《国际工程数值方法杂志》发表了原创论文，描述了适用于工程问题的数值方法的重大、新颖的发展。该杂志以欢迎在计算工程广泛领域的贡献而闻名，包括模型简化中的计算问题，不确定性量化、验证和确认、逆分析和随机方法、优化、元素技术、求解技术和并行计算、损伤和断裂、微观和纳米尺度力学、低速流体动力学、流固耦合、电磁学、耦合扩散现象，以及误差估计和网格生成。需要强调的是，这绝不是一份详尽的清单，尤其欢迎有关多尺度、多物理或多学科问题以及新兴主题的论文。

The International Journal for Numerical Methods in Engineering publishes original papers that describe significant and novel developments in numerical methods applicable to engineering problems. The journal is known for welcoming contributions across a wide range of computational engineering fields, including computational issues in model simplification, uncertainty quantification, validation and verification, inverse analysis and stochastic methods, optimization, element techniques, solution techniques and parallel computing, damage and fracture, micromechanics and nanomechanics, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, as well as error estimation and mesh generation. It is important to emphasize that this is by no means an exhaustive list, and papers on multiscale, multiphysics, or interdisciplinary issues, as well as emerging topics, are especially encouraged.

《International Journal for Numerical Methods in Engineering》发表原创论文，介绍适用于工程问题的数值方法的重大和新颖发展。该杂志以欢迎计算工程广泛领域的贡献而闻名，包括模型简化中的计算问题、不确定性量化、验证与确认、逆分析和随机方法、优化、元素技术、求解技术与并行计算、损伤与断裂、微观和纳米尺度力学、低速流体动力学、流固耦合、电磁学、耦合扩散现象，以及误差估计和网格生成。需要强调的是，这并不是一份详尽的清单，尤其欢迎有关多尺度、多物理或多学科问题以及新兴主题的论文。

International Journal for Numerical Methods in Engineering

A new method, termed autoprogressive training, for training neural networks to learn complex stress–strain behaviour of materials using global load–deflection response measured in a structural test is described. The richness of the constitutive information that is generally implicitly contained in the results of structural tests may in many cases make it possible to train a neural network material model from only a small number of such tests, thus overcoming one of the perceived limitations of a neural network approach to modelling of material behaviour; namely, that a voluminous amount of material test data is required. The method uses the partially-trained neural network in a central way in an iterative non-linear finite element analysis of the test specimen in order to extract approximate, but gradually improving, stress–strain information with which to train the neural network. An example is presented in which a simple neural network constitutive model of a T300/976 graphite/epoxy unidirectional lamina is trained, using the load–deflection response recorded during a destructive compressive test of a [(±45)6]S laminated structural plate containing an open hole. The results of a subsequent forward analysis are also presented, in which the trained material model is used to simulate the response of a compressively loaded [(±30)6]S structural laminate containing an open hole. Avenues for further improvement of the neural network model are also suggested. The proposed autoprogressive algorithm appears to have wide application in the general area of Non-Destructive Evaluation (NDE) and damage detection. Most NDE experiments can be viewed as structural tests and the proposed methodology can be used to determine certain damage indices, similar to the way in which constitutive models are determined. © 1998 John Wiley & Sons, Ltd.

Jamshid Ghaboussi

David A. Pecknold

Mingfu Zhang

Rami M. Haj-Ali

Autoprogressive training of neural network constitutive models

神经网络本构模型的自回归训练

Abstract The present paper is concerned with the layout optimization of resonating actuators using topology optimization techniques. The goal of the optimization is a maximization of the magnitude of steady‐state vibrations for a given excitation frequency. The problem formulation includes an external viscous damper at the output port which models a working load on the structure. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Dmitri Tcherniak

Int. J. Numer. Meth. Engng.

Topology optimization of resonating structures using SIMP method

使用SIMP方法的共振结构拓扑优化

Abstract A new method for non‐linear programming in general and structural optimization in particular is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and solved. The generation of these subproblems is controlled by so called ‘moving asymptotes’, which may both stabilize and speed up the convergence of the general process.

