Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"DR-PDEE-based probabilistic response analysis for high-dimensional nonlinear dynamical systems under general non-white and non-stationary random excitations via constructing the auxiliary diffusion process","authors":"T.-T. Sun ,&nbsp;J.-B. Chen ,&nbsp;Y. Luo ,&nbsp;J.H. Lyu","doi":"10.1016/j.cma.2025.118029","DOIUrl":"10.1016/j.cma.2025.118029","url":null,"abstract":"<div><div>Accurately analyzing the probabilistic responses of high-dimensional nonlinear dynamical structures subjected to non-white and non-stationary stochastic excitations is a critical and challenging task. To address this issue, an efficient stochastic response analysis method is proposed by constructing an auxiliary diffusion process related to the non-white and non-stationary excitation process and incorporating it into the dimension-reduced probability density evolution equation (DR-PDEE). In the proposed method, the non-white stochastic excitation is represented through a spectral process with independent increments, and a white noise process associated with the excitation is constructed by modulating the amplitude of this spectral process to be a constant over the frequency domain. Subsequently, an auxiliary diffusion process is built by setting its governing equation driven by the constructed white noise, which guarantees that the auxiliary diffusion process has a non-zero intrinsic diffusion function and is correlated with the system response. The probability density function (PDF) of the response of interest for a high-dimensional nonlinear system can then be immediately obtained by solving the two-dimensional DR-PDEE, which governs the joint PDF of the response quantity and the constructed auxiliary diffusion process. The intrinsic drift functions in the DR-PDEE are expressed as the first-order conditional derivate moments, and a numerical scheme is developed to determine these terms based on the data from representative response trajectories. The proposed method guarantees that there are non-zero intrinsic diffusion functions in the corresponding DR-PDEE, which is realized without requiring a linear filter to simulate the non-white excitation from white noise, thus providing a broader scope of application. Several numerical examples, including linear and nonlinear multi-degree-of-freedom (MDOF) systems, are studied to illustrate the effectiveness of the proposed method. The stochastic excitations in these systems include stationary processes with power spectral densities (PSDs) that cannot be expressed as rational functions, as well as non-stationary processes characterized by the non-uniformly modulated evolutionary PSD (EPSD) model.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118029"},"PeriodicalIF":6.9,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903997","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 novel implicit cell-based material point method with particle boundaries and its application to contact problems","authors":"Jae-Uk Song,&nbsp;Hyun-Gyu Kim","doi":"10.1016/j.cma.2025.118067","DOIUrl":"10.1016/j.cma.2025.118067","url":null,"abstract":"<div><div>In this paper, an implicit cell-based material point method (MPM) with particle boundaries is proposed to effectively solve large deformation static problems. The volume integrals of the incremental weak form based on an updated Lagrangian approach are evaluated at integration points defined by equally sub-dividing grid cells, which eliminates the cell-crossing error and reduces the integration error in solving problems with particles not aligned with a background grid. A level set function based on the particle volume is used to define a particle boundary. The number of integration points of the boundary grid cells intersected by the particle boundary is increased to more accurately perform the numerical integration of the incremental weak form over the boundary grid cells. The present method is applied to solve contact problems of two bodies discretized by particles. Contact between particles is detected using the level set values ​​at the integration points of the boundary grid cells. The surface integral of the contact weak form is replaced by a volume integral in the contact penetration domain. Numerical results show that large deformation contact problems can be effectively solved by the implicit cell-based MPM with particle boundaries.