Engineering Analysis with Boundary Elements最新文献_第6页

Nonlinear resonant responses and chaotic dynamics of braided composite truncated conical shell 编织复合材料截顶锥形壳的非线性共振响应与混沌动力学

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-09 DOI: 10.1016/j.enganabound.2025.106590

Tao Liu , Yifeng Li , Xiangying Guo , Yan Zheng

Against the research background of rocket fairings, this study investigates the vibration characteristics and nonlinear dynamic behavior of two-phase braided composite truncated conical shells under complex environments. We establish a dynamic model via FSDT and Hamilton's principle, studying the two-phase braided composite truncated conical shell's natural vibration. FEA comparison shows ≤2.95 % error. Higher fiber volume boosts frequency and stiffness. Subsequently, we analyze the occurrence of 1:1 internal resonance when the half apex angle is 60° On this basis, external excitation, aerodynamic forces, and damping effects are introduced to further establish a nonlinear dynamic model. The Galerkin method is used to discretize the nonlinear governing equations, and the pseudo-arclength continuation method is used to analyze the effects of parameter variations on the 1:1 internal resonance behavior. The results reveal that increasing the fiber volume fraction, braiding angle, and damping can effectively reduce the resonance peak. Finally, we examine the nonlinear dynamic behavior of the structure, with a focus on revealing the mechanisms by which external excitation and damping affect the dynamic stability of the system. The results provide important theoretical support for the vibration control and structural reliability design of braided composite thin-walled components.

以火箭整流罩为研究背景，研究了复杂环境下两相编织复合材料截顶圆锥壳的振动特性和非线性动力行为。利用FSDT和Hamilton原理建立了两相编织复合材料截锥壳的动力学模型，研究了两相编织复合材料截锥壳的自振特性。有限元对比表明误差≤2.95%。更高的纤维体积可以提高频率和硬度。在此基础上，引入外部激励、气动力和阻尼效应，进一步建立非线性动力学模型。采用伽辽金法对非线性控制方程进行离散化，并采用伪弧长延延法分析了参数变化对1:1内共振特性的影响。结果表明，增加纤维体积分数、编织角和阻尼可以有效地降低共振峰。最后，我们研究了结构的非线性动力行为，重点揭示了外部激励和阻尼影响系统动态稳定性的机制。研究结果为编织复合材料薄壁构件的振动控制和结构可靠性设计提供了重要的理论支持。

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引用次数: 0

Axisymmetric crack in transversely isotropic FGM Full-space under tractions on crack surfaces 横向各向同性FGM全空间裂纹表面牵拉作用下的轴对称裂纹

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-08 DOI: 10.1016/j.enganabound.2025.106587

Sha Xiao , Zhongqi Quentin Yue

This paper develops a discontinuous displacement method to analyze an axisymmetric crack in an infinite functionally graded material (FGM) with transverse isotropy. The fundamental solution for a transversely isotropic layered solid of infinite extent subjected to point concentrated loads is employed to establish boundary integral equations only over one side of crack surfaces. Both continuous and discontinuous elements are employed to discretize the crack surface. A discretization technique is utilized to model arbitrary variations of the FGM along a graded direction. Verifications are conducted to illustrate that the numerical solutions presented by the proposed approach are in very good agreement with the classical analytical solutions. Examples are given for penny-shaped cracks in isotropic and transversely isotropic FGMs under different types of tractions, and the stress intensity factors (SIF) for two types of elastic media are analyzed and compared in detail. Results illustrate the effect of the heterogeneity and anisotropy of the materials on the fracture behavior of crack problems.

本文提出了一种分析具有横向各向同性的无限功能梯度材料轴对称裂纹的不连续位移法。利用横向各向同性无限宽层状固体受点集中荷载作用的基本解，建立了仅在裂纹表面一侧的边界积分方程。采用连续单元和不连续单元对裂纹表面进行离散化。利用离散化技术对梯度方向上FGM的任意变化进行了建模。验证表明，所提出的数值解与经典解析解非常吻合。给出了各向同性和横向各向同性fgm中便士形裂纹在不同牵引力作用下的算例，并对两种弹性介质的应力强度因子进行了详细的分析和比较。结果说明了材料的非均质性和各向异性对裂纹问题断裂行为的影响。

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引用次数: 0

C-SPH+ST: A novel stabilized corrected smoothed particle hydrodynamics scheme for high Weissenberg number problem of viscoelastic fluids C-SPH+ST：粘弹性流体高Weissenberg数问题的一种新的稳定修正光滑粒子流体力学格式

