Structural and Multidisciplinary Optimization最新文献

{"title":"Geometrically nonlinear high-fidelity aerostructural optimization for highly flexible wings.","authors":"Alasdair C Gray, Graeme J Kennedy, Joaquim R R A Martins","doi":"10.1007/s00158-025-04181-x","DOIUrl":"10.1007/s00158-025-04181-x","url":null,"abstract":"<p><p>Over the past decade, advances in MDO have enabled the aerodynamic and structural design of aircraft wings to be simultaneously optimized using high-fidelity models. Using RANS CFD and detailed structural finite element models in these optimizations enables an accurate trade-off between cruise drag and structural mass. Modeling the coupling of aerodynamics and structures allows the optimizer to aeroelastically tailor the wing, taking advantage of flexibility for improved performance. These capabilities make MDO a key enabling technology for the next generation of flexible and efficient high-aspect-ratio transport aircraft. However, as their aspect ratios increase, these wings increasingly exhibit geometrically nonlinear behavior that linear structural analysis methods cannot model. This work demonstrates the first simultaneous optimization of a wing's aerodynamic shape and structural sizing using high-fidelity geometrically nonlinear models. To enable this we implement a novel geometrically nonlinear shell element, an efficient nonlinear solver, and a constitutive model for stiffened shells. We then couple these nonlinear structural analysis tools to CFD through a geometrically nonlinear transfer scheme. Using these capabilities, we optimize a single-aisle commercial transport aircraft wing with 547 design variables and 1277 constraints. Although the optimized designs exhibit extreme flexibility-an aspect ratio above 19 and deflections exceeding 30% semispan-geometric nonlinearity has minimal impact on aerodynamic performance, planform design, and overall aircraft mass. However, the Brazier effect causes internal loads that linear analysis misses, requiring geometrically nonlinear analysis to produce a feasible design. The developed framework enables the pursuit of next-generation high-aspect-ratio wing designs by providing the computational foundation needed to exploit extreme wing flexibility as a design opportunity rather than a constraint.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"69 1","pages":"6"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12689710/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145744587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reinforcement learning-based control co-design of digital twin-enabled full-vehicle active suspension systems.","authors":"Ying-Kuan Tsai, Yi-Ping Chen, Vispi Karkaria, Wei Chen","doi":"10.1007/s00158-026-04304-y","DOIUrl":"10.1007/s00158-026-04304-y","url":null,"abstract":"<p><p>Active suspension systems are critical for enhancing vehicle comfort, safety, and stability, yet their performance is often limited by fixed hardware designs and control strategies that cannot adapt to uncertain and dynamic operating conditions. Recent advances in Digital Twins (DTs) and Reinforcement Learning (RL) offer new opportunities for real-time, data-driven optimization across a vehicle's lifecycle. However, integrating these technologies into a unified framework for co-optimizing physical and control systems remains an open challenge. This work presents an RL-based Control Co-Design (CCD) framework for full-vehicle active suspensions using multi-generation design and DT concepts. Through integrating automatic differentiation into Deep Reinforcement Learning (DRL), we jointly optimize physical components of suspension systems and control policies under varying driver behaviors and environmental uncertainties. The DRL technique also addresses the challenge of partial observability, where only limited states can be sensed and fed back to the controller, by learning optimal control actions directly from available sensor information. The framework incorporates model updating with quantile learning to quantify data uncertainty, enabling real-time decision-making and adaptive learning from digital-physical interactions. The approach demonstrates personalized optimization of autonomous suspension systems under two distinct driving settings (mild and aggressive). The results show that the optimized systems achieve smoother trajectories and reduce control efforts by approximately 58% and 12% for mild and aggressive while improving ride comfort by approximately 17% and 28%, respectively. Contributions of this work include: (1) developing a DT-enabled CCD framework integrating DRL and uncertainty-aware model updating for full-vehicle active suspensions, (2) introducing a multi-generation design framework for self-improving systems across the whole lifecycle, and (3) demonstrating personalized optimization of active suspension systems for distinct types of drivers.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"69 4","pages":"108"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13070092/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147676788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"GELATO: multi-material topology optimization of programmable gel-elastomer structures.","authors":"Aaditya Chandrasekhar, Dex Doksoo Lee, Hyunwoo Kwon, Wei Chen","doi":"10.1007/s00158-026-04402-x","DOIUrl":"10.1007/s00158-026-04402-x","url":null,"abstract":"<p><p>Gel-elastomer composites, comprising an active swellable hydrogel and a passive elastomer, are a compelling class of programmable material systems (PMS) capable of shape morphing under multiphysics actuation. The precise design of the topology and material distribution unlocks complex programmability instrumental in wearable electronics, soft robots, and drug delivery; however, the structure-function relationship is highly non-intuitive, rendering both trial-and-error and conventional design approaches largely intractable due to the nonlinear coupled chemo-mechanical response and the combinatorial nature of the multi-material design space. To address this, we present a topology optimization (TO) framework for the automated design of such structures, enabling systematic exploration of the design space for target functionalities realized via programmable shape morphing. In particular, we propose a multi-material TO framework that concurrently optimizes the structural topology and the spatial distribution of the gel-elastomer phases. The design is represented via a coordinate-based neural network, and the mechanical response of both phases is described within a unified constitutive framework based on the Flory-Rehner theory. Furthermore, we present an end-to-end differentiable design framework with implicit differentiation that accommodates various objective functions, constraints, and discretizations. We demonstrate the framework on shape-programming structures and soft actuators. The framework is further validated through the design of organogel-hydrogel composites for multi-stimuli responsiveness across chemically distinct solvent environments, and of anisotropic hydrogels wherein the local fiber orientation is optimized concurrently with the topology. The codebase implemented in JAX is publicly shared to support benchmarking and reproducibility.