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118067"},"PeriodicalIF":6.9,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903998","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":"Second-order computational homogenization of flexoelectric composites with isogeometric analysis","authors":"Bin Li ,&nbsp;Ranran Zhang ,&nbsp;Krzysztof Kamil Żur ,&nbsp;Timon Rabczuk ,&nbsp;Xiaoying Zhuang","doi":"10.1016/j.cma.2025.118031","DOIUrl":"10.1016/j.cma.2025.118031","url":null,"abstract":"<div><div>Flexoelectricity is an electromechanical coupling phenomenon in which electric polarization is generated in response to strain gradients. This effect is size-dependent and becomes increasingly significant at micro- and nanoscale dimensions. While heterogeneous flexoelectric materials demonstrate enhanced electromechanical properties, their effective application in nanotechnology requires robust homogenization methods. In this study, we propose a novel second-order computational homogenization framework for flexoelectricity, which combines isogeometric analysis and the finite cell method. Key innovations include the introduction of high-order periodic boundary conditions and homogenized high-order stresses, which ensure consistent multiscale analysis. Periodic boundary conditions are applied using penalty methods, and perturbation analysis is employed to efficiently compute equivalent material coefficients. The effectiveness of the proposed method is validated through numerical examples, demonstrating its ability to generate piezoelectric effects in flexoelectric microstructured materials.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118031"},"PeriodicalIF":6.9,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903999","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 stress-driven bi-level design method for variable radius Voronoi porous structures with enhanced mechanical performance","authors":"Bin Liu,&nbsp;Longcheng Cai,&nbsp;Wei Cao,&nbsp;Ping Lu","doi":"10.1016/j.cma.2025.118063","DOIUrl":"10.1016/j.cma.2025.118063","url":null,"abstract":"<div><div>Porous structures have gained widespread applications in aerospace, biomedical, and other fields due to their lightweight, high specific strength, and energy absorption properties. However, existing gradient design methods for Voronoi porous structures predominantly rely on iterative optimization and explicit modeling, which suffer from high computational costs, insufficient precision in local density control, and stress concentration at strut junctions. To address these challenges, this study proposes a stress-driven bi-level design method for three-dimensional variable radius Voronoi strut structures, enabling precise control of relative density distribution through macroscopic-global and cellular-local synergistic regulation. At the macroscopic level, finite element analysis (FEA) is employed to obtain stress distributions, and a weighted random sampling strategy is implemented to regulate Voronoi site distribution, thereby generating an initial constant-radius strut structure. At the cellular level, a stress-relative density mapping function is constructed, and weighting factors are embedded into an implicit surface potential energy model to dynamically adjust strut radius, achieving adaptive optimization of local density. The proposed method leverages implicit surface modeling to circumvent geometric discontinuities caused by explicit Boolean operations, ensuring smooth transitions in variable radius struts. FEA and mechanical experiments demonstrate that, compared to constant radius structures with random sites, the variable radius structure designed in this work reduces the maximum von Mises stress by 53.8 %, enhances three-point bending load capacity by 42.3 %, and significantly diminishes failure regions under identical porosity conditions. This approach provides an efficient and high-precision solution for lightweight component design under complex loading scenarios, with experimental validation confirming its effectiveness in improving material utilization and stress uniformity.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118063"},"PeriodicalIF":6.9,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898696","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 machine-learning enabled digital-twin framework for tactical drone-swarm design","authors":"T.I. Zohdi","doi":"10.1016/j.cma.2025.117999","DOIUrl":"10.1016/j.cma.2025.117999","url":null,"abstract":"<div><div>The goal of this work is to develop a machine-learning enabled digital-twin to rapidly ascertain optimal programming to achieve desired tactical multi-drone swarmlike behavior. There are two main components of this work. The <em>first main component</em> is a framework comprised of a multibody dynamics model for multiple interacting agents, augmented with a machine-learning paradigm that is based on the capability of agents to identify (a) desired targets, (b) obstacles and (c) fellow agents, as well as the resulting collective actions of the drone-swarm of agents. The objective is to construct a system with entirely autonomous behavior by optimizing the actuation parameter values that are embedded within the coupled multibody differential equations for drone-swarm dynamics. This is achieved by minimizing a cost-error function that represents the difference between the simulated overall group behavior and in-field behavior from observed <em>ground truth</em> synthetic data in the form of temporal snapshots corresponding to multiple camera frames. The <em>second main component</em> of the analysis is to deeply assess the structural performance of drone-swarm members, by studying chassis design, deployment and dynamic-structural performance. As an example, we investigate a tactical quadcopter drone under attack, specifically by subjecting it to series of launched explosions. A Discrete Element Method (DEM) is developed to rapidly design a quadcopter of any complex shape, attach motors and then to subject it to a hostile environment, in order to ascertain its performance. The method also allows one to describe structural damage to the quadcopter drone, its loss of functionality (thrust), etc. Furthermore, the use of DEM can also capture fragmentation of the quadcopter and can ascertain the resulting debris field. Numerical examples are provided to illustrate the two components of the overall model, the computational algorithm and its ease of implementation.