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-08 DOI: 10.1016/j.enganabound.2025.106573

Jinlian Ren , Wei Zhang , Weigang Lu , Tao Jiang

In this paper, a novel stabilization term (ST) is introduced into the nonlinear constitutive model, and a corrected smoothed particle hydrodynamics approximation scheme incorporating the stabilization term, which is termed as C-SPH+ST, is developed to address the High Weissenberg Number Problem (HWNP) in viscoelastic fluids based on the Oldroyd-B constitutive model. To establish a high-accuracy, enhanced-stability algorithm for solving the HWNP of viscoelastic fluids, we perform the improvements based on a corrected SPH method in our previous work which enforces the corrected kernel gradient, particle shifting and density reinitialization techniques in the original SPH framework. Meanwhile, a novel stabilization term, distinct from existing artificial stress terms, is proposed and integrated into the C-SPH+noST method. In numerical experiments, the validity of the proposed stabilized corrected SPH scheme is first verified by simulating classical viscoelastic flows with HWNP, with results compared against reference solutions. The proposed stable particle scheme is then applied to predict the complex nonlinear behavior of viscoelastic Wannier flow, and focusing primarily on the influence of high Weissenberg Number on unstable viscoelastic flow. Additionally, the effects of the parameters in the given stabilization term and other techniques are also analyzed and discussed. All numerical results indicate that the proposed C-SPH+ST algorithm is a robust tool for addressing the HWNP in viscoelastic fluids, and can efficiently prevent non-physical particle clustering and accurately capture the complex phenomena in viscoelastic flows with high Weissenberg numbers.

本文在非线性本构模型中引入了一种新的稳定项（ST），并基于Oldroyd-B本构模型，提出了一种包含稳定项的修正光滑颗粒流体力学近似格式C-SPH+ST，以解决粘弹性流体中的高Weissenberg数问题（HWNP）。为了建立一种高精度、增强稳定性的黏弹性流体HWNP求解算法，我们在之前工作的修正SPH方法的基础上进行了改进，该方法在原始SPH框架中加强了修正的核梯度、粒子移动和密度重新初始化技术。同时，提出了一种新的稳定项，区别于现有的人工应力项，并将其集成到C-SPH+noST方法中。在数值实验中，首先用HWNP模拟经典粘弹性流动，验证了所提出的稳定修正SPH格式的有效性，并与参考解进行了比较。然后将所提出的稳定粒子格式应用于粘弹性万尼尔流的复杂非线性行为预测，重点研究了高Weissenberg数对不稳定粘弹性流的影响。此外，还分析和讨论了在给定稳定期限内参数和其他技术的影响。所有数值结果表明，C-SPH+ST算法是解决粘弹性流体中HWNP问题的有力工具，可以有效地防止非物理颗粒聚集，准确捕捉高Weissenberg数粘弹性流动中的复杂现象。

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引用次数: 0

A novel multi-loading deep energy method for 3D hyperelastic problems using a separable structure 基于可分离结构的三维超弹性问题多载荷深能新方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-05 DOI: 10.1016/j.enganabound.2025.106567

Linh Nguyen Hoai Le, Nha Thanh Nguyen

In recent years, physics-informed neural networks (PINNs) have become an active research field in computational mechanics. Among the PINN variants, the energy-based PINN, known as the deep energy method (DEM), is regarded as particularly effective. Unlike traditional PINNs, DEM merges multiple objective functions into one energy formulation, making convergence easier. Requiring only lower-order derivatives, DEM is also simpler to implement. This paper introduces a multi-loading model for nonlinear analysis that incorporates load factors as inputs during training. By training with a small set of loads, the resulting network can predict approximated fields for any load factor. To enhance efficiency, a separable structure is employed as a low-rank approximator, and its performance is compared with conventional approaches. Due to the well-conditioned and convex nature of hyperelastic energy functions, the model focuses on hyperelastic materials. A regression-based criterion is developed to estimate convergence. To assess robustness, three-dimensional problems are analyzed. The network is trained over a wide range of load factors, and the Adaptive Moment Estimation (Adam) optimizer is used. Results are compared with reference data for validation. Findings demonstrate that the proposed multi-loading model provides accurate, highly correlated predictions in both interpolation and extrapolation regions.

