Finite Elements in Analysis and Design最新文献_第6页

A simplified gradient-enhanced damage model based on energy limiters for crack propagation under time-dependent loading 基于能量限制器的时效加载下裂纹扩展梯度增强损伤简化模型

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-13 DOI: 10.1016/j.finel.2025.104443

Hung Thanh Tran

This paper presents the development and investigation of a simplified energy limiter-based nonlocal damage model for dynamic crack propagation in brittle media. The key idea underlying the proposed model is that crack growth under impact loading is primarily influenced by the tensile component of the strain tensor. Consequently, the energy-based damage-driving term is simplified to a strain-based counterpart, which is integrated using the first principal strain. This simplification leads to a model that is not only easier to implement but also more effective in capturing dynamic crack propagation compared to the original theory. In addition, the computational framework incorporates an energy limiter-based gradient damage formulation with a damage threshold, enabling natural crack initiation and propagation while significantly reducing spurious damage. One of the distinctive features of the proposed approach is the treatment of the nonlocal crack field as a primary unknown, alongside displacements. This allows the use of identical shape functions for both fields within the finite element analysis, enhancing consistency and computational efficiency. Consistent with classical continuum damage mechanics, the model can accurately simulate arbitrary and complex multiple crack paths, including three-dimensional (3D) crack propagation. Furthermore, to provide a more efficient numerical framework under time-dependent loading conditions with complex crack patterns, an explicit dynamic fracture algorithm is employed. This algorithm utilizes the central difference method, the row-sum technique for mass lumping, and a consistent procedure for updating the kinematic and damage-related terms. The advantages and modeling capabilities of the proposed strain-based gradient-enhanced damage formulation are demonstrated through representative numerical examples of dynamic fracture under shear, tension, and compression loading scenarios.

本文提出了一种基于能量限制器的脆性介质动态裂纹扩展非局部损伤简化模型。提出的模型的关键思想是，裂纹在冲击载荷下的扩展主要受应变张量的拉伸分量的影响。因此，基于能量的损伤驱动项被简化为基于应变的对应项，并使用第一主应变进行积分。与原始理论相比，这种简化导致的模型不仅更容易实现，而且在捕获动态裂纹扩展方面也更有效。此外，该计算框架结合了一个基于能量限制器的梯度损伤公式，该公式具有损伤阈值，可以实现自然裂纹的起始和扩展，同时显着减少虚假损伤。该方法的一个显著特点是将非局部裂纹场与位移一起作为主要未知数处理。这允许在有限元分析中对两个领域使用相同的形状函数，增强一致性和计算效率。该模型与经典连续介质损伤力学一致，能够准确模拟任意复杂的多重裂纹路径，包括三维裂纹扩展。此外，为了在具有复杂裂纹模式的时变加载条件下提供更有效的数值框架，采用了显式动态断裂算法。该算法利用中心差分法、行和技术进行质量集总，并采用一致的程序更新运动学和损伤相关项。通过具有代表性的剪切、拉伸和压缩加载情景下的动态断裂数值实例，证明了所提出的基于应变的梯度增强损伤公式的优势和建模能力。

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引用次数: 0

POD-RBF hyper-reduction method for fast finite element analysis of nonlinear dynamic problems 非线性动力问题快速有限元分析的POD-RBF超约简方法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-13 DOI: 10.1016/j.finel.2025.104455

Lam Vu-Tuong Nguyen, Hyun-Gyu Kim

This paper proposes a new hyper-reduction method for fast finite element analysis of nonlinear dynamic problems using proper orthogonal decomposition (POD) and radial basis function (RBF) interpolation. In the offline stage, displacement and internal force snapshots are collected from full-order FE simulations of nonlinear dynamic problems with training load cases. POD basis vectors are extracted from the displacement snapshots using the singular value decomposition (SVD). RBF coefficients for the internal force snapshots are also computed in the offline stage. The proposed POD-RBF hyper-reduction method efficiently estimates the reduced internal force vectors and the reduced tangent stiffness matrices using RBF interpolation with respect to reduced generalized coordinates. A snapshot selection strategy combining K-means clustering and greedy sampling algorithms is used to reduce the size of solution snapshots, which further enhances the efficiency of the present method. Numerical results show that the POD-RBF hyper-reduction method can be efficiently and effectively used to quickly solve nonlinear dynamic problems in a reduced-order space.

