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At least 1,387 records · Page 77

Advancing GRCop-based Bimetallic Additive Manufacturing to Optimize Component Design and Applications for Liquid Rocket Engines

Additive manufacturing (AM) is advancing many applications of component design for liquid rocket engines. The ability to rapidly design and manufacture components has provided significant opportunities for development and flight programs across the propulsion industry. AM has demonstrated significant advantages that include cost and schedule savings in addition to performance improvements through new design opportunities. While these performance advantages can be in the characteristics of complex design features, they can also be in the form of new materials. AM has been demonstrated in these various component applications using a variety of metal alloys, many of which are traditional alloys for extreme environments. Additional developments were completed using AM to provide new alloys and maturing these material uses for high performance applications. Almost all of the prior developments across component applications have focused on single-alloys in these AM processes. NASA and industry partners have focused in recent years to advance processing to create bimetallic and multicomponent AM processes and materials. The role of multi-alloy AM offers advantages since it can further optimize weight, optimize reliability and performance by increasing the strength to weight ratio of a component, and can optimize materials for various engineering requirements. This is particularly important in liquid rocket engine combustion devices that must reject heat in high heat flux environments yet maintain adequate structural margins under high operational pressure. NASA has been exploring several AM processes, materials, and applications for combustion devices, specifically combustion chambers, injectors, nozzles, and ignition systems. These components require fine geometric features for internal flow or cooling functionality. They experience high thermal gradients across thin-walls and must survive high pressures and temperatures from propellants and the combustion process. A copper-based alloy is normally used to provide high thermal conductivity, but at the detriment of increased weight if used as a single alloy in an AM chamber. Various AM processes were demonstrated on these components using a copper-based alloy/superalloy bimetallic solution. The AM processes being explored individually and in combination for bimetallic applications include Laser Powder Bed Fusion (L-PBF), Laser Powder Directed Energy Deposition (LP-DED), and cold spray. The combination of bimetallic material combinations explored in this research include copper-based material primarily and superalloys, Inconel 625 or NASA HR-1. The various aspects of the additive manufacturing processes and challenges, materials characterization, and the testing of bimetallic components in a relevant environment will be discussed.

Additive Manufacturing↗

Advancing GRCop-based Bimetallic Additive Manufacturing to Optimize Component Design and Applications for Liquid Rocket Engines

Additive manufacturing (AM) is advancing many applications of component design for liquid rocket engines. The ability to rapidly design and manufacture components has provided significant opportunities for development and flight programs across the propulsion industry. AM has demonstrated significant advantages that include cost and schedule savings in addition to performance improvements through new design opportunities. While these performance advantages can be in the characteristics of complex design features, they can also be in the form of new materials. AM has been demonstrated in these various component applications using a variety of metal alloys, many of which are traditional alloys for extreme environments. Additional developments were completed using AM to provide new alloys and maturing these material uses for high performance applications. Almost all of the prior developments across component applications have focused on single-alloys in these AM processes. NASA and industry partners have focused in recent years to advance processing to create bimetallic and multicomponent AM processes and materials. The role of multi-alloy AM offers advantages since it can further optimize weight, optimize reliability and performance by increasing the strength to weight ratio of a component, and can optimize materials for various engineering requirements. This is particularly important in liquid rocket engine combustion devices that must reject heat in high heat flux environments yet maintain adequate structural margins under high operational pressure. NASA has been exploring several AM processes, materials, and applications for combustion devices, specifically combustion chambers, injectors, nozzles, and ignition systems. These components require fine geometric features for internal flow or cooling functionality. They experience high thermal gradients across thin-walls and must survive high pressures and temperatures from propellants and the combustion process. A copper-based alloy is normally used to provide high thermal conductivity, but at the detriment of increased weight if used as a single alloy in an AM chamber. Various AM processes were demonstrated on these components using a copper-based alloy/superalloy bimetallic solution. The AM processes being explored individually and in combination for bimetallic applications include Laser Powder Bed Fusion (L-PBF), Laser Powder Directed Energy Deposition (LP-DED), and cold spray. The combination of bimetallic material combinations explored in this research include copper-based material primarily and superalloys, Inconel 625 or NASA HR-1. The various aspects of the additive manufacturing processes and challenges, materials characterization, and the testing of bimetallic components in a relevant environment will be discussed.

