Computer Methods in Applied Mechanics and Engineering最新文献_第6页

Numerical simulation of heat transfer across partial discontinuities using the peridynamic differential operator 局部不连续面传热的动态微分算符数值模拟

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-16 DOI: 10.1016/j.cma.2026.118749

Sunwoo Kim , Suyeong Jin , Jung-Wuk Hong

Simulating heat conduction has been studied using approaches including peridynamics. However, accurately capturing heat transfer across discontinuities such as cracks and material interfaces remains a major challenge. This study presents a computational framework for heat transfer that utilizes a peridynamic differential operator approach to offer a unified modeling approach for both continuous and discontinuous media. The classical heat conduction equation is computed by using peridynamic differential operators, enabling natural treatment of discontinuities. A bond-wise function is defined by the interaction state between nodes, enabling a consistent representation of heat transfer for both intact and broken bonds. For broken bonds, thermal contact conductance is incorporated into the bond-wise function to capture heat transfer across partial discontinuities. The framework is verified through numerical analyses of a two-panel contact problem and a three-dimensional L-shaped bimaterial panel. The results demonstrate accurate prediction of interfacial phenomena, including temperature drops and localized heat flux concentration. The analyses further show that the bond-wise function successfully captures the influence of the thermal contact conductance on both the degree of heat transfer across crack interfaces and the resulting alteration of singularity characteristics. Overall, the framework provides a general and computationally efficient tool for simulating heat conduction in heterogeneous systems with partial discontinuities and establishes a basis for fully coupled thermomechanical analyses.

模拟热传导已经用包括周动力学在内的方法进行了研究。然而，准确地捕捉裂缝和材料界面等不连续区域的传热仍然是一个主要挑战。本研究提出了一个传热计算框架，该框架利用周动力学微分算子方法为连续和不连续介质提供了统一的建模方法。经典的热传导方程是用周动力微分算子计算的，使得不连续的自然处理成为可能。键方向函数由节点之间的相互作用状态定义，使得完整键和断裂键的热传递一致。对于断裂的键，热接触电导被纳入键方向函数，以捕获部分不连续的热传递。通过两面板接触问题和三维l型双材料面板的数值分析验证了该框架。结果表明，该方法可以准确地预测界面现象，包括温度下降和局部热流密度。进一步分析表明，键向函数成功地捕获了接触热导对裂纹界面传热程度和由此产生的奇异特性变化的影响。总的来说，该框架为模拟具有部分不连续的非均质系统中的热传导提供了一个通用且计算效率高的工具，并为完全耦合的热-力学分析奠定了基础。

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引用次数: 0

A physics-informed neural network framework for simulating creep buckling in growing viscoelastic biological tissues 模拟生长粘弹性生物组织蠕变屈曲的物理信息神经网络框架

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-06 DOI: 10.1016/j.cma.2025.118715

Zhongya Lin , Jinshuai Bai , Shuang Li , Xindong Chen , Bo Li , Xi-Qiao Feng

Modeling viscoelastic behavior is crucial in engineering and biomechanics, where materials undergo time-dependent deformations, including stress relaxation, creep buckling and biological tissue development. Traditional numerical methods, like the finite element method, often require explicit meshing, artificial perturbations or embedding customised programs to capture these phenomena, adding computational complexity. In this study, we develop an energy-based physics-informed neural network (PINN) framework using an incremental approach to model viscoelastic creep, stress relaxation, buckling, and growth-induced morphogenesis. Physics consistency is ensured by training neural networks to minimize the system’s potential energy functional, implicitly satisfying equilibrium and constitutive laws. We demonstrate that this framework can naturally capture creep buckling without pre-imposed imperfections, leveraging inherent training dynamics to trigger instabilities. Furthermore, we extend our framework to biological tissue growth and morphogenesis, predicting both uniform expansion and differential growth-induced buckling in cylindrical structures. Results show that the energy-based PINN effectively predicts viscoelastic instabilities, post-buckling evolution and tissue morphological evolution, offering a promising alternative to traditional methods. This study demonstrates that PINN can be a flexible robust tool for modeling complex, time-dependent material behavior, opening possible applications in structural engineering, soft materials, and tissue development.