Krister Svanberg

Numerical Meth Engineering

The method of moving asymptotes—a new method for structural optimization

移动渐近线法——一种新的结构优化方法

Summary This paper will propose a more effective and efficient topology optimization method based on isogeometric analysis, termed as isogeometric topology optimization (ITO), for continuum structures using an enhanced density distribution function (DDF). The construction of the DDF involves two steps. (1) Smoothness: the Shepard function is firstly utilized to improve the overall smoothness of nodal densities. Each nodal density is assigned to a control point of the geometry. (2) Continuity: the high‐order NURBS basis functions are linearly combined with the smoothed nodal densities to construct the DDF for the design domain. The nonnegativity, partition of unity, and restricted bounds [0, 1] of both the Shepard function and NURBS basis functions can guarantee the physical meaning of material densities in the design. A topology optimization formulation to minimize the structural mean compliance is developed based on the DDF and isogeometric analysis to solve structural responses. An integration of the geometry parameterization and numerical analysis can offer the unique benefits for the optimization. Several 2D and 3D numerical examples are performed to demonstrate the effectiveness and efficiency of the proposed ITO method, and the optimized 3D designs are prototyped using the Selective Laser Sintering technique.

Jie Gao

Liang Gao

Zhen Luo

Peigen Li

Isogeometric topology optimization for continuum structures using density distribution function

使用密度分布函数对连续体结构进行等几何拓扑优化的研究

Abstract A stabilized conforming nodal integration scheme is implemented in the natural neighbour method in conjunction with non‐Sibsonian interpolation. In this approach, both the shape functions and the integration scheme are defined through use of first‐order Voronoi diagrams. The method illustrates improved performance and significant advantages over previous natural neighbour formulations. The method also shows substantial promise for problems with large deformations and for the computation of higher‐order gradients. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Jeong Wahn Yoo

Brian Moran

Jiun‐Shyan Chen

Stabilized conforming nodal integration in the natural‐element method

自然单元法中的稳定协调节点积分

ABSTRACT The traditional approach to structural lightweight optimization design, which is based on the elastic limit rule, often results in a structure that exhibits either weight redundancy or strength redundancy to some extent. This study introduces a novel integration of shakedown analysis with structural topology optimization, departing from the conventional elastic limit rule. Shakedown analysis identifies a non‐failure external load region beyond the elastic limit but below the plastic limit, independent of loading history. The proposed method, for the first time, accounts for the influence of self‐equilibrium residual stress at the element level, redefining effective and ineffective elements in topology optimization. Shakedown total stress replaces elastic equivalent stress, offering a comprehensive measure. Utilizing Melan's lower bound theorem, a gradient‐based topology optimization framework for shakedown analysis is developed, ensuring structures stay within the elastic–plastic range, preventing excessive plastic deformation. The approach, employing the moving asymptotes method after adjoint sensitivity analysis of shakedown total stress, is applied to a three‐dimensional L‐shaped bracket. Even with a remarkable 50% reduction in weight, the maximum total shakedown stress of the bracket reveals that it only increases by a modest 17.20% from its initial value. Moreover, compared to traditional topology optimization methods based on either elastic stress or stiffness, the proposed method based on total shakedown stress leads to a higher shakedown limit. Specifically, the configuration designed using the total shakedown stress exhibited increases of 2.01% and 9.82% in the shakedown limit compared to those obtained using stiffness and equivalent elastic stress, respectively. This suggests that the proposed method can effectively balance the trade‐off between shakedown strength and structural stiffness, achieving a 2.01% rise in shakedown strength with only a 2.24% compromise in structural stiffness. These findings highlight the method's effectiveness and potential, emphasizing the benefit of redefining effective and ineffective elements using shakedown stress in topology optimization.

Songhua Huang

Lele Zhang

Geng Chen

Yugong Xu

Min Chen

Zhiyuan Liu

Eng Gee Lim

Topology Optimization of Elastoplastic Structure Based on Shakedown Strength

基于安定强度的弹塑性结构拓扑优化

ABSTRACT Smoothed Finite Element Method (S‐FEM) has been widely used in many engineering simulations. However, there are still a lot of theoretical problems to be solved, especially with regard to composite materials and convergence proof. Based on a novel least‐squares approximation and conservation property, we extend S‐FEM to heterogeneous materials. Firstly, the orthogonality, Softening Effect, and energy function are checked. Secondly, the interpolation error in the maximum norm is estimated in any dimension. Consequently, we get a theoretical convergence rate which has been sought since the year 2010. When restricted to one‐dimensional problems, we construct a special test function to prove the superconvergence: (1) S‐FEM flux is exact in the meaning of element‐wise integral; (2) numerical flux is exact at some point in each element; (3) physical flux can be quadratically approximated at the center of each element. At last, we present two numerical experiments: (1) conventional S‐FEM fails in high‐contrast composite materials while our new scheme performs well; (2) our flux converges quadratically.

