Computers & Structures最新文献

{"title":"Meta-learning Gaussian processes for engineering surrogate modeling with cross-validation- and variance-guided adaptive sampling","authors":"Guangquan Yu ,&nbsp;Ning Li ,&nbsp;Cheng Chen ,&nbsp;Xiaohang Zhang ,&nbsp;Xiaoshu Gao","doi":"10.1016/j.compstruc.2026.108158","DOIUrl":"10.1016/j.compstruc.2026.108158","url":null,"abstract":"<div><div>Surrogate models significantly reduce computational costs by minimizing calls to expensive simulations, enabling efficient reliability analysis and uncertainty quantification. However, traditional surrogate modeling often overlooks transferable knowledge from related tasks, requiring models to be built from scratch. To overcome this limitation, we propose a meta-learning-based adaptive sampling framework for global surrogate modeling that integrates knowledge via a learning-to-learn approach and autonomously selects informative samples for rapid task adaptation. The framework employs meta-learning Gaussian processes (MLGP) to transfer knowledge across tasks during meta-training, while sensitive subdomains are detected using Voronoi partitioning combined with cross-validation error. Within the most sensitive subdomain, variance-guided adaptive sampling is then conducted to further improve convergence. Three numerical case studies, illustrate how varying the number of meta-tasks and samples per task affects prediction accuracy. Applications to composite beams with varying reinforcement parameters and offshore wind structures under different load conditions further demonstrate the framework’s effectiveness in practical engineering contexts. These highlight the framework’s strong potential for scalable, knowledge-efficient surrogate modeling in complex engineering systems.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"323 ","pages":"Article 108158"},"PeriodicalIF":4.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777916","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":"Multi-fidelity Bayesian data-driven design of energy absorbing spinodoid cellular structures","authors":"Leo Guo ,&nbsp;Hirak Kansara ,&nbsp;Siamak F. Khosroshahi ,&nbsp;GuoQi Zhang ,&nbsp;Wei Tan","doi":"10.1016/j.compstruc.2026.108155","DOIUrl":"10.1016/j.compstruc.2026.108155","url":null,"abstract":"<div><div>Finite element (FE) simulations of structures and materials are becoming increasingly accurate, but also more computationally expensive as a collateral result. This development occurs in parallel with a growing demand for data-driven design. To reconcile the two, a robust and data-efficient optimization method called Bayesian optimization (BO) has been previously established as a technique to optimize expensive objective functions. The mesh width of an FE model can be exploited to evaluate an objective at a lower or higher fidelity (cost &amp; accuracy) level, which is the domain of multi-fidelity BO (MFBO) applications. However, BO and MFBO are usually not directly compared in the literature. Moreover, sampling quality and assessing design parameter sensitivity are often underrepresented parts of data-driven design. This paper combines global sensitivity analysis and (MF) BO into a novel, efficient Bayesian data-driven framework. We compare the performance of BO with that of MFBO by maximizing the energy absorption (EA) problem of spinodoid cellular structures. The findings show that similar or better designs are suggested by MFBO with 16% fewer expensive objective evaluations compared to BO when maximizing the EA. The results, which are made open-source, serve to support the utility of multi-fidelity techniques across expensive data-driven design problems.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"323 ","pages":"Article 108155"},"PeriodicalIF":4.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777917","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":"Implicit Runge Kutta physics informed neural network for parameter identification of structural systems","authors":"Nikhil Mahar ,&nbsp;Subhamoy Sen ,&nbsp;Laurent Mevel","doi":"10.1016/j.compstruc.2026.108157","DOIUrl":"10.1016/j.compstruc.2026.108157","url":null,"abstract":"<div><div>System identification (SI) is essential for ensuring the reliability of structural and mechanical components across engineering applications. Traditional model-based SI methods often struggle with complex systems due to modeling uncertainties and the limited availability of accurate physical models. In contrast, data-driven approaches are computationally efficient but typically lack physical interpretability. Physics-informed neural networks (PINNs) have recently emerged as a promising alternative by combining data with physical laws. However, conventional PINNs are computationally expensive for parameter identification due to collocation-based physics enforcement and multi-objective loss optimization. To overcome these challenges, this study proposes an implicit Runge-Kutta physics-informed neural network based on the Radau IIA discretization scheme, termed as Radau IIA PINN. In the proposed framework, physical laws are embedded directly into the architecture of a recurrent neural network through physics-based time integration, eliminating the need for collocation points and complex regressor construction. A comprehensive comparison with state-of-the-art approaches, including Parallel PINNs, Kalman Filters, Physics-Informed Long Short Term Memory network, and fourth-order Runge–Kutta PINN, demonstrates superior robustness, numerical stability, and accuracy under sparse and noisy measurements. Numerical simulations on various structural systems further confirm faster convergence and reliable identification of localized structural deterioration, highlighting the method’s potential for practical system identification.