Additive Manufacturing↗

Comparative study of machine learning techniques for post-combustion carbon capture systems

Computational analysis of countercurrent flows in packed absorption columns, often used in solvent-based post-combustion carbon capture systems (CCSs), is challenging. Typically, computational fluid dynamics (CFD) approaches are used to simulate the interactions between a solvent, gas, and column's packing geometry while accounting for the thermodynamics, kinetics, heat, and mass transfer effects of the absorption process. These simulations can then be used explain a column's hydrodynamic characteristics and evaluate its CO 2 -capture efficiency. However, these approaches are computationally expensive, making it difficult to evaluate numerous designs and operating conditions to improve efficiency at industrial scales. In this work, we comprehensively explore the application of statistical ML methods, convolutional neural networks (CNNs), and graph neural networks (GNNs) to aid and accelerate the scale-up and design optimization of solvent-based post-combustion CCSs. We apply these methods to CFD datasets of countercurrent flows in absorption columns with structured packings characterized by several geometric parameters. We train models to use these parameters, inlet velocity conditions, and other model-specific representations of the column to estimate key determinants of CO 2 -capture efficiency without having to simulate additional CFD datasets. We also evaluate the impact of different input types on the accuracy and generalizability of each model. We discuss the strengths and limitations of each approach to further elucidate the role of CNNs, GNNs, and other machine learning approaches for CO 2 -capture property prediction and design optimization.

97 MATHEMATICS AND COMPUTING↗

Integrated analysis and applications

A select overview is provided of ongoing research focusing on the development and verification of integrated structural analysis and optimal design capabilities for advanced aerospace propulsion and power systems. Subjects discussed include the following: (1) Composites - analytical models (composite mechanics), integrated computational methods, and characterization of composite structural response and durability for resin-, metal-, and ceramic-matrix systems; (2) Advanced inelastic analysis - algorithm/numerical methods for more accurate and efficient analysis; (3) Constitutive modeling - theoretical formulation and characterization of thermoviscoplastic material behavior; (4) Computational simulation - engine structures from components to assembly, and up to an entire engine system subjected to simulated test-stand and mission load histories; (5) Probabilistic structural analysis - quantification of the effects of uncertainty in geometry, material, loads, and boundary conditions on structural response for true reliability assessment; and (6) Interdisciplinary optimization - incorporation of mathematical optimization and multidisciplinary analyses to provide streamlined, autonomous optimal design systems.

Hopkins, Dale A.↗

Device Architecture Simplification of Laser Pattering in High-Volume Crystalline Silicon Solar Cell Fabrication using Intensive Computation for Design and Optimization

Prices of Si based solar modules have been continuously declining in recent years. Goodrich is pointing out that a significant portion of these cost reductions have come about due to ‘economies of scale’ benefits, but there is a point of diminishing returns when trying to lower cost by simply expanding production capacity. Developing innovative high volume production technologies resulting in an increase of conversion efficiency without adding significant production cost will be necessary to continue the projected cost reductions. The Foundational Program to Advance Cell Efficiency (FPACE) is seeking to achieve this by closing the PV efficiency gap between theoretical achievable maximum conversion efficiency - 29% for c-Si - and the current typical production - 18.5% for a typical full area back contact c-Si Solar cell – while targeting a module cost of $0.50/Watt . The research conducted by SolarWorldUSA and it’s partners within the FPACE framework focused on the development of a Hybrid metal-wrap-through (MWT) and laser-ablated PERC solar cell design employing a extrusion metallization scheme to achieve >20% efficient devices. The project team was able to simulate, develop and demonstrate the technologies necessary to build p-type MWT PERC cells with extruded front contacts. Conversion efficiencies approaching 20% were demonstrated and a path for further efficiency improvements identified. A detailed cost of ownership calculation for such a device was based on a NREL cost model and is predicting a $/Watt cost below 85 cents on a 180 micron substrate.