粘弹性行为建模在工程和生物力学中是至关重要的，在这些领域中，材料会经历随时间的变形，包括应力松弛、蠕变屈曲和生物组织发育。传统的数值方法，如有限元法，通常需要明确的网格划分，人工扰动或嵌入定制程序来捕获这些现象，增加了计算复杂性。在这项研究中，我们开发了一个基于能量的物理信息神经网络（PINN）框架，使用增量方法来模拟粘弹性蠕变、应力松弛、屈曲和生长诱导的形态发生。物理一致性是通过训练神经网络最小化系统的势能泛函，隐式满足平衡和本构定律来保证的。我们证明，该框架可以自然地捕获蠕变屈曲，没有预先施加的缺陷，利用固有的训练动态来触发不稳定。此外，我们将我们的框架扩展到生物组织的生长和形态发生，预测圆柱形结构中的均匀膨胀和差异生长诱导的屈曲。结果表明，基于能量的PINN能有效预测粘弹性不稳定性、屈曲后演化和组织形态演化，为传统方法提供了一种有希望的替代方法。这项研究表明，PINN可以成为一种灵活可靠的工具，用于模拟复杂的、随时间变化的材料行为，在结构工程、软材料和组织发育方面开辟了可能的应用。

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引用次数: 0

A staggered training framework for mechanics-informed neural networks in tractable multiscale homogenization with application to woven fabrics 可处理多尺度均匀化中力学信息神经网络的交错训练框架及其在机织织物中的应用

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-09 DOI: 10.1016/j.cma.2025.118666

Faisal As’ad, Charbel Farhat

We introduce a computationally tractable framework for multiscale homogenization of path-dependent heterogeneous materials that combines mechanics-informed artificial neural networks with a staggered training procedure. The proposed approach decomposes complex, multiscale problems into a sequence of two-scale subproblems, efficiently bridging the scales through data-driven, neural network-based surrogate models that are, by construction, consistent with fundamental laws of continuum mechanics. The staggered training strategy ensures that the offline computational cost scales linearly with the number of scales, rather than exponentially, thereby achieving substantial efficiency gains over conventional nested multiscale finite element methods. As an illustrative application, the framework is demonstrated on woven fabrics, capturing viscoelastic and fiber-resolved material behaviors while maintaining computational efficiency. The results demonstrate that the proposed method achieves high-fidelity predictions comparable to those of fully resolved models reconstructed from real-material imaging, establishing a general and flexible methodology for modeling complex materials with many interacting scales.

我们引入了一个计算易于处理的框架，用于路径依赖的非均质材料的多尺度均质化，该框架将力学信息人工神经网络与交错训练过程相结合。该方法将复杂的多尺度问题分解为一系列双尺度子问题，通过数据驱动的、基于神经网络的替代模型有效地桥接这些尺度，这些模型的构建符合连续介质力学的基本定律。交错训练策略确保离线计算成本随尺度数量线性增长，而不是指数增长，从而获得比传统嵌套多尺度有限元方法更大的效率提升。作为一个说明性应用，该框架在机织物上进行了演示，在保持计算效率的同时捕获粘弹性和纤维分解的材料行为。结果表明，该方法实现了与真实材料成像重建的全分辨率模型相当的高保真预测，为具有许多相互作用尺度的复杂材料建模建立了一种通用而灵活的方法。

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引用次数: 0

A unified multiscale framework for stress-Based topology optimization using local constraint enforcement 基于局部约束的应力拓扑优化统一多尺度框架

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-13 DOI: 10.1016/j.cma.2025.118692

George Kazakis , Nikos D. Lagaros

This study presents a robust multiscale formulation for stress-constrained topology optimization aimed at designing lightweight and structurally resilient components. Unlike classical compliance-based methods, which may result in topologies unable to support applied loads, the proposed approach minimizes structural volume while rigorously enforcing local stress constraints. A dual-scale framework integrates macro-structural optimization with periodic micro-structural design, leveraging the Solid Isotropic Material with Penalization (SIMP) method; though it remains adaptable to other established topology optimization techniques. To address the computational challenges arising from numerous local stress constraints, we implement an Augmented Lagrangian strategy combined with polynomial vanishing constraints, eliminating the need for aggregation functions such as the p-norm or Kreisselmeier-Steinhauser functions. The resulting optimization algorithm is accurate and scalable, supported by a detailed sensitivity analysis and adjoint-based gradient computation. Numerical experiments in two dimensions validate the effectiveness of the method, demonstrating superior stress distribution and structural efficiency compared to classical formulations. This work contributes a comprehensive and scalable methodology for multiscale topology optimization under stress constraints, suitable for high-performance engineering applications.

