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":"https://doi.org/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":4.0,"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":"https://doi.org/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":4.0,"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":"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":4.0,"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":"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":"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}

{"title":"Topology-inclusive aerodynamic shape optimisation using a cellular automata parameterisation.","authors":"M J Wood, T C S Rendall, C B Allen, L J Kedward, N J Taylor, J Fincham, N E Leppard","doi":"10.1007/s00158-024-03916-6","DOIUrl":"https://doi.org/10.1007/s00158-024-03916-6","url":null,"abstract":"<p><p>A novel geometry parameterisation method constructed from a volume-of-solid driven cellular automata is presented. The method is capable of describing complex geometry of arbitrary topology using a set of volume-of-solid parameters applied to a geometry control mesh. This is done by approximating the smooth geometry of minimum surface area subject to a set of localised constraints on contained volume defined by both the control mesh and volume-of-solid parameters. Localised control mesh refinement is possible through splitting of control mesh cells to provide additional degrees of freedom where necessary. The parameterisation is shown to reconstruct over 98% of a library of aerofoil geometries to within a standard wind tunnel-equivalent geometric tolerance, and to recover known analytical optima in supersonic flow. Using gradient-free optimisation methods, the parameterisation is then shown to construct aerodynamic geometries consisting of multiple objects to package a set of existing geometries. Finally, the parameterisation is used to construct an optimal supersonic multi-body geometry with less than half the drag of the equivalent volume optimal single body.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"68 2","pages":"23"},"PeriodicalIF":3.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11903545/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143650881","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":"Configurational-force-driven adaptive refinement and coarsening in topology optimization.","authors":"Gabriel Stankiewicz, Chaitanya Dev, Paul Steinmann","doi":"10.1007/s00158-025-04096-7","DOIUrl":"https://doi.org/10.1007/s00158-025-04096-7","url":null,"abstract":"<p><p>The iterative nature of topology optimization, especially in combination with nonlinear state problems, often requires the solution of thousands of linear equation systems. Furthermore, due to the pixelated design representation, the use of a fine mesh is essential to obtain geometrically well-defined structures and to accurately compute response quantities such as the von Mises stress. Therefore, the computational cost of solving a fine-mesh topology optimization problem quickly adds up. To address this challenge, we consider a multi-level adaptive refinement and coarsening strategy based on configurational forces. Configurational forces based on the Eshelby stress predict configurational changes such as crack propagation or dislocation motion. Due to a relaxation in the calculation of (Eshelby) stresses with respect to the design variables, discrete configurational forces increase not only in highly stressed regions, but also in gray transition regions (design boundaries). For this reason, they constitute an ideal criterion for mesh adaptivity in topology optimization, especially when avoiding stress failure is a priority. By using configurational forces for refinement, we obtain a high-resolution structure where the refined mesh is present along the design boundaries as well as in stress-critical regions. At the same time, multi-level coarsening using the same criterion drastically minimizes the computational effort.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"68 8","pages":"152"},"PeriodicalIF":4.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12364982/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144969455","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":"Combined truss and continuum topology optimization of structures.","authors":"Hongjia Lu, Helen E Fairclough, Linwei He, Matthew Gilbert","doi":"10.1007/s00158-025-04063-2","DOIUrl":"10.1007/s00158-025-04063-2","url":null,"abstract":"<p><p>Truss layout optimization and continuum topology optimization are both well-established methods, with each having a wide range of applications. Whereas truss layout optimization is best suited for low volume fraction problems (i.e. where the optimal structure occupies a low proportion of the original design domain), continuum topology optimization is best suited for medium and high volume fraction problems. However, real-world design problems often include both high and low volume fraction regions. To address this, a two-step hybrid optimization approach is proposed. First, low and high volume fraction regions are identified within a problem. These are then populated with truss and continuum elements respectively, which are connected via suitable interfaces. The combined optimization formulation is conic, and can be efficiently solved using interior point solvers. Numerical examples are presented to demonstrate the efficacy of the proposed approach. The results show that the approach is capable of identifying structures which contain a mixture of length scales, incorporating both bulk continuum regions and fine truss elements.</p>","PeriodicalId":21994,"journal":{"name":"Structural and Multidisciplinary Optimization","volume":"68 7","pages":"142"},"PeriodicalIF":4.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12307569/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144761299","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}