近年来，物理信息神经网络（pinn）已成为计算力学领域的一个活跃研究领域。在PINN变体中，基于能量的PINN，称为深能量法（DEM），被认为是特别有效的。与传统的pinn不同，DEM将多个目标函数合并到一个能量公式中，使收敛更容易。只需要低阶导数，DEM也更容易实现。本文介绍了一种多载荷非线性分析模型，该模型在训练过程中将载荷因子作为输入。通过使用一小组负载进行训练，得到的网络可以预测任何负载因子的近似场。为了提高效率，采用可分离结构作为低秩逼近器，并与传统逼近方法进行了性能比较。由于超弹性能量函数的良好条件和凸性，该模型主要研究超弹性材料。提出了一种基于回归的准则来估计收敛性。为了评估鲁棒性，分析了三维问题。采用自适应矩估计（Adam）优化器对网络进行了大范围负载因子的训练。结果与参考数据进行了对比验证。研究结果表明，所提出的多载荷模型在内插和外推区域都提供了准确的、高度相关的预测。

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引用次数: 0

A Trefftz collocation method for multiple interacting cylindrical nanofibers with the Steigmann-Ogden interface model 基于Steigmann-Ogden界面模型的多圆柱形纳米纤维的Trefftz配点法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-05 DOI: 10.1016/j.enganabound.2025.106563

Cheng Chen , Yezeng Huang , Junbo Wang , Leiting Dong

In this study, a Trefftz collocation method (TCM) is proposed for modeling multiple interacting cylindrical nanofibers with the Steigmann-Ogden interface model. The Trefftz trial displacement fields are assumed in terms of the Papkovich-Neuber (P-N) solutions with the cylindrical harmonics as P-N potentials. The non-singular and singular harmonic functions from multiple source points are included for investigating multiple interacting nanofibers. The displacement continuity and the stress jump across the matrix/nanofiber interfaces and the boundary conditions are satisfied by the collocation method. To avoid the ill-conditioning of the resulting system of equations, a two-step scaling method is implemented: first, three characteristic lengths are introduced to scale the Trefftz trial functions; and second, a multi-scale characteristic length is adopted to scale each column of the coefficient matrix to equalize the norm. The good agreements between the numerical results and analytical solutions demonstrate the accuracy of the proposed method in simulating the interface effects of nanofiber composites. The numerical results reveal that the stress distributions in nanofibers are significantly size-dependent, which are influenced by interface elasticity parameters. Besides, the interactions of multiple nanofibers are also studied. The TCM developed in this work can be contributed to the design of advanced nanofiber composites.

本文提出了一种基于Steigmann-Ogden界面模型的多圆柱形纳米纤维的Trefftz配置方法（TCM）。用Papkovich-Neuber （P-N）解来假设Trefftz试验位移场，其柱面谐波为P-N势。采用多源点的非奇异和奇异谐波函数来研究多相互作用的纳米纤维。配置方法满足了基体/纳米纤维界面间的位移连续性和应力跳变，并满足了边界条件。为了避免结果方程组的病态化，实现了两步缩放方法：首先，引入三个特征长度对Trefftz试函数进行缩放；其次，采用多尺度特征长度对系数矩阵的每一列进行尺度化，使范数相等。数值结果与解析解吻合较好，证明了该方法在模拟纳米纤维复合材料界面效应方面的准确性。数值结果表明，纳米纤维中的应力分布具有明显的尺寸依赖性，受界面弹性参数的影响。此外，还研究了多种纳米纤维的相互作用。本研究所建立的纳米复合材料理论可以为高级纳米纤维复合材料的设计做出贡献。

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引用次数: 0

Evaluating singular and near-singular integrals on C2 smooth surfaces with quadratic geometric approximation and closed form expressions 用二次几何近似和封闭形式表达式求C2光滑曲面上的奇异积分和近奇异积分

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-04 DOI: 10.1016/j.enganabound.2025.106588

Andrew Zheng, Spyros Alexakis, Adam R. Stinchcombe

Fredholm integral equations that appear in Boundary Element Methods often involve integrals with weakly singular kernels. Once the domain of integration is discretized into flat triangular elements, these weakly singular kernels become strongly singular or near-singular. Common methods to compute these integrals when the kernel is a Green’s function include coordinate transformations, polar coordinates with closed analytic formulas, and singularity extraction. However, these methods do not generalize well to the normal derivatives of Green’s functions due to the strongly singular behavior of these functions on triangular elements. We provide methods to integrate both the Green’s function and its normal derivative on smooth surfaces discretized by triangular elements in three dimensions for many commonly encountered differential operators. For strongly singular integrals involving normal derivatives of Green’s functions, we introduce a more refined approximation called Quadratic Surface Approximation. By using geometric information of the true surface of integration in combination with push-forward maps, it is significantly more accurate than the naive method of setting the singular integrals to zero, while being faster than adaptive refinement methods. We provide an algorithm for explicit computations on triangles, and present necessary analytic formulas that the algorithm requires in the appendix.