14 SOLAR ENERGY↗

The use of optimization techniques to design controlled diffusion compressor blading

A method for automating compressor blade design using numerical optimization, and applied to the design of a controlled diffusion stator blade row is presented. A general purpose optimization procedure is employed, based on conjugate directions for locally unconstrained problems and on feasible directions for locally constrained problems. Coupled to the optimizer is an analysis package consisting of three analysis programs which calculate blade geometry, inviscid flow, and blade surface boundary layers. The optimizing concepts and selection of design objective and constraints are described. The procedure for automating the design of a two dimensional blade section is discussed, and design results are presented.

Sanger, N. L.↗

Improving LiNiO 2 cathode performance through particle design and optimization

We report to enable further development of Ni-rich LiNi x Mn y Co 1-x-y O 2 (NMC, x ≥ 0.9) cathodes for commercial applications, fundamental understanding of the synthesis–property–performance relationships in the LiNiO 2 (LNO) parent phase is essential. In the present study, we report synthesis approaches to produce well-formed, similar-sized single-crystal LiNiO 2 (SC-LNO) with different shapes and dominating surface facets, and reveal the dependence of cathode rate performance and cycling stability on particle morphology and surface. While octahedron-shaped SC-LNO with the (012) surface shows better rate capability and improved ability in utilizing the kinetically slow anodic process in the 3.5 V region, cubic-shaped SC-LNO with the (104) surface delivers superior cycling stability, especially upon cycling at a high upper cutoff voltage of 4.6 V. Improvement in cycling stability is correlated with reduced surface reconstruction and preferential LiF formation through the interaction with the electrolyte on the (104) surface. Our study not only demonstrates the importance of particle morphology and surface design, it also provides key insights into desirable material properties for developing future LNO-based cathode materials with better performance.

25 ENERGY STORAGE↗

Leveraging visible and near-infrared spectroelectrochemistry to calibrate a robust model for Vanadium(IV/V) in varying nitric acid and temperature levels

Spectroelectrochemistry and optimal design of experiments can be used to rapidly build accurate models for species quantification and enable a greater level of process awareness. Optical spectroscopy can provide vital elemental and molecular information, but several hurdles must be overcome before it can become a widely adopted analytical method for remote analysis in the nuclear field. Analytes with varying oxidation state, acid concentration, and fluctuating temperature must be efficiently accounted for to minimize time and resources in restrictive hot cell environments. The classic one-factor-at-a-time approach is not suitable for frequent calibration/maintenance operations in this setting. Therefore, a novel alternative was developed to characterize a system containing vanadium(IV/V) (0.01–0.1 M), nitric acid (0.1–4 M), and varying temperatures (20–45 °C). Here, spectroelectrochemistry methods were used to acquire a sample set selected by optimal design of experiments. This new approach allows for the accurate analysis of vanadium and HNO 3 concentration by leveraging UV–Vis–NIR absorption spectroscopy with robust and accurate chemometric models. The top model's root mean squared error of prediction percent values were 3.47%, 4.06%, 3.40%, and 10.9% for V(IV), V(V), HNO 3 , and temperature, respectively. These models, efficiently developed using the designed approach, exhibited strong predictive accuracy for vanadium and acid with varying oxidation states and temperature using only spectrophotometry, which advances current technology for real-world hot cell applications. Additionally, Nernstian analysis of the V(IV/V) standard potential was performed using traditional absorbance methods and multivariate curve resolution (MCR). The successful tests demonstrated that MCR Nernst tests may be valuable in highly convoluted spectral systems to better understand the redox processes' behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

adaptation models↗

A modeling study of ocean thermal energy conversion resource and potential environmental effects around Kailua-Kona, Hawaii