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"69 9","pages":"214"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13569571/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148956525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel multi-thickness topology optimization method for balancing structural performance and manufacturability.","authors":"Gabriel Stankiewicz, Chaitanya Dev, Paul Steinmann","doi":"10.1007/s00158-026-04267-0","DOIUrl":"10.1007/s00158-026-04267-0","url":null,"abstract":"<p><p>Topology optimization in two dimensions often presents a trade-off between structural performance and manufacturability, with unpenalized (variable-thickness) methods yielding superior but complex designs, and penalized methods producing simpler, truss-like structures with compromised performance. This paper introduces a multi-thickness, density-based topology optimization method designed to bridge this gap. The proposed approach guides the design toward a predefined set of discrete, allowable thicknesses by employing a novel multilevel penalization scheme and a multilevel smoothed Heaviside projection. A continuation strategy for the penalization and projection parameters, combined with an adaptive mesh refinement technique, ensures robust convergence and high-resolution geometric features. The method is validated on standard cantilever and MBB beam benchmarks. Results demonstrate that as the number of allowable thicknesses increases, the designs systematically transition from conventional truss-like structures to high-performance, sheet-like structures. Notably, designs with as few as three discrete thickness levels achieve compliance values within 2% of those from fully unpenalized, variable-thickness optimization. The method inherently eliminates impractically thin regions and features, both in the out-of-plane and in-plane directions and produces designs well-suited for both additive manufacturing and conventional fabrication using standard-thickness stock materials, thus maximizing both performance and manufacturability.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"69 3","pages":"78"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12971805/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147435689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deblurring structural edges in variable thickness topology optimization via density-gradient-informed projection.","authors":"Gabriel Stankiewicz, Chaitanya Dev, Paul Steinmann","doi":"10.1007/s00158-026-04343-5","DOIUrl":"10.1007/s00158-026-04343-5","url":null,"abstract":"<p><p>Variable thickness topology optimization (VTTO) is a potent methodology for designing high-performance, high-stiffness sheet structures. However, this method frequently encounters two primary challenges: (1) the formation of undesirable low-thickness regions, which present manufacturing difficulties, and (2) the blurring of structural edges. This blurring is an artifact inherent to the regularization filters required for well-posedness. This paper proposes solutions to address both challenges. First, to mitigate low-thickness regions, we introduce a robust, combined approach. This strategy utilizes a SIMP-based penalization and an updated projection method, which effectively suppresses nearly all low-thickness domains. Second, the main contribution of this work is a novel method to deblur structural edges, termed the density-gradient-informed (DGI) projection. This projection utilizes local density gradient information. It selectively applies a strong projection in high-gradient regions (i.e., structural edges) to restore sharpness, while minimally affecting low-gradient regions within the structure's interior. Numerical examples demonstrate that the DGI projection successfully deblurs the structural edges, restoring a distinct solid-void transition, while preserving the internal form. Most importantly, this significant improvement in edge definition is achieved with a negligible impact on the final structural compliance. This establishes the DGI projection as a non-invasive and effective regularization tool for enhancing VTTO designs.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"69 6","pages":"147"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13230317/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148164303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Differentiable modelling and optimization of multi-planar slicing for multi-axis additive manufacturing.","authors":"Vibhas Mishra, Jun Wu","doi":"10.1007/s00158-025-04240-3","DOIUrl":"10.1007/s00158-025-04240-3","url":null,"abstract":"<p><p>Multi-planar deposition, enabled by multi-axis additive manufacturing, provides an opportunity to address challenging issues in wire arc additive manufacturing, such as residual stresses and distortions. This strategy involves sequentially building sub-parts, by depositing material in each sub-part with a distinct printing direction. In this paper, we present a novel continuous and differentiable formulation to model the multi-planar slicing strategy. The strategy is parameterized using a pseudo-time field, which allows the part to be segmented into sub-parts. An orientation field is used to define the distinct printing direction for each sub-part. This differentiable formulation enables gradient-based optimization of the multi-planar slicing. We apply the method to reduce distortion in wire arc additive manufacturing. The method is tested on several numerical examples with complex geometries, including holes, overhangs, and underhangs. Numerical results show that the multi-planar deposition approach reduces distortion by an order of magnitude compared with the conventional planar strategy.