边界元法中出现的Fredholm积分方程通常涉及弱奇异核积分。一旦将积分域离散成平面三角元，这些弱奇异核就变成强奇异或近奇异核。当核函数为格林函数时，计算这些积分的常用方法包括坐标变换、带封闭解析公式的极坐标和奇点提取。然而，由于格林函数在三角元上的强奇异性，这些方法不能很好地推广到格林函数的正规导数。对于许多常见的微分算子，我们提供了在三维三角形离散光滑表面上对格林函数及其法向导数进行积分的方法。对于涉及格林函数法向导数的强奇异积分，我们引入了一种更精细的近似，称为二次曲面近似。利用积分真曲面的几何信息与推前映射相结合，其精度明显高于将奇异积分设为零的朴素方法，同时速度也快于自适应细化方法。我们在附录中提供了一种对三角形进行显式计算的算法，并给出了该算法所需的必要解析公式。

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引用次数: 0

A reproducing kernel gradient smoothing meshfree method with least squares stabilization for nearly incompressible elasticity 近乎不可压缩弹性的最小二乘稳定再现核梯度平滑无网格方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-04 DOI: 10.1016/j.enganabound.2025.106571

Yingjie Chu , Junchao Wu , Penglin Chen , Canhui Zhang , Dongdong Wang

A reproducing kernel gradient smoothing meshfree method with least squares stabilization is developed for the nearly incompressible elasticity problems. This meshfree scheme is formulated in the context of the Hellinger-Reissner (HR) variational principle, where the displacement and stress fields are independently approximated and the incompressibility constraint is implicitly embedded in the formulation. It is noteworthy that the total stress field is directly approximated herein, as does not need the conventional tedious decomposition of the stress field into deviatoric stress and pressure components. The variational integration consistency is naturally fulfilled by the reproducing kernel gradient smoothing framework, which ensures the optimal convergence of meshfree solutions. Meanwhile, the least squares stabilization is introduced to suppress the pressure oscillation. A thorough theoretical analysis evinces that the proposed reproducing kernel gradient smoothing meshfree method with least squares stabilization displays the desirable stability through satisfying both Ladyzhenskaya-Babuška-Brezzi (LBB) and kernel-coercivity conditions, which is thus conveniently termed as the stabilized variationally consistent meshfree method. The accuracy and stability of the proposed method for nearly incompressible elasticity problems are systematically validated by numerical results.

针对几乎不可压缩弹性问题，提出了一种具有最小二乘稳定性的再现核梯度平滑无网格方法。这种无网格格式是在Hellinger-Reissner （HR）变分原理的背景下制定的，其中位移和应力场是独立近似的，不可压缩性约束隐式嵌入在公式中。值得注意的是，本文直接逼近了总应力场，而不需要将应力场分解为偏应力和压力分量。再现核梯度平滑框架自然地满足了变分积分一致性，保证了无网格解的最优收敛性。同时，引入最小二乘镇定来抑制压力振荡。理论分析表明，该方法在满足Ladyzhenskaya-Babuška-Brezzi （LBB）条件和核矫顽力条件的前提下，具有较好的稳定性，可方便地称为稳定变分一致无网格方法。数值结果系统地验证了所提方法对近不可压缩弹性问题的准确性和稳定性。

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引用次数: 0

An adaptive cell-based smoothed finite element method with arbitrary polygonal elements for coupled thermo-mechanical analysis 基于自适应单元的任意多边形单元光滑有限元法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-03 DOI: 10.1016/j.enganabound.2025.106553

Ruiping Niu , Shijie Zhao , Xinglong Lu , Qiuxia Fan , Lei han Wang

This paper proposes, for the first time, an adaptive cell-based smoothed finite element method (A-CS-FEM) based on arbitrary polygonal elements for thermo-mechanical coupling problems. By utilizing mean value coordinates, the proposed model accommodates non-convex polygons without self-intersection, enabling robust handling of diverse polygonal elements. The approach integrates constrained Delaunay triangulation with adaptive techniques to partition triangulation-cell-based smoothing domains, naturally ensuring the positivity condition for a normed

G_{h}^{1}

space without additional stabilization, while maintaining the high-quality meshes. The gradient smoothing technique in CS-FEM eliminates the coordinate mapping inherent in traditional polygonal finite element methods, because it requires only the shape function values along the segments of cell smoothing domains instead of the shape function derivatives. Numerical results demonstrate that A-CS-FEM significantly improves the quality of smoothing domains for complex geometries with arbitrary convex and concave polygonal discretization, thereby achieving high-precision solutions for both displacement and temperature.