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 117999"},"PeriodicalIF":6.9,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143894676","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":"CFGLSs: Conformal filling gradient lattice structures designed by multiscale isogeometric topology optimization for 3D swept volume","authors":"Sheng Zhou ,&nbsp;Ran Tao ,&nbsp;Qidong Sun","doi":"10.1016/j.cma.2025.118023","DOIUrl":"10.1016/j.cma.2025.118023","url":null,"abstract":"<div><div>3D swept volume, enabled by advancements in additive manufacturing, present new opportunities for lightweight and functional optimization. However, efficient design methodologies for conformal filling gradient lattice structures (CFGLSs) remain scarce. This paper proposes a modified level set function (MLSF) that matches lattice structures to the geometry of 3D swept volume. Furthermore, a multiscale isogeometric topology optimization (MITO) approach is used to adaptively optimize the distribution of graded lattices, ensuring optimal integration. A surrogate constitutive model is developed using polynomial interpolation in conjunction with the MLSF and the homogenization method. Incorporating the surrogate constitutive model into the MITO, the relative density distribution of the swept volume is obtained. Continuous CFGLSs are generated using the updated MLSF method, with the equivalent density distribution guiding the simultaneous optimization of both the micro-scale lattice geometry and its macro-scale distribution. The proposed approach is validated through the design, fabrication, and experimental evaluation of semi-circular specimens and engineering rudders, exhibiting its effectiveness and practicality.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118023"},"PeriodicalIF":6.9,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143886866","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":"An isogeometric assumed natural strain method to alleviate locking in solid beams","authors":"Alessia Patton ,&nbsp;Leonardo Leonetti ,&nbsp;Josef Kiendl","doi":"10.1016/j.cma.2025.118024","DOIUrl":"10.1016/j.cma.2025.118024","url":null,"abstract":"<div><div>This work proposes a novel Isogeometric Analysis (IGA) extension of the assumed natural strain (ANS) method to alleviate locking phenomena in solid beams, which are modeled as 3D elements accounting for displacement degrees of freedom solely and designed such that accurate analyses can be generally obtained using only one element to discretize the structure’s cross-section. ANS methods substitute covariant compatible strains that cause locking in solid beams, when, e.g., constrained to be thin, with a so-called assumed strain field. Namely, the compatible strains are interpolated at suitable locations, termed tying points, and the assumed strains are then derived using an <em>ad hoc</em> element-based extrapolation. This local operation involves, in principle, the inversion of extrapolation matrices; yet, these quantities can be computed at once and in closed form, using a linear extrapolation in the quadratic case, without needing any inversion operation. The introduced IGA ANS technique, specifically tailored to mitigate membrane and shear locking, given the superior geometric approximation provided by the adopted IGA framework, as well as the high regularity of the utilized computer-aided design basis functions, is also able to naturally alleviate thickness and curvature-thickness locking phenomena and its effectiveness is proven through extensive numerical testing.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118024"},"PeriodicalIF":6.9,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891334","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":"The Aggregated Material Point Method (AgMPM)","authors":"William M. Coombs,&nbsp;Robert E. Bird,&nbsp;Giuliano Pretti","doi":"10.1016/j.cma.2025.118012","DOIUrl":"10.1016/j.cma.2025.118012","url":null,"abstract":"<div><div>The Material Point Method (MPM) has been shown to be an effective approach for analysing large deformation processes across a range of physical problems. However, the method suffers from a number of spurious artefacts, such as a widely documented cell crossing instability, which can be mitigated by adopting basis functions with higher order continuity. The larger stencil of these basis functions exacerbate a less widely discussed issue - <em>small cuts</em>. The small cut issue is linked to the arbitrary interaction between the physical body and the background mesh that is used to assemble and solve the