Yun Chen

Guirong Liu

Junzhi Cui

Qiaofu Zhang

Ziqiang Wang

Heterogeneous Smoothed Finite Element Method: Convergence/Superconvergence Proof and Its Performance in High‐Contrast Composite Materials

异质平滑有限元法：收敛/超收敛证明及其在高对比度复合材料中的性能

ABSTRACT We present a novel method for generating sequential parameter estimates and quantifying epistemic uncertainty in dynamical systems within a data‐consistent (DC) framework. The DC framework differs from traditional Bayesian approaches due to the incorporation of the push‐forward of an initial density, which performs selective regularization in parameter directions not informed by the data in the resulting updated density. This extends a previous study that included the linear Gaussian theory within the DC framework and introduced the maximal updated density (MUD) estimate as an alternative to both least squares and maximum a posterior (MAP) estimates. In this work, we introduce algorithms for operational settings of MUD estimation in real‐ or near‐real time where spatio‐temporal datasets arrive in packets to provide updated estimates of parameters and identify potential parameter drift. Computational diagnostics within the DC framework prove critical for evaluating (1) the quality of the DC update and MUD estimate and (2) the detection of parameter value drift. The algorithms are applied to estimate (1) wind drag parameters in a high‐fidelity storm surge model, (2) thermal diffusivity field for a heat conductivity problem, and (3) changing infection and incubation rates of an epidemiological model.

Carlos del‐Castillo‐Negrete

Rylan Spence

Troy Butler

Clint Dawson

Sequential Maximal Updated Density Parameter Estimation for Dynamical Systems With Parameter Drift

动态系统参数漂移的顺序最大更新密度参数估计

ABSTRACT This article investigates the use of the block low rank (BLR) factorization, recently proposed in the MUMPS solver, to define efficient and cheap preconditioners for primal domain decomposition methods, such as the Balancing Domain Decomposition method (BDD) and its adaptive multipreconditioned variant. To be scalable, these methods are equipped with an augmentation projector built from the local preconditioners nullspaces. The determination of these nullspaces is a complex task in the case of ill conditioned system, the use of block low rank compression makes this task even more complex as MUMPS' automatic detection no longer works properly. Two alternatives based on incomplete factorization with a well‐chosen Schur complement are proposed. Also, the first massively parallel implementation of the adaptive multipreconditioned BDD solver (AMPBDD) is introduced. The performance of the methods is assessed with two weak scalability studies on problems up to 24,576 cores and about 790 millions of unknowns, on the Sator and Topaze supercomputers. BLR preconditioning proves to be an interesting strategy both in terms of memory usage and time to solution for reasonably conditioned problems.

Christophe Bovet

Théodore Gauthier

Pierre Gosselet

On the Use of Block Low Rank Preconditioners for Primal Domain Decomposition Methods

关于原始域分解方法中块低秩预处理器的应用

ABSTRACT The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high‐dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. To enhance robustness against noise, we incorporate the weak‐form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak‐form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent‐space dynamics of high‐dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced‐order modeling. Furthermore, the greedy physics‐informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time‐dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10 Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7 relative errors. Compared with the high‐fidelity models, WgLaSDI achieves 121 to 1779 speed‐up.

Xiaolong He

April Tran

David M. Bortz

Youngsoo Choi

Physics‐Informed Active Learning With Simultaneous Weak‐Form Latent Space Dynamics Identification

物理信息引导的主动学习与同时弱形式潜在空间动力学识别

Abbreviation	Int. J. Numer. Meth. Engng.
Journal Impact	2.87
Quartiles(Global)	MATHEMATICS, INTERDISCIPLINARY APPLICATIONS(Q1)

ISSN	0029-5981, 1097-0207
h-index	194

Publication Information	Publisher: John Wiley and Sons Ltd，Publishing cycle: Weekly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 1969，Proportion of original research papers: 99.18%，Self Citation Rate:7.40%， Gold OA Rate: 26.19%
Average review cycle	网友分享经验：平均6.0个月
Average recruitment ratio	网友分享经验：较易

International Journal for Numerical Methods in Engineering

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