Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Active evolutionary Gaussian process for structural large-scale full-field reliability analysis and critical domain prognosis with only few initial samples","authors":"Xinlong Li,&nbsp;Chensen Ding","doi":"10.1016/j.cma.2025.118418","DOIUrl":"10.1016/j.cma.2025.118418","url":null,"abstract":"<div><div>Reliability analysis is crucial for ensuring structural integrity, yet it requires repeated, time-consuming evaluations of responses and multivariate limit state functions, while struggling to provide full-field estimations efficiently. Therefore, we propose an active evolutionary reduced Gaussian Process framework (<strong>AER-GP</strong>) for fast and large-scale full-field reliability analysis and critical domain prognosis, utilizing only a few initial samples. In which we first define a novel probability indicator of erroneously evaluating the sign of the minimum of the full-field limit state function. Based on this, we then develop an efficient convergence criterion that relies on the expected error in failure probability estimates. Furthermore, we advance the dual order-reduced Gaussian process coupled Monte Carlo methods to accurately predict the large-scale full-field stochastic response under material and load uncertainty. Where the preliminary design of experiments starts from a significantly small number of sets (e.g.,5), and is progressively added by those samples containing the most information to distinguish the failure boundary. More importantly, we propose a novel mechanism for structural critical domain prognosis mechanism based on the failure probability of each single material point within the entire field, and make accurate critical domain prognosis. Real-world examples, including a car wheel hub and a single-tower cable-stayed bridge, demonstrate that the proposed algorithm achieves high prediction accuracy, computational efficiency, and robustness in large-scale structural reliability analysis and critical domain prognosis. It consistently outperforms widely used methods such as AK-MCS, EFF-MCS, ERF-MCS, and H-MCS. Notably, the proposed AER-GP method requires only a small number of initial DoE samples (fewer than 40), and through adaptive learning, it can reliably produce results with very low errors (typically less than 2%).</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"448 ","pages":"Article 118418"},"PeriodicalIF":7.3,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Overlapping Schwarz preconditioners for isogeometric discretizations of acoustic wave problems","authors":"Elena Zampieri ,&nbsp;Simone Scacchi ,&nbsp;Luca F. Pavarino","doi":"10.1016/j.cma.2025.118397","DOIUrl":"10.1016/j.cma.2025.118397","url":null,"abstract":"<div><div>The aim of this work is to construct and analyze two-level overlapping additive Schwarz (OAS) preconditioners for isogeometric discretizations of the acoustic wave equation with absorbing boundary conditions. Both Collocation and Galerkin isogeometric methods are employed for space discretization, while time advancing is performed by means of a Newmark implicit scheme. The linear systems to be solved at each time step are ill conditioned, especially in case of highly regular splines, thus their solution requires the use of effective preconditioners. Two-level OAS solvers consist of partitioning the domain into overlapping subdomains, solving independent local problems on each subdomain and an additional coarse problem associated with the subdomain mesh. Several two-dimensional numerical results validate our theoretical estimates, showing the scalability and quasi-optimality of the algorithms proposed. We also investigate numerically the robustness of the OAS preconditioners with respect to the spline polynomial degree, the spline regularity and the overlap parameter.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"448 ","pages":"Article 118397"},"PeriodicalIF":7.3,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DGTO: Derivable geodesics-coupled topology optimization for multi-axis 3D printing of continuous fiber-reinforced spatial structures","authors":"Kaixian Liang ,&nbsp;Jikai Liu ,&nbsp;Shuzhi Xu ,&nbsp;Yifan Guo","doi":"10.1016/j.cma.2025.118419","DOIUrl":"10.1016/j.cma.2025.118419","url":null,"abstract":"<div><div>Continuous fiber reinforced composites (CFRCs) are composite materials with exceptional mechanical properties to enhance structural mechanical performance. In comparison with traditional three-axis 3D printing (also referred to as 2.5D printing), multi-axis 3D printing simultaneously moves the nozzle and rotates the build platform during the printing process, making it particularly suited for fabricating spatial structures made of CFRCs due to better alignment between the fiber depositions and principal stress directions. In this research, we propose a Derivable Geodesics-coupled Topology Optimization (DGTO) method for design of CFRCs given the manufacturing scheme of multi-axis 3D printing. A prominent feature of DGTO is the introduction of two geodesic fields to achieve curved layer generation and continuous fiber path planning. The heat diffusion equation and Poisson equation are solved to produce the geodesic fields, and hence, all objective functions and constraints related to the slices and paths are derivable, making them perfectly suitable to be integrated with topology optimization. Hence, the proposed method concurrently optimizes the density field and the auxiliary geodesic fields, simultaneously tuning the material distribution and spatial fiber distribution, thereby attaining optimal performance while fulfilling the manufacturing constraints of multi-axis printing, i.e., self-support of structure and overlap/gap-free of continuous fibers. Four numerical examples are presented to demonstrate the effectiveness of the algorithm, especially showing outstanding performances than designs for traditional three-axis 3D printing.