本文提出了一种利用正交分解和径向基函数插值的超约化方法，用于非线性动力问题的快速有限元分析。在离线阶段，从具有训练载荷的非线性动力问题的全阶有限元模拟中获取位移和内力快照。利用奇异值分解（SVD）从位移快照中提取POD基向量。在脱机阶段还计算了内力快照的RBF系数。提出的POD-RBF超约简方法利用RBF插值在广义约简坐标下有效地估计约简内力矢量和约简切刚度矩阵。采用k均值聚类和贪婪采样算法相结合的快照选择策略，减小了解快照的大小，进一步提高了方法的效率。数值结果表明，POD-RBF超约简方法可以高效、有效地快速求解降阶空间中的非线性动态问题。

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引用次数: 0

Sensitivity analysis of any hyperelastic evaluation functions coupled with adjoint method and automatic differentiation 结合伴随法和自动微分的超弹性评价函数敏感性分析

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-12 DOI: 10.1016/j.finel.2025.104440

S. Ogawa, K. Yonekura, K. Suzuki

This study introduces a new sensitivity analysis method for the topology optimization of a static hyperelastic material, which combines the adjoint variable method with automatic differentiation (AD). The adjoint variable method, frequently used in sensitivity analysis, requires mathematical formulations. Therefore, any changes in the design problem require reformulating the sensitivity analysis and updating the calculation program. The proposed method allows for the calculation of design sensitivities without being tied to specific evaluation functions, constitutive laws, or interpolation methods. This method effectively addresses the considerable memory requirements often associated with AD. To showcase the versatility of the proposed approach, we assessed both the compliance and the maximum von Mises stress of the second Piola–Kirchhoff stress tensor. We examined two hyperelastic materials: St. Venant-Kirchhoff, Neo-Hookean, and Mooney–Rivlin. For broader applicability, we used the discrete material optimization (DMO) method to address multimaterial problems, evaluating the adaptability in the interpolation of material properties based on the design variables. Through numerical examples, we validated the sensitivity analysis, analyzed the computational time and memory usage, and confirmed the efficacy of the proposed method. Examples involving two-dimensional problems highlight the practical application of this method in topology optimization.

提出了一种将伴随变量法与自动微分法相结合的静态超弹性材料拓扑优化灵敏度分析新方法。伴随变量法在灵敏度分析中经常使用，它需要数学公式。因此，设计问题的任何变化都需要重新制定灵敏度分析和更新计算程序。提出的方法允许计算设计灵敏度，而不需要绑定到特定的评估函数，本构律，或插值方法。这种方法有效地解决了通常与AD相关的大量内存需求。为了展示所提出方法的通用性，我们评估了第二Piola-Kirchhoff应力张量的顺应性和最大von Mises应力。我们研究了两种超弹性材料：St. Venant-Kirchhoff， Neo-Hookean和Mooney-Rivlin。为了更广泛的适用性，我们使用离散材料优化（DMO）方法来解决多材料问题，评估基于设计变量的材料性能插值的适应性。通过数值算例验证了灵敏度分析，分析了计算时间和内存使用情况，验证了所提方法的有效性。涉及二维问题的例子突出了该方法在拓扑优化中的实际应用。

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引用次数: 0

Geometric compensation of process-induced deformation in hybrid unidirectional/woven CFRP composites with multi-layup sequence using a physics-driven reverse deformation approach 基于物理驱动反向变形方法的复合材料过程变形几何补偿

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-11 DOI: 10.1016/j.finel.2025.104446