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"323 ","pages":"Article 108157"},"PeriodicalIF":4.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777920","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":"Application of Gaussian expansion element method to a wedge-shaped plate with an acoustic black hole","authors":"Yaxin Zhen ,&nbsp;Lei Chen ,&nbsp;Ye Tang","doi":"10.1016/j.compstruc.2026.108138","DOIUrl":"10.1016/j.compstruc.2026.108138","url":null,"abstract":"<div><div>Non-uniform and variable cross-section structures with Acoustic Black Hole (ABH) features have excellent vibration and noise reduction properties, but accurately analyzing their dynamic behavior is challenging. The Gaussian Expansion Method (GEM) is commonly used in non-uniform structure dynamic analysis, yet it has limitations in calculating high-order derivatives of the mode shapes. This paper presents the Gaussian Expansion Element Method (GEEM), which combines GEM, element division, and boundary-handling concepts from the Improved Fourier Series Method (IFSM). GEEM divides non-uniform structures into elements, uses two types of Gaussian basis functions to meet boundary and continuity conditions, and applies the Rayleigh-Ritz method to establish element dynamic models. Through numerical simulations of a uniform thin plate and ABH (a wedge-shaped thin plate), GEEM demonstrates higher accuracy, efficiency, and numerical stability compared to GEM and the Finite Element Method (FEM), especially in calculating high-order derivatives of the mode shapes. The research results contribute to understanding the dynamic behavior of complex non-uniform structures and can promote the development of vibration-control strategies in engineering applications.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"323 ","pages":"Article 108138"},"PeriodicalIF":4.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146152959","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":"Structural reanalysis method based on separation-reconstruction mode for structures with large-scale modifications","authors":"Wenxiong Li ,&nbsp;Jiayuan Huang ,&nbsp;Suiyin Chen ,&nbsp;Gengying Li ,&nbsp;Jianhua Wen","doi":"10.1016/j.compstruc.2026.108113","DOIUrl":"10.1016/j.compstruc.2026.108113","url":null,"abstract":"<div><div>Efficient structural reanalysis for high-rank modifications is of significant importance in engineering computations that involve repeated solution of equilibrium equations, such as structural optimization and nonlinear analysis. This paper proposes a novel reanalysis method based on separation and reconstruction operations for structures with large-scale modifications. The core idea is to replace the solution of the structural equations corresponding to large-scale modifications with a sequence of solutions for locally modified structures. Consequently, the displacement solution of the modified structure can be reconstructed by aggregating the solutions from these locally modified structures. In the implementation, the relationship between each locally modified structure and the large-scale modified structure is formally characterized using high-dimensional model representation, and the reanalysis of locally modified structures is performed through an efficient computational framework that incorporates system reduction and preconditioned iterative solvers. To mitigate the errors arising from the omission of higher-order terms, a correction mechanism is introduced to eliminate residual errors in the equilibrium equations, thereby ensuring the accuracy of displacement solutions. The efficacy and computational advantages of the proposed method are demonstrated through numerical experiments. The results confirm that the method exhibits superior performance in handling structural reanalysis problems involving both large-scale modifications and local modifications.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108113"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071719","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":"Adaptive bubble-enriched face-based smoothed finite element method for 3D structural yield design","authors":"Phuc L.H. Ho ,&nbsp;Canh V. Le ,&nbsp;Dung T. Tran ,&nbsp;Changkye Lee","doi":"10.1016/j.compstruc.2026.108139","DOIUrl":"10.1016/j.compstruc.2026.108139","url":null,"abstract":"<div><div>This paper presents a novel three-dimensional adaptive kinematic yield design framework based on the bubble-enriched face-based smoothed finite element method (bFS-FEM). The enrichment of face-based smoothing with bubble functions enhances approximation capability and effectively eliminates volumetric locking, a common limitation of conventional low-order FEM in incompressible materials. To further improve accuracy without compromising efficiency, an adaptive mesh refinement strategy is incorporated into the formulation. In addition, a plastic dissipation error estimator based on the three-dimensional displacement fields of bFS-FEM is developed to guide the refinement process. The resulting discretization leads to a second-order cone programming (SOCP) problem, which ensures numerical robustness and scalability to large-scale analyses. Numerical benchmarks demonstrate that the proposed method delivers locking-free, accurate, and physically consistent solutions, highlighting its potential as an efficient and reliable tool for collapse analysis of complex three-dimensional structures.