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"448 ","pages":"Article 118419"},"PeriodicalIF":7.3,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Concurrent 3D topology optimization method for hierarchical hybrid structures under static and dynamic loads with CPU-GPU heterogeneous parallelism","authors":"Yunfei Liu ,&nbsp;Ruxin Gao ,&nbsp;Ying Li ,&nbsp;Daining Fang","doi":"10.1016/j.cma.2025.118408","DOIUrl":"10.1016/j.cma.2025.118408","url":null,"abstract":"<div><div>Topology optimization of 3D hierarchical hybrid structures (HHS) is constrained by the coupling of high-dimensional design spaces and multiscale computational complexity, often addressed by restricting certain designable components, which limits the full exploration of the design space and realization of performance potential. This paper proposes a novel concurrent topology optimization method for 3D-HHS, achieving concurrent optimization of all designable components, including macroscopic topology, substructural topology, and their spatial distribution, under static and dynamic loads. This approach significantly expands the design space, enhancing the mechanical performance of hierarchical structures. To address the computational challenges of large-scale 3D problems, we employ CPU-GPU heterogeneous parallel computing to improve the efficiency of structural response and sensitivity analysis. Numerical examples demonstrate that this method delivers superior 3D-HHS designs with markedly improved optimization efficiency, providing an innovative solution for efficient 3D structural optimization.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"448 ","pages":"Article 118408"},"PeriodicalIF":7.3,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators","authors":"Ponkrshnan Thiagarajan ,&nbsp;Tamer A. Zaki ,&nbsp;Michael D. Shields","doi":"10.1016/j.cma.2025.118401","DOIUrl":"10.1016/j.cma.2025.118401","url":null,"abstract":"<div><div>Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. We show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118401"},"PeriodicalIF":7.3,"publicationDate":"2025-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 BDDC preconditioners for the bidomain model on unstructured ventricular finite element meshes","authors":"Talaat Abdelhamid ,&nbsp;Ngoc Mai Monica Huynh ,&nbsp;Stefano Zampini ,&nbsp;Rongliang Chen ,&nbsp;Luca F. Pavarino ,&nbsp;Simone Scacchi","doi":"10.1016/j.cma.2025.118366","DOIUrl":"10.1016/j.cma.2025.118366","url":null,"abstract":"<div><div>This study aims to develop and numerically analyze adaptive balancing domain decomposition by constraints (BDDC) preconditioners for unstructured finite element discretizations of the Bidomain model of electrocardiology on patient-specific ventricular geometries. The Bidomain model, one of the most comprehensive mathematical representations of the cardiac bioelectrical activity, consists of a system of an elliptic and a parabolic partial differential equation of reaction-diffusion type. These equations govern the propagation of electrical potentials in the cardiac tissue. They are strongly coupled with a stiff system of ordinary differential equations that describe the evolution of ionic currents across the cardiac cell membrane. Minimizing the computational cost of simulating this bioelectrical activity requires the development of efficient and scalable preconditioners for the linear systems resulting from the model’s discretization. BDDC preconditioners are nonoverlapping domain decomposition algorithms that consist of the solution of concurrent local problems on each subdomain plus a global coarse problem, whose unknowns are vertex and edge/face average values. Adaptive BDDC preconditioners represent an evolution of standard BDDC methods, where the coarse problem is enriched by adding further constraints obtained by solving suitable generalized eigenvalue problems on subdomain edges and faces. The novelty of the present study is to analyze the effectiveness of such adaptive BDDC methods for unstructured finite element discretizations of the Bidomain model on patient-specific left ventricular geometries, using modern high-performance computing parallel architectures. Different refined left ventricular meshes were generated, each incorporating fiber data. The results highlight the efficiency and accuracy of the implemented preconditioners, confirming their optimality and scalability on CPUs architectures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118366"},"PeriodicalIF":7.3,"publicationDate":"2025-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spectral-element SBPML for 3D infinite transient wave problems","authors":"Junru Zhang ,&nbsp;Mi Zhao ,&nbsp;Guoliang Zhang ,&nbsp;Junqi Zhang ,&nbsp;Xiuli Du","doi":"10.1016/j.cma.2025.118407","DOIUrl":"10.1016/j.cma.2025.118407","url":null,"abstract":"<div><div>This study develops a novel spectral-element scaled boundary perfectly matched layer (SBPML) coupled the spectral elements method (SEM) to simulate wave problems in 3D unbounded domains. The SBPML can accommodate boundary of general shapes and consider the planar physical interfaces and surfaces that extend infinitely. Furthermore, it supports direct coupling with 3D spectral elements of any orders in interior domain, leading to significantly higher computation accuracy. The spectral-element SBPML can flexibly and adaptively adjust the elements orders within the SBPML domain according to those used in the finite domain. Moreover, by generalizing the flexibility matrix, this method can model 3D transversely isotropic (TI) unbounded media, thereby enhancing its applicability to realistic geological scenarios. Firstly, quadrilateral spectral element shape functions are introduced in the circumferential direction of scaled boundary coordinates, which is compatible with 3D spectral elements of any orders of the finite domain. Subsequently, a complex coordinate stretching function is introduced along the radial direction, transforming the unbounded domain into a complex-valued space that defines the SBPML domain. This SBPML formulation employs a 2nd-order mixed unsplit-field displacement-stress form via spatial discretization of the SBPML domain. This mixed element is formulated by using shape functions of an <em>n</em>-th order spectral element for the displacement field and an (<em>n</em>-1)-th order element for the auxiliary stress field. This method allows for the use of different interpolation orders along the radial and circumferential directions in SBPML, achieving an optimal balance between numerical accuracy and computational efficiency. Ultimately, the accuracy, convergence, and robustness of the proposed approach are validated by three wave propagation problems and two seismic response analyses of complex sites.