本研究提出了一种鲁棒的多尺度应力约束拓扑优化公式，旨在设计轻量化和结构弹性构件。与传统的基于顺应性的方法不同，这种方法可能导致拓扑结构无法支持施加的载荷，而所提出的方法在严格执行局部应力约束的同时最小化了结构体积。双尺度框架将宏观结构优化与周期性微观结构设计相结合，利用固体各向同性材料惩罚（SIMP）方法；尽管它仍然适用于其他已建立的拓扑优化技术。为了解决由众多局部应力约束引起的计算挑战，我们实现了一种结合多项式消失约束的增广拉格朗日策略，消除了对p-范数或Kreisselmeier-Steinhauser函数等聚集函数的需求。通过详细的灵敏度分析和基于伴随的梯度计算，所得到的优化算法具有准确性和可扩展性。二维数值实验验证了该方法的有效性，表明与经典公式相比，该方法具有更好的应力分布和结构效率。这项工作为应力约束下的多尺度拓扑优化提供了一种全面、可扩展的方法，适用于高性能工程应用。

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引用次数: 0

Optimal control of a hemivariational inequality of stationary convective Brinkman-Forchheimer extended Darcy equations with numerical approximation 平稳对流Brinkman-Forchheimer扩展Darcy方程半变分不等式的最优控制

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-24 DOI: 10.1016/j.cma.2026.118755

Wasim Akram, Manil T. Mohan

We investigate an optimal control problem governed by a stationary convective Brinkman-Forchheimer extended Darcy (CBFeD) model formulated as a hemivariational inequality in both two- and three-dimensional settings. This framework captures complex incompressible fluid flow through porous media by simultaneously accounting for convection, viscous damping, and nonlinear resistance effects, while naturally incorporating non-smooth frictional interactions through a subdifferential boundary condition. A key contribution of this work is a rigorous stability analysis of the CBFeD hemivariational inequality with respect to perturbations in both the external force density and the associated superpotential. Building on this analysis, we establish the existence of optimal controls when the external force density is treated as the control variable under admissible constraints. This result extends existing optimal control theories to a broader class of nonsmooth, nonlinear flow models in porous media. From a computational perspective, we propose a fully implementable numerical scheme for the resulting optimal control problem and prove its convergence. The method is based on finite element discretization and is applicable in both two and three dimensions, making it suitable for practical simulations. Numerical experiments are presented to illustrate the effectiveness of the proposed approach and to confirm the theoretical findings.

我们研究了一个由静态对流Brinkman-Forchheimer扩展Darcy （CBFeD）模型控制的最优控制问题，该模型在二维和三维环境中被表述为半分不等式。该框架通过同时考虑对流、粘性阻尼和非线性阻力效应来捕获复杂的不可压缩流体在多孔介质中的流动，同时通过次微分边界条件自然地纳入非光滑摩擦相互作用。这项工作的一个关键贡献是对CBFeD半变分不等式在外力密度和相关超势的扰动下的严格稳定性分析。在此基础上，建立了在允许约束条件下以外力密度为控制变量的最优控制的存在性。这一结果将现有的最优控制理论扩展到更广泛的非光滑、非线性多孔介质流动模型。从计算的角度，我们提出了一个完全可实现的最优控制问题的数值格式，并证明了其收敛性。该方法基于有限元离散化，适用于二维和三维，适合于实际仿真。数值实验证明了所提方法的有效性，并证实了理论结论。

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引用次数: 0

The inference of Fokker-Planck equations via transport maps 通过输运图的福克-普朗克方程的推断

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-22 DOI: 10.1016/j.cma.2026.118760

Saem Han , Krishna Garikipati

We present a framework, which, from the trajectories detailing the spatiotemporal dynamics of a population, simultaneously reconstructs a transport map as well as the Fokker-Planck equation governing the coarse-grained probability distribution. Leveraging the Knothe-Rosenblatt rearrangement, we model the transport map from a fixed reference distribution to the target distribution, and derive the velocity fields of the flows from the trajectory of transport maps. Exploiting the velocity fields, we circumvent spatial gradients to infer the Fokker-Planck equation’s potential and diffusivity. The sparsity of trajectories injects uncertainty, which we treat in a Bayesian setting using variational inference. The approach is applied to inferring the Fokker-Planck dynamics in spaces of up to five dimensions, demonstrating both accurate identification of the system and efficiency with respect to data size.