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108139"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134535","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":"Microstructural characterization of PZT–thin metal layer–air and PZT–air composites employing a random representative volume element (RVE) and heterogeneous polarization models","authors":"Mohamed Elsayed Nassar ,&nbsp;Ali Kandil ,&nbsp;Andrey Nasedkin","doi":"10.1016/j.compstruc.2026.108123","DOIUrl":"10.1016/j.compstruc.2026.108123","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Polarization is a key stage in the manufacture of piezoelectric materials/composites. In a dense piezoceramic material, it is usually uniform with the polarization vector directed along the polarization axis. However, in non-uniform piezoceramic materials, such as piezocomposites with pores or inclusions, the polarization field is non-uniform and can significantly affect the properties of the composite. The heterogeneity of the polarization field is especially pronounced in piezocomposites with conductive inclusions or in porous composites with metal particles deposited on the pore boundaries. This study explores how the polarization process affects the primary elastic, piezoelectric, and dielectric coefficients of two piezoelectric composites, PZT–Air and PZT–Thin Metal Layer–Air (PZT–TML–Air). It is worth noting that the metal phase in PZT–TML–Air is a very thin layer around the outside surface of each pore, therefore the electrical conductivity characteristics are the primary influence of this layer, and the elastic properties of the metal are not significant. Therefore, the PZT–TML–Air composite can be considered as a two-phase material. A numerical homogenization approach including finite element analysis, representative volume element (RVE), perfect contact between different phases, linear essential boundary conditions, and the Hill-Mendel’s principle was employed to calculate the equivalent properties. A new random RVE, applicable to diverse two-phase dispersed composites, and an algorithm for its quick creation were introduced. This RVE is a cubic piezoelectric matrix with randomly distributed spherical inclusions of various volumes. It has a fill factor of up to 50%. We used two simplified strategies for determining inhomogeneous properties for the piezoceramic matrix, which are associated with the orientations of element coordinate systems (ECS) with inhomogeneous polarization fields. The first method solely analyzes inhomogeneities caused by ECS rotations, whereas the second takes into consideration changes in material moduli magnitudes and ECS directions caused by the polarization field. The polarization vectors were determined by solving the corresponding dielectric problem using the finite element approach. To carry out the computations, a set of programs for the ANSYS Mechanical APDL package was created, allowing for the automation of all steps of modeling and determining equivalent moduli. Therefore, the following procedures were automated for the most complicated instance of the PZT–TML-Air composite with non-uniform polarization, accounting for the change in the moduli and orientations of the ECS: computation of the moduli of non-uniformly polarized piezoelectric ceramics; construction of the RVE with specified properties and the finite element mesh; definition of ECS and polarization vector for each finite element; solution of a set of boundary value problems for a non-uniform piezoelectric material with post-processo","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108123"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072492","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":"A relative configuration vector method for solving geometrically exact beam problems","authors":"Ziheng Huang ,&nbsp;Ju Chen ,&nbsp;Shixing Liu ,&nbsp;Yongxin Guo","doi":"10.1016/j.compstruc.2026.108119","DOIUrl":"10.1016/j.compstruc.2026.108119","url":null,"abstract":"<div><div>The geometrically exact beam problems are often solved based on total Lagrangian method and updated Lagrangian method. However, these methods are prone to singularities and poor convergence when dealing with large deformations. The relative configuration vector method is proposed to obtain a singularity-free solution of the static equilibrium equations even for models with large deformation. First, the kinematic description of geometrically exact beams based on Lie group SE(3) is presented, along with an SE(3)-interpolation for the beam elements. The advantages of SE(3)-interpolation, such as objectivity and shear-locking-free behavior are then discussed. Next, an interpolation scheme for the variation of the average convective strain is derived, which allows for the computation of strain operators and static equilibrium equations without introducing complex operators. Subsequently, a detailed comparison is made among the three computing methods in terms of singularities, equivalence conditions for multivariable substitution, and the tangent stiffness matrix. Theoretically, the relative configuration vector method can inherently avoid the logarithm map and thereby eliminates the associated singularities. Finally, numerical examples are taken to show that the proposed relative configuration vector method avoids singularities and enhances convergence behavior under large deformations compared with the total and updated Lagrangian methods.