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118407"},"PeriodicalIF":7.3,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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-motivated geometric method for overheating prevention in topology optimization for additive manufacturing","authors":"Manabendra Nath Das ,&nbsp;Rajit Ranjan ,&nbsp;Kai Wu ,&nbsp;Jun Wu ,&nbsp;Can Ayas","doi":"10.1016/j.cma.2025.118363","DOIUrl":"10.1016/j.cma.2025.118363","url":null,"abstract":"<div><div>Designs generated by topology optimization are often geometrically too complex for conventional manufacturing techniques. While additive manufacturing holds promise for producing such complex designs, several manufacturability constraints must be addressed, including overhang and overheating. Unlike the well-studied overhang constraints, which can be described geometrically, overheating lacks a straightforward and reliable geometric characterization and therefore requires thermal process simulations to identify regions prone to it. However, these simulations are computationally expensive and thus unsuitable for topology optimization, which involves numerous design evaluations. This paper proposes a computationally efficient alternative for detecting zones prone to overheating. The key idea is to estimate local thermal conductivity—and thereby potential overheating—by analyzing the local material distribution. This geometric approach provides a physically motivated approximation of thermal behavior. The method is then integrated into topology optimization, resulting in optimized structures that exhibit clear heat conduction paths to the baseplate. Comparisons with high-fidelity thermal simulations demonstrate the effectiveness and efficiency of the proposed method in mitigating overheating in topology optimization.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118363"},"PeriodicalIF":7.3,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite deformation analysis of flexoelectric shells","authors":"Farzam Dadgar-Rad ,&nbsp;Shahab Sahraee ,&nbsp;Mokarram Hossain ,&nbsp;Stefan Hartmann","doi":"10.1016/j.cma.2025.118384","DOIUrl":"10.1016/j.cma.2025.118384","url":null,"abstract":"<div><div>In this work, a nonlinear shell model for the coupled mechanical and electrical analysis of thin flexoelectric polymers is developed. In addition to the classical terms, contributions from the second gradient of deformation, electro-mechanical coupling and flexoelectricity are incorporated into the free energy density of these materials. Furthermore, starting from a variational framework, a nonlinear finite element formulation in the material setting is developed to provide numerical solutions for various problems. By neglecting the electrical and flexoelectric effects, the present formulation can reflect the deformation of purely mechanical gradient shells. Conversely, by disregarding the gradient and flexoelectric effects, the present formulation is greatly capable of modeling the deformation of electro-active shells. The midsurface displacement and director difference vectors are interpolated using <span><math><msup><mi>C</mi><mn>1</mn></msup></math></span> shape functions, while <span><math><msup><mi>C</mi><mn>0</mn></msup></math></span>-continuous interpolation functions are used for the thickness stretching and voltage parameters. Several numerical examples are solved to evaluate performance and robustness of the proposed formulation. The results show that the present formulation yields excellent agreement with those available in the literature. Moreover, the proposed formulation effectively captures the flexoelectric response of both initially flat and initially curved thin structures experiencing finite deformations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118384"},"PeriodicalIF":7.3,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symplectic Hamiltonian hybridizable discontinuous Galerkin methods for linearized shallow water equations","authors":"Cristhian Núñez ,&nbsp;Manuel A. Sánchez","doi":"10.1016/j.cma.2025.118383","DOIUrl":"10.1016/j.cma.2025.118383","url":null,"abstract":"<div><div>This paper focuses on the numerical approximation of the linearized shallow water equations using hybridizable discontinuous Galerkin (HDG) methods, leveraging the Hamiltonian structure of the evolution system. First, we propose an equivalent formulation of the equations by introducing an auxiliary variable. Then, we discretize the space variables using HDG methods, resulting in a semi-discrete scheme that preserves a discrete version of the Hamiltonian structure. The use of an alternative formulation with the auxiliary variable is crucial for developing the HDG scheme that preserves this Hamiltonian structure. The resulting system is subsequently discretized in time using symplectic integrators, ensuring the energy conservation of the fully discrete scheme. We present numerical experiments that demonstrate optimal convergence rates for all variables and showcase the conservation of total energy, as well as the evolution of other physical quantities.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118383"},"PeriodicalIF":7.3,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}