我们提出了一个框架，该框架从详细描述人口时空动态的轨迹中，同时重建了运输图以及控制粗粒度概率分布的福克-普朗克方程。利用Knothe-Rosenblatt重排法，我们建立了从固定参考分布到目标分布的输运图模型，并从输运图的轨迹推导出了流的速度场。利用速度场，我们绕过空间梯度来推断Fokker-Planck方程的势和扩散率。轨迹的稀疏性注入了不确定性，我们使用变分推理在贝叶斯设置中处理。该方法被应用于在多达五个维度的空间中推断福克-普朗克动力学，证明了系统的准确识别和数据大小方面的效率。

引用次数: 0

Stability analyses and instability mitigation for the material point method 物质点法的稳定性分析与不稳定性缓解

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-29 DOI: 10.1016/j.cma.2026.118784

Wen-Chia Yang , Deborah L. Sulsky

This study investigates the numerical stability of the Material Point Method (MPM) by analyzing the energy behavior and spectral properties of single-step updates. An energy-based analysis is first performed to quantify the energy variation introduced during each time step, followed by a spectral analysis that identifies critical time step constraints through the amplification matrix. Closed-form expressions for the critical integration parameter and the non-dimensional critical time step are derived, highlighting their dependence on mass parameters and particle distribution. The stability analyses identify key factors affecting the stability limits in MPM, including mass matrix selection, velocity projection, partially occupied grid cells, and integration errors in the particle-based formulation. Numerical experiments validate the analytical predictions and reveal the influence of particle-based integration errors on stability. A simple stabilization coefficient is proposed, which modifies shape function gradients in partially filled edge cells, significantly extending the stable time step range without increasing computational cost. The proposed framework offers practical guidelines for selecting stable time steps and enhancing the robustness of MPM simulations.

通过分析单步更新的能量行为和谱特性，研究了物质点法的数值稳定性。首先进行基于能量的分析，以量化每个时间步长期间引入的能量变化，然后进行光谱分析，通过放大矩阵确定关键时间步长约束。导出了临界积分参数和无因次临界时间步长的封闭表达式，强调了它们对质量参数和粒子分布的依赖。稳定性分析确定了影响MPM稳定性极限的关键因素，包括质量矩阵选择、速度投影、部分占用的网格单元以及基于颗粒的公式中的积分误差。数值实验验证了分析预测，揭示了基于粒子的积分误差对稳定性的影响。提出了一种简单的稳定系数，该系数可以修改部分填充边缘单元的形状函数梯度，在不增加计算成本的情况下显著延长稳定时间步长范围。提出的框架为选择稳定的时间步长和增强MPM仿真的鲁棒性提供了实用的指导。

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引用次数: 0

Simulation of effective scale-size dependent heat conduction in rigid microgeometries 刚性微几何中有效尺度相关热传导的模拟

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-16 DOI: 10.1016/j.cma.2026.118752

Mario Setta, Eddie Wadbro, Grigor Nika

We present homogenization and simulation results for an enhanced heat equation model that captures thermal scale-size effects through higher-gradient corrections involving characteristic internal lengths. The resulting equation is a fourth-order parabolic equation that incorporates thermal scale effects inherent to microstructured materials. We derive effective thermal coefficients for the time-stationary problem using asymptotic homogenization. This enables accurate simulation via a quadratic B-spline-based finite element approach. Our results quantify the influence of microstructure shape and volume fraction on the effective thermal behavior, demonstrating how scale-size-induced phenomena critically affect heat transport in micro- and nanoscale devices.

我们提出了一个增强的热方程模型的均匀化和模拟结果，该模型通过涉及特征内部长度的更高梯度修正来捕获热尺度尺寸效应。所得方程是一个包含微观结构材料固有的热垢效应的四阶抛物方程。利用渐近均匀化方法导出了时间平稳问题的有效热系数。这使得通过基于二次b样条的有限元方法进行精确模拟成为可能。我们的研究结果量化了微观结构形状和体积分数对有效热行为的影响，展示了尺度尺寸诱导的现象如何严重影响微纳米级器件的热传输。

引用次数: 0

COMMET: Orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates 注释：通过批量化神经本构更新，有限元方法的数量级加速

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-14 DOI: 10.1016/j.cma.2026.118728

Benjamin Alheit , Mathias Peirlinck , Siddhant Kumar

Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs), i.e., neural network-based constitutive models, offer a highly expressive and flexible framework for modeling complex material behavior in solid mechanics. However, their practical adoption in large-scale FE simulations remains limited due to significant computational costs, especially in repeatedly evaluating stress and stiffness. NCMs thus represent an extreme case: their large computational graphs make stress and stiffness evaluations prohibitively expensive, restricting their use to small-scale problems. In this work, we introduce COMMET, an open-source FE framework whose architecture has been redesigned from the ground up to accelerate high-cost constitutive updates. Our framework features a novel assembly algorithm that supports batched and vectorized constitutive evaluations, compute-graph-optimized derivatives that replace automatic differentiation, and distributed-memory parallelism via MPI. These advances dramatically reduce runtime, with speed-ups exceeding three orders of magnitude relative to traditional non-vectorized automatic differentiation-based implementations. While we demonstrate these gains primarily for NCMs, the same principles apply broadly wherever for-loop based assembly or constitutive updates limit performance, establishing a new standard for large-scale, high-fidelity simulations in computational mechanics.