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108119"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071720","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":"A physics-informed meta-learning framework for the continuous solution of parametric PDEs on arbitrary geometries","authors":"Reza Najian Asl ,&nbsp;Yusuke Yamazaki ,&nbsp;Kianoosh Taghikhani ,&nbsp;Mayu Muramatsu ,&nbsp;Markus Apel ,&nbsp;Shahed Rezaei","doi":"10.1016/j.compstruc.2026.108102","DOIUrl":"10.1016/j.compstruc.2026.108102","url":null,"abstract":"<div><div>In this work, we introduce <strong>implicit Finite Operator Learning (iFOL)</strong> for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decoder network to establish the mapping between continuous parameter and solution spaces. The decoder constructs the parametric solution field by leveraging an implicit neural field network conditioned on a latent or feature code. Instance-specific codes are derived through a PDE encoding process based on the second-order meta-learning technique. iFOL employs a purely physics-informed loss function derived via the Method of Weighted Residuals. The predicted neural field serves as the test function, resulting in the backpropagation of discrete residuals during the PDE encoding and decoding stages.</div><div>Compared to the state-of-the-art neural operators, iFOL introduces several key innovations: (1) it bypasses the costly multi-network and supervised encode–process–decode pipeline of conditional neural fields for parametric PDEs; (2) it yields accurate parametric fields and solution-to-parameter gradients, enabling efficient sensitivity analysis regardless of response count; (3) it effectively captures sharp solution discontinuities, which are often challenging for some neural operator models; and (4) it is mesh and geometry agnostic, enabling zero-shot generalization to arbitrary domains. We critically assess these features and analyze the network’s ability to generalize to unseen samples across both stationary and transient PDEs. The method is also compared against baseline operator-learning approaches, demonstrating its potential for tackling complex problems in computational mechanics.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108102"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110194","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":"Robust topology optimization under uncertain transient loads based on unit impulse response functions","authors":"Delin Cao ,&nbsp;Yan Zeng ,&nbsp;Zeng Meng ,&nbsp;Gang Li","doi":"10.1016/j.compstruc.2026.108125","DOIUrl":"10.1016/j.compstruc.2026.108125","url":null,"abstract":"<div><div>Robust topology optimization under uncertain transient loads faces the challenge of high computational cost due to the repeated execution of structural dynamic responses and worst-case scenarios during the optimization process. In this study, unit impulse response functions are introduced for linear dynamic systems to leverage the superposition principle for the explicit computation of structural responses and interval variable sensitivities. The computational complexity analysis shows that, when the objective function involves only a small number of degrees of freedom, the speedup achieved by the proposed method increases significantly and may approach its theoretical upper bound. Under such conditions, the worst-case scenario can be efficiently approached numerically using the multi-start local search method. Additional constraints are introduced as necessary conditions for maintaining a scenario as the worst-case scenario, aiming to mitigate potential convergence issues caused by neglecting the sensitivity of the worst-case scenario with respect to the design variables. During the optimization, the additional constraints are updated based on clusters obtained using the density-based spatial clustering of applications with noise algorithm. Numerical examples are presented to validate the effectiveness and efficiency of the proposed method. The results support the validity of the speedup derivation and indicate that, once unit impulse response functions are available, the cost of identifying the worst-case scenario can be significantly reduced. When local structural performance is used as the objective, the additional constraints help improve optimization convergence. Compared with deterministic designs, the proposed method shows a noticeable reduction in the upper bound of the objective function.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108125"},"PeriodicalIF":4.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134541","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}