Ocean Thermal Energy Conversion (OTEC) offers a promising renewable energy solution through a heat exchange process using the temperature difference between warm surface seawater and cold deep seawater. Because accurate resource characterization is critical for the optimal design and implementation of OTEC systems, a high-resolution numerical model is employed to better characterize the OTEC resource at Kona, Hawaii. Our model provides detailed spatial and temporal variability of the thermal gradient, which is essential for assessing the viability and efficiency of OTEC systems. The model results reveal distinct patterns and dynamics not captured by existing observations or models (e.g., lower-resolution information). These findings highlight the importance of using high-resolution models for accurate predictions of thermal gradient variability, ultimately supporting more efficient and sustainable OTEC deployment. Additionally, the study investigates the impacts of mixed water discharge from OTEC plants that can cause shock to organisms living in the surface water and potentially destabilize the water column. Understanding these effects is vital for minimizing any potential negative environmental consequences and ensuring the long-term viability of OTEC operations. Further, our model improves OTEC resource characterization, which can lead to optimal design and deployment of OTEC systems. The analysis of OTEC water discharge impacts can accelerate the development of OTEC technologies, overcoming permitting/consenting challenges. These findings contribute to the broader adoption of high-resolution modeling in ocean energy resource characterization, particularly for OTEC applications.

30 DIRECT ENERGY CONVERSION↗

FOILPOLARS (Grassmannian Foil Shape Sweeps for Polar Generation) [SWR-26-095]

FOILPOLARS (Grassmannian Foil Shape Sweeps for Polar Generation): Multifidelity aerodynamic polar data generation for hydrofoil/tidal-turbine airfoil sections. Foilpolars ties together three pieces: *AeroSandbox supplies the baseline airfoil coordinates (UIUC database). *G2Aero parameterizes those shapes on a Grassmannian manifold (Karcher mean + PGA basis) and samples new perturbed shapes around that basis. *XFoil (panel method) and NeuralFoil (neural-network surrogate, shipped with AeroSandbox) each solve the resulting shapes for lift, drag, moment, and pressure at the swept angles of attack, Reynolds numbers, and n_crit values. Design optimization of foil shapes in a computationally efficient way requires polars data across many candidate shapes, not just a handful of baseline foils. However, high-fidelity CFD at that scale is too costly, and naive shape perturbation strays from realistic geometries. FOILPOLARS addresses this by loading baseline airfoils (via AeroSandbox) and mapping them onto a Grassmannian manifold (via G2Aero), computing a Karcher mean and principal geodesic analysis (PGA) basis. New shapes are sampled by perturbing PGA coefficients, keeping them close to the manifold of realistic foils. Each sampled shape is evaluated across a configurable sweep of angle of attack, Reynolds number, and critical amplification factor using two solvers: XFoil (panel method) and NeuralFoil (neural-network surrogate), producing a paired dataset of lift, drag, moment, pressure, convergence, and confidence, indexed alongside each shape's PGA coefficients and shared Grassmannian basis in a single xarray dataset. From this, FOILPOLARS produces convergence summaries and comparison plots per shape, Reynolds number, and n_crit. A command-line interface exposes each pipeline stage independently, supporting data-driven design, optimization, and machine-learning workflows for foils.

Sandhu, Rimple [National Laboratory of the Rockies↗

Low-noise heterodyne receiver for electron cyclotron emission imaging and microwave imaging reflectometry

The critical component enabling electron cyclotron emission imaging (ECEI) and microwave imaging reflectometry (MIR) to resolve 2D and 3D electron temperature and density perturbations is the heterodyne imaging array that collects and downconverts radiated emission and/or reflected signals (50–150 GHz) to an intermediate frequency (IF) band (e.g. 0.1–18 GHz) that can be transmitted by a shielded coaxial cable for further filtering and detection. New circuitry has been developed for this task, integrating gallium arsenide (GaAs) monolithic microwave integrated circuits (MMICs) mounted on a liquid crystal polymer (LCP) substrate. The improved topology significantly increases electromagnetic shielding from out-of-band interference, leads to 10× improvement in the signal-to-noise ratio, and dramatic cost savings through integration. The current design, optimized for reflectometry and edge radiometry on mid-sized tokamaks, has demonstrated >20 dB conversion gain in upper V-band (60-75 GHz). Implementation of the circuit in a multi-channel electron cyclotron emission imaging (ECEI) array will improve the diagnosis of edge-localized modes and fluctuations of the high-confinement, or H-mode, pedestal.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Predicted performance of InP solar cells in Cassegrainian and slats space concentrator arrays at 20 to 100 AM0, 80 to 100 C