governing equations in the MPM. There is the potential for degrees of freedom near the boundary of the body to have very small contributions from material points, which causes two problems: (i) artificially large accelerations/displacements at the boundary and (ii) ill conditioning of the global linear system. This paper provides a new mesh Aggregated MPM, or AgMPM, that mitigates the small cut issue by forming aggregated elements, tying the ill-behaved degrees of freedom to well posed interior elements. Implicit quasi-static and explicit dynamic formulations are provided and demonstrated through a series of numerical examples. The approach does not introduce any new numerical parameters and can be applied to implementations that adopt a lumped mass matrix. Aggregation is shown to significantly improve the stability of implicit implementations of the MPM, often at a lower computational cost compared to standard, non-aggregated, implementations. The technique improves the energy conservation and the stress field of explicit dynamic MPMs.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118012"},"PeriodicalIF":6.9,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891275","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":"Asymptotic homogenization-based strain gradient elastodynamics: Governing equations, well-posedness and numerical examples","authors":"Quanzhang Li ,&nbsp;Yipeng Rao ,&nbsp;Zihao Yang ,&nbsp;Junzhi Cui ,&nbsp;Meizhen Xiang","doi":"10.1016/j.cma.2025.118010","DOIUrl":"10.1016/j.cma.2025.118010","url":null,"abstract":"<div><div>We develop a strain gradient elastodynamics model for heterogeneous materials based on the two-scale asymptotic homogenization theory. Utilizing only the first-order cell functions, the present model is more concise and more computationally efficient than previous works with high-order truncations. Furthermore, we rigorously prove that the coefficient tensors, including the homogenized elasticity tensor, the strain gradient stiffness tensor, and the micro-inertial tensor are symmetric positive definite, thereby establishing the well-posedness of the strain gradient elastodynamics model, i.e., the existence and uniqueness of solutions. Numerical simulations are performed to confirm the theoretical findings and illustrate the characteristics of the present model in comparison with classical elastodynamics model (without strain gradient terms) and strain gradient models with higher-order truncations. The results indicate that the strain gradient model derived based on the first-order truncation can achieve an optimal balance between accuracy and computational cost.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118010"},"PeriodicalIF":6.9,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143882308","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":"An efficient discrete physics-informed neural networks for geometrically nonlinear topology optimization","authors":"Jichao Yin ,&nbsp;Shuhao Li ,&nbsp;Yaya Zhang ,&nbsp;Hu Wang","doi":"10.1016/j.cma.2025.118043","DOIUrl":"10.1016/j.cma.2025.118043","url":null,"abstract":"<div><div>The application of geometrically nonlinear topology optimization (GNTO) poses a substantial challenge due to the extensive memory requirements and prohibitive computational demands involved. To tackle this challenge, a discrete physics-informed neural network (dPINN) is suggested as a promising approach to alleviate computational demands and enhance the applicability to large-scale problems. In comparison to collocation point-based PINNs, the most distinctive characteristic of dPINN is its mesh-based local interpolation for the evaluation of the system energy. This approach not only circumvents the issue of material mapping between elements and collocation points, but also provides improved robustness. Moreover, the partial differential equation (PDE) that corresponds to the adjoint equations lacks explicit expressions. The dPINN is capable of naturally evaluating equivalent energy through discrete expressions, a capability that collocation point-based PINNs lack. Furthermore, the activation state of sub-networks in series is determined in accordance with the density variation, thereby saving computational costs by dynamically incorporating each sub-network to reduce the trainable parameters in certain optimization steps, while conserving computational resources. The dPINN demonstrates exceptional accuracy and efficiency, along with enhanced resilience against mesh distortion compared to the finite element method (FEM), thereby enabling the application of larger loads. The dPINN-based GNTO is validated to be robust with regard to different geometries, loads, and volume fractions through several examples, and the outcomes are largely consistent with those of the FEM-based approach. Of greater significance is the fact that dPINN is capable of solving a million-DOFs 3D GNTO problem, which represents a notable advantage.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118043"},"PeriodicalIF":6.9,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878823","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}