Dong-Hyeop Kim , Sang-Woo Kim

This study proposes a novel physics-based geometric compensation methodology to mitigate process-induced deformation (PID) in hybrid unidirectional/woven CFRP composite structures. Reverse deformation to compensate PID is induced by inverting the layup sequence, while the deformation magnitude is precisely adjusted using scaling factors, which are determined via fitting-based optimization and applied to thermochemical strain coefficients. The methodology is implemented through thermo-mechanical simulations using the finite element method, integrating cure-dependent material behavior, effective material properties, and thermal and chemical strains to accurately predict PID. The capability of the proposed methodology is demonstrated through extensive simulations of hybrid CFRP laminates, specifically incorporating multiple layup sequences and thickness configurations within a single laminate to reflect realistic structural design configurations encountered in composite manufacturing. In all simulation results, the optimized compensation reduced nodal displacements by more than 93%, resulting in significant improvements in both local and global geometric accuracy. The proposed methodology comprehensively considers complex cure-induced physical behaviors, enabling accurate, robust, and highly efficient nodal-level deformation compensation and providing practical applicability across a wide range of composite structures, including both unidirectional and textile-reinforced laminates.

本研究提出了一种新的基于物理的几何补偿方法来减轻单向/编织复合材料结构的过程诱导变形。通过反转铺层序列引起的逆变形补偿PID，通过基于拟合优化确定的比例因子精确调节变形大小，并将其应用于热化学应变系数。该方法是通过使用有限元方法进行热力学模拟来实现的，集成了固化相关材料行为，有效材料特性以及热应变和化学应变，以准确预测PID。所提出的方法的能力通过对混合CFRP层压板的广泛模拟得到了证明，特别是在单个层压板中结合了多个层叠序列和厚度配置，以反映复合材料制造中遇到的实际结构设计配置。在所有仿真结果中，优化后的补偿将节点位移减少了93%以上，从而显著提高了局部和全局几何精度。所提出的方法全面考虑了复杂的固化诱发的物理行为，实现了精确、鲁棒和高效的节点级变形补偿，并提供了广泛的复合材料结构的实际适用性，包括单向和纺织品增强层压板。

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引用次数: 0

Coupled crystal plasticity-cohesive zone modeling of rock salt viscoplasticity 岩盐粘塑性耦合晶体塑性-黏结区建模

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-09 DOI: 10.1016/j.finel.2025.104438

Nour Habib, Saber El Arem, Amine Ammar

Rock salt, owing to its viscoplastic behavior and structural integrity under high pressure, is a promising candidate for safe and large-scale underground energy storage. This study presents a comprehensive numerical framework for modeling the viscoplastic deformation of rock salt, accounting for both intragranular and grain boundary (GB) deformation mechanisms. Intragranular deformation is modeled using a crystal plasticity approach governed by a power-law relation, capturing the activity of crystallographic slip systems. Concurrently, a cohesive zone model (CZM) is introduced to simulate grain boundary sliding (GBS) and opening via a rate-dependent traction–separation law. This modeling strategy enables a detailed analysis of the coupled interplay between crystal plasticity and intergranular decohesion phenomena.

岩盐由于其在高压下的粘塑性特性和结构完整性，是安全、大规模地下蓄能的理想选择。本研究提出了一个综合的数值框架来模拟岩盐的粘塑性变形，同时考虑了粒内和晶界（GB）变形机制。使用幂律关系控制的晶体塑性方法来模拟晶内变形，捕捉晶体滑移系统的活动。同时，引入内聚带模型（CZM），通过速率相关的牵引分离规律来模拟晶界滑动（GBS）和打开。这种建模策略可以详细分析晶体塑性和晶间脱黏现象之间的耦合相互作用。

引用次数: 0

An expandable local and parallel two-grid finite element scheme for Stokes problem Stokes问题的可扩展局部并行双网格有限元格式

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-08 DOI: 10.1016/j.finel.2025.104375

Hongwei Song , Jianping Zhao , Yanren Hou

A novel locally parallel finite element algorithm for addressing the Stokes problem has been developed, leveraging the two-grid method and the unit splitting technique. This innovative algorithm boasts several key advantages: (1) it operates independently of the hyperapproximation property, enhancing its applicability across various scenarios; (2) the decomposition of regions is solely dependent on the unit splitting technique, simplifying the computational process; and (3) by incorporating constraints on local corrections, the algorithm employs the penalized form of the Stokes problem. This strategic choice facilitates the exclusive resolution of the velocity field function under specific assumptions, thereby streamlining the solution process and potentially reducing computational complexity.