Researchers have calculated the expected performance dependence of near-optimally designed shallow homojunction n+pp+InP solar cells on incident intensities up 200 AM0 and temperatures up to 100 C (373K). Both circular and rectangular cells have been considered, the former for use in a Cassegrainian concentrator array at 100 AM0, 80 to 100 C and the latter for use in a Slats type concentrator array at 20 AM0 80 to 100 C. Calculation of the temperature dependence of the performance parameters I sub sc, V sub oc, FF and eta was done by first verifying that the use of the measured temperature variation of I sub sc, of the best published value of the temperature dependence of the bandgap of InP, and of the temperature dependences of the lifetimes and mobilities of electrons and holes the same as in equivalently doped GaAs, gave calculated results that closely matched measured data on the temperature variation of I sub sc, V sub oc, and FF of four existing InP cells at 1 AM0. It was then assumed that the same temperature dependences of I sub sc, the bandgap and lifetimes and mobilities would hold in the near-optimally designed cells at the higher concentrations.

Goradia, Chandra↗

Atomic to Nanoscale Investigation of Functionalities of an Al2O3 Coating Layer on a Cathode for Enhanced Battery Performance

Surface coating has been identified as an effective approach for enhancing the capacity retention of layered structure cathode. However, the underlying operating mechanism of such a thin coating layer, in terms of surface chemical functionality and capacity retention, remains unclear. In this work, we use aberration-corrected scanning transmission electron microscopy and high-efficiency spectroscopy to probe the delicate functioning mechanism of an Al2O3 coating layer on a Li1.2Ni0.2Mn0.6O2 cathode. We discovered that in terms of surface chemical function, the Al2O3 coating suppresses the side reaction between the cathode and the electrolyte during battery cycling. At the same time, the Al2O3 coating layer also eliminates the chemical reduction of Mn from the cathode particle surface, therefore preventing the dissolution of the reduced Mn into the electrolyte. In terms of structural stability, we found that the Al2O3 coating layer can mitigate the layer to spinel phase transformation, which otherwise will be initiated from the particle surface and propagate toward the interior of the particle with the progression of battery cycling. The atomic to nanoscale effects of the coating layer observed here provide insight into the optimized design of a coating layer on a cathode to enhance the battery properties.

Yan, Pengfei↗

Occupant Preference-Aware Load Scheduling for Resilient Communities

The load scheduling of resilient communities in the islanded mode is subject to many uncertainties such as weather forecast errors and occupant behavior stochasticity. To date, it remains unclear how occupant preferences affect the effectiveness of the load scheduling of resilient communities. This paper proposes an occupant thermal preference-aware load scheduler for resilient communities operating in the islanded mode. First, key resilience indicators are selected to quantify its impacts on the load scheduling of a resilient community. A deterministic model predictive control-based load scheduling framework is adopted as the baseline. Then, a chance-constrained controller is proposed to address the occupant-induced uncertainty in room temperature setpoints. Finally, the chance-constrained controller is compared with the deterministic controller on a virtual community testbed based on a real-world net-zero energy community in Florida, U.S. Results have shown that the proposed chance-constrained controller performs better in terms of serving occupants’ thermal preference and the required battery sizes compared to the deterministic controller with the presence of the assumed stochastic occupant behavior. This work indicates that it is necessary to consider the stochasticity of the occupant behavior when designing optimal load schedulers for resilient communities.

Wang, Jing↗

Turbomachinery design for Space Shuttle auxiliary power systems.

Review of the major factors affecting Space Shuttle auxiliary power system design decisions, and discussion of turbine aerodynamic design optimization techniques. The working fluid to be used and the vehicle mission requirements are shown to be the two major factors that affect auxiliary power system design decisions. Analytical techniques developed for optimization of turbine aerodynamic design parameters are shown to be applicable to transient-state simulation and design optimization of other components, including the turbine controller.