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"69 2","pages":"31"},"PeriodicalIF":4.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12819540/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146031081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adjoint-based PDE-constrained optimization of viscoelastic floating membrane for maximum wave power absorption.","authors":"Kareem El Sayed, Shagun Agarwal, Andrei Metrikine, Oriol Colomés","doi":"10.1007/s00158-026-04270-5","DOIUrl":"10.1007/s00158-026-04270-5","url":null,"abstract":"<p><p>Viscoelastic floating membranes can be used as flexible wave breakers to protect coastal and offshore structures or as flexible wave energy converters. Despite their potential, the role of viscoelastic floating membranes in optimally harvesting or dissipating wave energy remains largely unexplored, particularly regarding how spatially varying material properties influence their performance. To address this gap, we develop an adjoint-based PDE-constrained optimization framework, built on a monolithic finite element formulation of the coupled fluid-structure interaction problem, to investigate and optimize the viscoelastic properties of floating membranes. This methodology enables a systematic optimization of design parameters such as the mass, tension, and damping, which govern the response of the membrane at different wave conditions. In this study we demonstrate that the proposed methodology allows for the optimization of homogeneous and inhomogeneous properties of membranes for different wave excitation frequencies, leading to significant improvements in energy absorption. The framework is implemented in Julia using the Gridap package ecosystem, which enables automatic differentiation of adjoints and avoids the need to derive complex adjoint formulations.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"69 3","pages":"71"},"PeriodicalIF":4.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12945959/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147327095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Risk twin: real-time risk visualization and control for structural systems","authors":"Zeyu Wang, Ziqi Wang","doi":"10.1007/s00158-025-04014-x","DOIUrl":"https://doi.org/10.1007/s00158-025-04014-x","url":null,"abstract":"","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"68 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147881847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mixed-integer, multi-objective layerwise optimization of variable-stiffness composites with gaps and overlaps.","authors":"D Zamani, A Racionero Sánchez-Majano, A Pagani","doi":"10.1007/s00158-025-04043-6","DOIUrl":"10.1007/s00158-025-04043-6","url":null,"abstract":"<p><p>Automated fiber placement (AFP) has made it possible to vary the steering angle along curvilinear fiber paths, thus improving mechanical performance compared to traditional composite materials. Variable-angle tow (VAT) or variable-stiffness composites (VSC) have been developed to enhance structural performance through material optimization and effective load-bearing configurations. These advanced materials contribute to achieving optimal performance while reducing the weight of aircraft and aerospace structures. However, defects such as gaps and overlaps may arise during the manufacturing process. Whereas the latter increases local thickness, the former causes resin-rich areas within each lamina. The mass and structural optimization of this kind of structure is challenging as it combines discrete and continuous design variables, namely the number of layers and the fiber path parameters, where the latter influence the presence of defects within the laminate. To tackle this optimization problem, this work proposes a mixed-integer strategy specifically designed to select the least-weight design of a VAT laminate while also fulfilling requirements on the first natural frequency and buckling load while accounting for the manufacturing signature of the AFP process. This study combines the Carrera unified formulation (CUF) and the defect layer method (DLM) to model the VAT laminates and incorporating the fabrication defects. The research has two main aims: (i) to determine the minimum number of layers required to satisfy the fundamental frequency and buckling constraints, considering the manufacturing signature, and (ii) to investigate the influence of the selected structural theory on the optimal design solutions.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"68 6","pages":"107"},"PeriodicalIF":3.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12167357/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144310386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fast and accurate Bayesian optimization with pre-trained transformers for constrained engineering problems.","authors":"Rosen Ting-Ying Yu, Cyril Picard, Faez Ahmed","doi":"10.1007/s00158-025-03987-z","DOIUrl":"https://doi.org/10.1007/s00158-025-03987-z","url":null,"abstract":"<p><p>Bayesian Optimization (BO) is a foundational strategy in engineering design optimization for efficiently handling black-box functions with many constraints and expensive evaluations. This paper introduces a novel constraint-handling framework for Bayesian Optimization (BO) using Prior-data Fitted Networks (PFNs), a foundation transformer model. Unlike traditional approaches requiring separate Gaussian Process (GP) models for each constraint, our framework leverages PFN's transformer architecture to evaluate objectives and constraints simultaneously in a single forward pass using in-context learning. Through comprehensive benchmarking across 15 test problems spanning synthetic, structural, and engineering design challenges, we demonstrate an order of magnitude speedup while maintaining or improving solution quality compared to conventional GP-based methods with constrained expected improvement (CEI). Our approach particularly excels at engineering problems by rapidly finding feasible, optimal solutions. This benchmark framework for evaluating new BO algorithms in engineering design will be published at https://github.com/rosenyu304/BOEngineeringBenchmark.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"68 3","pages":"66"},"PeriodicalIF":3.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11985669/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144000179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}