利用双网格法和单元分裂技术，提出了一种求解Stokes问题的局部并行有限元算法。该创新算法具有以下几个关键优势：(1)它独立于超逼近性质运行，增强了其在各种场景中的适用性；(2)区域分解完全依赖于单元分裂技术，简化了计算过程；(3)通过对局部修正的约束，该算法采用Stokes问题的惩罚形式。这种策略选择有助于在特定假设下对速度场函数进行独家解析，从而简化求解过程并可能降低计算复杂性。

引用次数: 0

An efficient higher-order triangulation based micromechanical model for fiber composites 基于高阶三角剖分的纤维复合材料细观力学模型

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-07 DOI: 10.1016/j.finel.2025.104441

Jamal F. Husseini , Eric J. Carey , Evan J. Pineda , Brett A. Bednarcyk , Farhad Pourkamali-Anaraki , Scott E. Stapleton

Composite microstructures are susceptible to localized stress concentrations between close or touching fibers where failure can initiate and propagate. Typically, representative volume elements are used to predict mechanical response by simulating random microstructure arrangements under different loading configurations. However, these simulations can be prohibitively expensive when considering large microstructures or closely packed fibers. The current work aims to provide a computationally efficient method for predicting homogenized and local properties of composite microstructures through a novel finite element mesh referred to as the fixed triangulation-mesh model. This triangulation-based meshing algorithm uses configured element sizes where the highest stresses occur and higher order elements to capture stress gradients between closely packed fibers. An efficient homogenization technique to fully characterize the stiffness matrix of the composite without the need for individual load perturbations or stress integration was derived and implemented. A progressive damage model using the smeared crack approach was implemented with higher order elements to simulate post-peak softening. The results for stiffness, transverse strength, and in-plane shear strength were verified against the high fidelity generalized method of cells for different microstructures of varying fiber volume fractions. Then, a comparison was made to a refined mesh finite element model with linear elements and a toughened matrix. The fixed triangulation-mesh model showed good agreement between the high fidelity generalized method of cells and linear element models, and computation time was reduced by approximately 104 times for the low-toughness matrix, and 55 times for the toughened matrix.

复合材料微结构容易受到紧密或接触纤维之间的局部应力集中的影响，在那里破坏可以开始和传播。通常，代表性体积单元通过模拟不同加载配置下的随机微观结构排列来预测力学响应。然而，当考虑到大型微观结构或紧密堆积的纤维时，这些模拟可能会非常昂贵。目前的工作旨在通过一种称为固定三角网格模型的新型有限元网格，提供一种计算效率高的方法来预测复合材料微结构的均质和局部特性。这种基于三角的网格划分算法使用最高应力发生的配置单元尺寸和高阶单元来捕获紧密排列的纤维之间的应力梯度。推导并实现了一种无需单独载荷扰动或应力积分即可充分表征复合材料刚度矩阵的有效均匀化技术。采用涂抹裂纹法建立了渐进式损伤模型，采用高阶元模拟峰后软化。采用高保真广义胞元法对不同纤维体积分数的微观结构进行了刚度、横向强度和面内抗剪强度的验证。在此基础上，对线性单元和增韧矩阵的精细化网格有限元模型进行了比较。所建立的固定三角网格模型与线形单元模型具有较好的一致性，低韧性矩阵计算时间缩短约104倍，增韧矩阵计算时间缩短约55倍。

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引用次数: 0

Sensitivity analysis for problems exhibiting geometric nonlinearities and follower loads using the complex-variable finite element method 用复变有限元法分析几何非线性和从动件载荷问题的灵敏度