每当材料模型比较复杂时，本构评估往往是有限元模拟的主要计算成本。神经本构模型（ncm），即基于神经网络的本构模型，为固体力学中复杂材料行为的建模提供了一个高度表达和灵活的框架。然而，由于大量的计算成本，特别是在反复评估应力和刚度时，它们在大规模有限元模拟中的实际应用仍然有限。因此，ncm代表了一个极端的情况：它们的大型计算图使得应力和刚度评估过于昂贵，限制了它们在小规模问题中的应用。在这项工作中，我们介绍了COMMET，这是一个开源的FE框架，其架构已经从头开始重新设计，以加速高成本的本构更新。我们的框架具有一种新颖的装配算法，支持批处理和矢量化的本构评估，计算机图优化的导数取代自动微分，以及通过MPI实现分布式内存并行性。这些进步大大缩短了运行时间，相对于传统的基于非矢量化的自动微分实现，速度提高了三个数量级。虽然我们主要为ncm展示了这些增益，但同样的原理广泛适用于基于for-loop的装配或本构更新限制性能的地方，为计算力学中的大规模高保真模拟建立了新的标准。

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引用次数: 0

A new hybrid strongly coupled multi-time step approach with enhanced robustness for fluid structure interaction problems 一种增强鲁棒性的混合强耦合多时间步方法求解流固耦合问题

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-08 DOI: 10.1016/j.cma.2025.118717

Roxan Pulicani , Michael Brun , Olivier Allain , Anthony Gravouil

This paper presents a strongly coupled approach within the Arbitrary Lagrangian-Eulerian (ALE) framework for solving Fluid-Structure Interaction (FSI) problems, such as those involving a deformable structure in a supersonic flow or subjected to a blast loading. The vertex-centered Finite Volume Method (FVM) for the fluid subdomain with two different explicit time integrators (first-order and third-order accurate Runge-Kutta schemes) is coupled with the Finite Element Method (FEM) for the structural subdomain with an implicit time integrator (Newmark Constant Average Acceleration scheme). This coupling is performed using mono- and multi-time step strategies. The proposed FSI algorithms adopts a monolithic and simultaneous FSI coupling, by introducing Lagrange Multipliers (LM) to ensure the continuity of the normal velocity at the Fluid-Structure (FS) interface. This adopted dual Schur approach allows decoupling the FSI problem into two solid and fluid discrete systems, along with an interface discrete system involving the time-dependent Steklov-Poincaré operator and the unknown Lagrange Multipliers. The proposed approach is hybrid (explicit-implicit), strongly coupled, with fluid subcycling, and is non-iterative in the sense that it does not require any subiteration. It provides a compromise between the flexibility of loosely coupled staggered schemes and the robustness of strongly coupled monolithic formulations. The proposed method has been validated for several academic cases and FSI benchmarks, including the classical half shock tube, the one-dimensional piston problem with a rod, the two-dimensional deformable panel subjected to a shock-wave, as well as a two-dimensional panel flutter problem in the supersonic flow regime.

本文提出了一种在任意拉格朗日-欧拉（ALE）框架内的强耦合方法，用于解决流固相互作用（FSI）问题，例如涉及超音速流动或爆炸载荷下的变形结构的问题。将具有两种显式时间积分器（一阶和三阶精确龙格-库塔格式）的流体子域的以顶点为中心的有限体积法（FVM）与具有隐式时间积分器（Newmark常数平均加速度格式）的结构子域的有限元法（FEM）相耦合。这种耦合是使用单时间步长和多时间步长策略执行的。本文提出的流固耦合算法采用单片同步流固耦合，通过引入拉格朗日乘法器（LM）来保证流固界面处法向速度的连续性。这种采用的双舒尔方法允许将FSI问题解耦为两个固体和流体离散系统，以及涉及时变steklov - poincar算子和未知拉格朗日乘子的界面离散系统。所提出的方法是混合（显式-隐式），强耦合，具有流体子循环，并且在不需要任何子迭代的意义上是非迭代的。它提供了松耦合交错方案的灵活性和强耦合整体公式的鲁棒性之间的折衷。该方法已通过经典的半激波管、带杆的一维活塞问题、受激波作用的二维可变形壁板以及超声速流动区二维壁板颤振问题等理论实例和FSI基准进行了验证。

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引用次数: 0