSTI2022

Topology optimization for the design of porous electrodes

Porous electrodes are an integral part of many electrochemical devices since they have high porosity to maximize electrochemical transport and high surface area to maximize activity. Traditional porous electrode materials are typically homogeneous, stochastic collections of small-scale particles and offer few opportunities to engineer higher performance. Fortunately, recent breakthroughs in advanced and additive manufacturing are yielding new methods to structure and pattern porous electrodes across length scales. These architected electrodes are emerging as a promising new technology to continue to drive improvement; however, it is still unclear which structures to employ and few tools are available to guide their design. Here we address this gap by applying topology optimization to the design of porous electrodes. We demonstrate our framework on two applications: a porous electrode driving a steady Faradaic reaction and a transiently operated electrode in a supercapacitor. We present computationally designed electrodes that minimize energy losses in a half-cell. For low-conductivity materials, the optimization algorithm creates electrode designs with a hierarchy of length scales. Further, the designed electrodes are found to outperform undesigned, homogeneous electrodes. Finally, we present three-dimensional porous electrode designs. We thus establish a topology optimization framework for designing porous electrodes.

25 ENERGY STORAGE↗
DOE OSTI2018

Density based topology optimization of turbulent flow heat transfer systems

The focus of this article is on topology optimization of heat sinks with turbulent forced convection. The goal is to demonstrate the extendibility, and the scalability of a previously developed fluid solver to coupled multi-physics and large 3D problems. The gradients of the objective and the constraints are obtained with the help of automatic differentiation applied on the discrete system without any simplifying assumptions. Thus, as demonstrated in earlier works of the authors, the sensitivities are exact to machine precision. The framework is applied to the optimization of 2D and 3D problems. Comparison between the simplified 2D setup and the full 3D optimized results is provided. A comparative study is also provided between designs optimized for laminar and turbulent flows. Overall, the comparisons highlight the importance and the benefits of full 3D optimization and including turbulence modeling in the optimization process, while also demonstrating extension of the methodology to include coupling of heat transfer with turbulent flows.

42 ENGINEERING↗
DOE OSTI2017

Combined shape and topology optimization for minimization of maximal von Mises stress

Here, this work shows that a combined shape and topology optimization method can produce optimal 2D designs with minimal stress subject to a volume constraint. The method represents the surface explicitly and discretizes the domain into a simplicial complex which adapts both structural shape and topology. By performing repeated topology and shape optimizations and adaptive mesh updates, we can minimize the maximum von Mises stress using the p-norm stress measure with p-values as high as 30, provided that the stress is calculated with sufficient accuracy.

42 ENGINEERING↗
DOE OSTI2023

Topology optimization of compliant mechanisms under transient thermal conditions

This work considers multi-material topology optimization of compliant mechanisms under transient thermal and quasi-static mechanical conditions wherein thermally actuated devices are optimized for different operating conditions. The materials are modeled using finite strain thermo-hyperelasticity and a two way coupling between the energy balance and equilibrium equations is investigated. The design updates are generated from the gradient-based method of moving asymptotes optimizer and the sensitivities are computed using the time dependent adjoint sensitivity analysis. Results show the impact of designing for short versus long actuation times.

42 ENGINEERING↗
DOE OSTI2025

Advanced Transmission Technologies – GETs and HPCs Session 2: Advanced Power Flow Control and Transmission Topology Optimization