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-04 DOI: 10.1016/j.finel.2025.104419

Hameed S. Lamy , David Avila , Mauricio Aristizabal , David Restrepo , Harry Millwater , Arturo Montoya

This study presents an enhanced approach for conducting sensitivity analysis of nonlinear problems involving a combination of geometric nonlinearities and follower loads, particularly those involving displacement-dependent forces. The method utilizes the complex-variable finite element method (ZFEM), incorporating complex algebra into the conventional finite element incremental-iterative procedure to achieve highly accurate derivative calculations. A crucial task in this process is computing a complex-valued, non-constant external force that depends on a complex-valued displacement. The key innovation lies in overcoming challenges associated with sensitivity computation for geometric nonlinearities and follower loads through a streamlined and computationally efficient methodology that can be integrated with commercial finite element software. The method enhances implementation efficiency by avoiding the need for intricate analytical derivations and not depending on unstable numerical approximations, such as the Finite Difference Method (FDM). ZFEM’s versatility and robustness were verified against sensitivity analytical solutions for cantilever beam problems undergoing large elastic rotations and displacements under static and dynamic loading conditions. The numerical examples demonstrated excellent agreement with analytical solutions and finite differencing results, maintaining accuracy and stability across all cases. This research demonstrates that ZFEM significantly increases accessibility for computing sensitivities in complex solid mechanics problems, providing a user-friendly and efficient method for both static and dynamic scenarios involving geometric and follower loads.

本研究提出了一种增强的方法，用于对涉及几何非线性和从动件载荷组合的非线性问题进行灵敏度分析，特别是涉及位移相关力的非线性问题。该方法采用复变有限元法（ZFEM），在传统的有限元增量迭代过程中引入复代数，实现了高精度的导数计算。这一过程的关键任务是计算依赖于复值位移的复值非恒定外力。关键的创新在于克服与几何非线性和从动件载荷的灵敏度计算相关的挑战，通过一种流线型和计算效率高的方法，可以与商业有限元软件集成。该方法通过避免复杂的解析推导和不依赖于不稳定的数值近似，如有限差分法（FDM），提高了实现效率。通过对静、动载荷条件下大弹性旋转和大弹性位移悬臂梁问题的灵敏度解析解验证了ZFEM的通用性和鲁棒性。数值算例证明了与解析解和有限差分结果的良好一致性，在所有情况下都保持了准确性和稳定性。该研究表明，ZFEM显著提高了复杂固体力学问题计算灵敏度的可及性，为涉及几何和从动载荷的静态和动态场景提供了一种用户友好且高效的方法。

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引用次数: 0

Analysis of the stability of frames composed of thin-walled beams with open cross-section using a High Order Continuation Method 用高阶延拓法分析开截面薄壁梁框架的稳定性

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-09-03 DOI: 10.1016/j.finel.2025.104437

Zaenab Bakhach , Bouazza Braikat , Abdellah Hamdaoui , Noureddine Damil

This study presents the numerical modeling of frames composed of thin-walled beams with open cross-section subjected to large torsions by a High Order Continuation Method (HOCM), based on Asymptotic Numerical Method (ANM) techniques. The theoretical model is developed using

3 D

beam kinematics, which accounts for flexion-torsion coupling and large rotations. The connection between beams is ensured by joints (stiffening plates) to avoid local deformations, mathematically modeled by compatibility conditions applied to the connection nodes. The equilibrium equations are established using the minimization of the Lagrangian. Discretization is performed with a two-node beam element having seven degrees of freedom per node. The transformation from local to global reference frames is done using Euler angles for the first six degrees of freedom, while the transformation of the seventh degree of freedom is related to the transmission of warping between elements. The equilibrium equations are solved using a HOCM. Tested examples of frames of thin-walled beams with open cross-section subjected to different loadings and boundary conditions are investigated. The obtained results are compared with those calculated by the commercial software ABAQUS and with those from the literature.