Burriss, W. L.↗

Coupling Subsurface and Above-Surface Models for Optimizing the Design of Borefields and District Heating and Cooling Systems

Accurate dynamic energy simulation is important for the design and sizing of district heating and cooling systems with geothermal heat exchange for seasonal energy storage. Current modeling approaches in building and district energy simulation tools typically consider heat conduction through the ground between boreholes without flowing groundwater. While detailed simulation tools for subsurface heat and mass transfer exist, these fall short in simulating above-surface energy systems. To support the design and operation of such systems, the study developed a coupled model including a software package for building and district energy simulation, and software for detailed heat and mass transfer in the subsurface. For the first, it uses the open-source Modelica Buildings Library, which includes dynamic simulation models for building and district energy and control systems. For the heat and mass transfer in the soil, it uses the TOUGH simulator. The TOUGH family of codes can model heat and multi-phase, multi-component mass transport for a variety of fluid systems, as well as chemical reactions, in fractured porous media. The study validated the coupled modeling approach by comparing the simulation results with one from the g-function based ground response model. It then looked into effects when the water table and the regional groundwater flow are considered in the ground, from the perspective of heat exchange between borehole and ground, and the electrical consumption of the district heating and cooling systems. To access the simulation models, please find the links in the submission: -- For coupled approach validation: see model Buildings.Fluid.Geothermal.Borefields.Examples.BorefieldsWithTough and Buildings.Examples.DistrictReservoirNetworks.Examples.Reservoir3Variable_TOUGH from the "Modelica Building Library" resource, branch issue1495_tough_interface, commit a2667c0. -- For the study of the effect of water table: see model Buildings.Examples.DistrictReservoirNetworks.Examples.Reservoir3Variable_TOUGH from he "Modelica Building Library" resource, branch issue1495_tough_interface_moreIO, commit 760de49. -- For the study of the effect of regional groundwater flow: see Buildings.Examples.DistrictReservoirNetworks.Examples.Reservoir3Variable_TOUGH from he "Modelica Building Library" resource, branch issue1495_tough_interface_moreIO_3D, commit c2a2d2a. The coupling interface script "GrounResponse.py" can be found from the above links in the folder Buildings/Resources/Python-Sources. Also, the needed files for TOUGH simulation are in the folder Buildings/Resources/Python-Sources/ToughFiles that can be accessed through the above links. A brief description of these files is given below; detailed specifications for the first three files may be found in the TOUGH3 Users Guide (Jung et al., 2018) https://tough.lbl.gov/documentation/tough-manuals/. (1) INCON - initial conditions for each grid block (2) INFILE - main input file with material properties and control parameters (3) MESH - description of the computational grid (4) readsave - Modelica/TOUGH interface program: read the final output of TOUGH simulation after TOUGH time step and prepare for transfer to Modelica for next Modelica time step (5) readsave.inp - input parameters for program readsave (6) writeincon - Modelica/TOUGH interface program: write the output of Modelica after Modelica time step and prepare for transfer to TOUGH as initial conditions for the next TOUGH step (7) writeincon.inp - input parameters for program writeincon

15 GEOTHERMAL ENERGY↗

A dual mesh method with adaptivity for stress-constrained topology optimization

This paper is concerned with the topological optimization of elastic structures, with the goal of minimizing the compliance and/or mass of the structure, subject to a stress constraint. It is well known that depending upon the geometry and the loading conditions, the stress field can exhibit singularities, if these singularities are not adequately resolved, the topological optimization process will be ineffective. For computational efficiency, adaptive mesh refinement is required to adequately resolve the stress field. This poses a challenge for the traditional Solid Isotropic Material with Penalization (SIMP) method that employs a one-to-one correspondence between the finite element mesh and the optimization design variables because as the mesh is refined, the optimization process must somehow be re-started with a new set of design variables. The proposed solution here is a dual mesh approach, one finite element mesh defines the material distribution, a second finite element mesh is used for the computation of the displacement and stress fields. This allows for stress-based adaptive mesh refinement without modifying the definition of the optimization design variables. A second benefit of this dual mesh approach is that there is no need to apply a filter to the design variables to enforce a length scale, instead the length scale is determined by the design mesh. This reduces the number of design variables and allows the designer to apply spatially varying length scale if desired. The efficacy of this dual mesh approach is established via several stress-constrained topology optimization problems.

36 MATERIALS SCIENCE↗