The INL TADA GETs Cohort Session 2, held on November 7, 2025, conducted in collaboration with ScottMadden, focused on two core Advanced Transmission Technologies (ATTs): Advanced Power Flow Control (APFC) and Transmission Topology Optimization (TTO). These technologies are pivotal in enhancing grid flexibility, reliability, and cybersecurity resilience. APFC, particularly through modular FACTS devices like Modular Static Synchronous Series Compensators (M-SSSCs), enables dynamic voltage injection to reroute power flows. The session highlighted the deployment benefits of APFC, such as rapid installation, minimal civil works, and re-deployability. Regulatory drivers like FERC Order 2023 mandate the inclusion of Grid-Enhancing Technologies (GETs) in interconnection studies. Case studies from Central Hudson, CAISO, and National Grid (UK) demonstrated APFC’s effectiveness in congestion relief and cost savings. The session also addressed cybersecurity concerns, including firmware vulnerabilities, SCADA integration risks, and supply chain dependencies. Participants engaged in interactive exercises to rank cybersecurity and supply chain risks, emphasizing the need for robust digital assurance strategies. TTO involves software-based reconfiguration of transmission networks to optimize power flow without new infrastructure. The session showcased its operational value, with examples from SPP, PJM, and MISO showing significant congestion cost reductions. Cybersecurity vulnerabilities were discussed, particularly in API security and software supply chains, referencing incidents like SolarWinds and attacks on Danish utilities. Digital assurance exercises explored worst-case scenarios, attack paths, and mitigation responsibilities between vendors and utilities. Reliability challenges such as algorithm stability, vendor dependency, and operator trust were also examined. Cross-cutting themes emphasized the importance of digital assurance tools, including Software Bills of Materials (SBOMs) and hardware-in-loop testing. Human performance, training, and operational confidence were identified as critical enablers of technology adoption. The session concluded with a preview of Session 3, which will focus on High Performance Conductors (HPCs) and risk-based cybersecurity tools. Session 2 of 3.

24 - POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach.

42 ENGINEERING↗
DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Scaled Aeroelastic Wind Tunnel Model Design with Topology Optimization

The goal of this work is to use numerical aeroelastic topology optimization to design flutter models to be tested in the Transonic Dynamics Tunnel, as part of an envisioned validation experiment for transonic flutter. The topological design develops the structural details of a variable-thickness aluminum plate located at the camber line of a scaled transport aircraft model, in order to satisfy the various conflicting design requirements, including a prescribed flutter boundary, flutter frequency, and static stress levels. Four designs are demonstrated here, where it is shown that the simultaneous design of a cylindrical tip store can help ease the conflict between low stiffness (to allow a wing to flutter in the tunnel envelope) and high strength (to ensure safe structural response). The tip store complicates the geometrical features of the wing, however, and is generally undesirable from the vantage point of a validation experiment.

Aeroelasticity↗
DOE OSTI2020

Topology optimization of multiple deformable bodies in contact with large deformations

Previous works in topology optimization of structures with contact boundary conditions have concentrated on the two-dimensional rigid obstacle problem. This is because the contact analysis of multiple three-dimensional deformable bodies with meshes that are non-matching across the contact interface requires computationally complex contact algorithms beyond the scope of previous optimization investigations. Here, our research is devoted to addressing topology design problems with multiple deformable three-dimensional components in contact using state-of-the-art contact algorithms.

42 ENGINEERING↗
DOE OSTI2019

Multi-scale topology optimization of multi-material structures with controllable geometric complexity — Applications to heat transfer problems

This study presents a topology optimization method to design assemblies of periodic cellular materials with controllable geometric complexity. The framework is based on a novel multi-scale and multi-material design model in which the structure, the layout of the material subdomains, and their micro-structures are optimized concurrently. To allow a tight control over its geometrical complexity, the layout at the macro-scale is described by level-set fields, parameterized by geometric primitives. The micro-scale geometry is represented through a density approach. A nonlinear programming algorithm drives the optimization process using design sensitivities computed by the discrete adjoint method. The proposed design framework is studied with heat transfer problems. Practical design problems, such as a heat sink and a thermal storage unit with phase change are discussed. The macro-scale analysis model relies on a generalized transient diffusion equation. At the micro-scale, homogenization is used to compute equivalent material properties. The numerical examples in this study show that the optimized multi-scale multi-material layouts outperform the corresponding mono-scale structures while maintaining geometric simplicity at the macro-scale level.

42 ENGINEERING↗
NASA NTRS2017

Aeroelastic Wingbox Stiffener Topology Optimization

This work considers an aeroelastic wingbox model seeded with run-out blade stiffeners along the skins. Topology optimization is conducted within the shell webs of the stiffeners, in order to add cutouts and holes for mass reduction. This optimization is done with a global-local approach in order to moderate the computational cost: aeroelastic loads are computed at the wing-level, but the topology and sizing optimization is conducted at the panel-level. Each panel is optimized separately under stress, buckling, and adjacency constraints, and periodically reassembled to update the trimmed aeroelastic loads. The resulting topology is baselined against a design with standard full-depth solid stiffener blades, and found to weigh 7.43% less.

Stanford, Bret K.↗