本文采用基于渐近数值方法（ANM）的高阶延拓方法（HOCM）对受大扭转作用的薄壁梁框架进行了数值模拟。利用三维梁运动学建立理论模型，考虑了挠曲-扭转耦合和大旋转。梁之间的连接由节点（加强板）保证，以避免局部变形，通过应用于连接节点的协调条件进行数学建模。利用拉格朗日量的最小化建立了平衡方程。离散化是用每个节点有七个自由度的双节点梁单元进行的。前6个自由度的局部参照系到全局参照系的转换是利用欧拉角实现的，而第7个自由度的转换则涉及到元件间翘曲的传递。利用HOCM求解了平衡方程。对开截面薄壁梁框架在不同荷载和边界条件下的试验实例进行了研究。所得结果与商业软件ABAQUS计算结果及文献结果进行了比较。

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引用次数: 0

Accelerating nonlinear finite element analysis via residual-aware neural network constitutive models 残差感知神经网络本构模型加速非线性有限元分析

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-08-30 DOI: 10.1016/j.finel.2025.104431

Pierre-Eliot Malleval , Victor Matray , Faisal Amlani , Ronan Scanff , Frédéric Feyel , David Néron

Nonlinear finite element analysis (FEA) relies heavily on iterative methods such as the Newton–Raphson algorithm, with computational cost primarily driven by the repeated solution of large linear systems (global stage) and the evaluation of nonlinear constitutive laws (local stage). This work proposes a neural network-based surrogate to accelerate the local stage by approximating explicit constitutive models. A compact feed-forward neural network is trained on synthetic data generated from standard material laws and embedded into the commercial solver Simcenter^TM Samcef®, replacing the local integration of nonlinear equations. To ensure accuracy and robustness, a residual-based safeguard is introduced to restore the original physics-based model when neural network predictions are insufficient. To further explore the benefits of the proposed approach in reducing overall simulation cost, the method is also applied within a reduced-order modeling framework. While such techniques effectively reduce the cost of solving large linear systems, the evaluation of nonlinear terms often remains a dominant bottleneck. The surrogate is therefore also assessed using the nonlinear model reduction method available in Samcef, namely the LATIN-PGD approach, although a detailed study of this method is not the focus of this paper. Beyond simplified test cases, the method is implemented and validated in full-scale, industrially relevant simulations involving elasto-viscoplastic materials. Results from academic and industrial-scale applications, including a high-pressure turbine blade, demonstrate that the proposed approach significantly reduces computation time while preserving solution accuracy. These findings highlight the potential of combining data-driven surrogates with residual-controlled correction to enhance the efficiency and scalability of nonlinear FEA workflows under realistic conditions.

非线性有限元分析（FEA）在很大程度上依赖于迭代方法，如牛顿-拉夫森算法，其计算成本主要由大型线性系统的重复解（全局阶段）和非线性本构律的评估（局部阶段）驱动。这项工作提出了一个基于神经网络的代理，通过近似显式本构模型来加速局部阶段。紧凑的前馈神经网络在标准材料定律生成的合成数据上进行训练，并嵌入到商业求解器SimcenterTM Samcef®中，取代非线性方程的局部积分。为了保证预测的准确性和鲁棒性，在神经网络预测不足的情况下，引入残差保护来恢复原始的物理模型。为了进一步探索所提出的方法在降低总体仿真成本方面的好处，该方法还在降阶建模框架中应用。虽然这些技术有效地降低了求解大型线性系统的成本，但非线性项的评估仍然是一个主要的瓶颈。因此，也使用Samcef中可用的非线性模型约简方法，即LATIN-PGD方法来评估代理，尽管对该方法的详细研究不是本文的重点。除了简化的测试案例外，该方法还在涉及弹粘塑性材料的全尺寸工业相关模拟中得到了实施和验证。包括高压涡轮叶片在内的学术和工业规模应用结果表明，该方法在保持求解精度的同时显着减少了计算时间。这些发现突出了将数据驱动替代与残差控制校正相结合的潜力，以提高非线性有限元工作流程在现实条件下的效率和可扩展性。

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引用次数: 0