本文首次提出了一种基于任意多边形单元的自适应单元光滑有限元法（A-CS-FEM）。该模型采用均值坐标，可容纳无自交的非凸多边形，实现对多种多边形元素的鲁棒处理。该方法将约束Delaunay三角剖分与自适应技术相结合，对基于三角剖分单元的平滑域进行划分，自然地保证了归一化Gh1空间的正性条件，而无需额外的稳定化，同时保持了高质量的网格。CS-FEM中的梯度平滑技术消除了传统多边形有限元方法固有的坐标映射问题，因为它只需要沿单元平滑域段的形状函数值，而不需要形状函数导数。数值结果表明，A-CS-FEM显著提高了具有任意凸、凹多边形离散化的复杂几何图形的光滑域质量，从而获得了位移和温度的高精度解。

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引用次数: 0

Point Jacobi-type preconditioning and parameter tuning for Calderon-preconditioned Burton–Miller method in transmission problems 传输问题中Calderon-preconditioned Burton-Miller方法的点jacobi型预处理和参数整定

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-03 DOI: 10.1016/j.enganabound.2025.106572

Keigo Tomoyasu, Hiroshi Isakari

It was recently demonstrated that the boundary element method based on the Burton–Miller formulation (BM-BEM), widely used for solving exterior problems, can be adapted to solve transmission problems efficiently. This adaptation utilises Calderon’s identities to improve the spectral properties of the underlying integral operator. Consequently, most eigenvalues of the squared BEM coefficient matrix, i.e., the collocation-discretised version of the operator, cluster at a few points in the complex plane. When these clustering points are closely packed, the resulting linear system is well-conditioned and can be solved efficiently using the generalised minimal residual (GMRES) method with only a few iterations. However, when multiple materials with significantly different material constants are involved, some eigenvalues become separated, deteriorating the conditioning. To address this, we propose an enhanced Calderon-preconditioned BM-BEM with two strategies. First, we apply a preconditioning scheme inspired by the point Jacobi method. Second, we tune the BM parameters to improve the conditioning of the coefficient matrix. Both strategies leverage a newly derived analytical expression for the eigenvalue clustering points of the relevant operator. Numerical experiments demonstrate that the proposed method, combining both strategies, is particularly efficient for solving scattering problems involving composite penetrable materials with high contrast in material properties.

近年来的研究表明，基于Burton-Miller公式的边界元法（BM-BEM）可以有效地适用于求解外部问题。这种自适应利用卡尔德隆恒等式来改善底层积分算子的谱性质。因此，平方的BEM系数矩阵的大多数特征值，即算子的配位离散版本，聚集在复平面上的几个点上。当这些聚类点紧密聚集时，得到的线性系统是条件良好的，并且可以使用广义最小残差（GMRES）方法，只需少量迭代即可有效地求解。然而，当涉及多个材料且材料常数显著不同时，一些特征值会分离，使条件恶化。为了解决这个问题，我们提出了一个具有两种策略的增强型卡尔德龙预置BM-BEM。首先，我们采用了一种受点Jacobi法启发的预处理方案。其次，我们调整了BM参数，以改善系数矩阵的条件。这两种策略都利用了相关算子的特征值聚类点的新导出的解析表达式。数值实验表明，本文提出的方法结合了这两种策略，特别有效地解决了材料性能具有高对比度的复合可穿透材料的散射问题。

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引用次数: 0

Physics-informed neural network based on layerwise theory for bending analysis of laminated plates 基于分层理论的层合板弯曲分析的物理信息神经网络

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-02 DOI: 10.1016/j.enganabound.2025.106569

Zefeng Liu , Jinshuai Bai , Yuantong Gu , Ping Xiang

This paper introduces a novel computational framework that integrates physics-informed neural network (PINN) with generalized layerwise theory (LW) for the bending analysis of laminated composite plates. The framework leverages the approximation capability of deep neural networks while incorporating the physical constraints from LW theory to accurately capture the displacement fields of laminated composite plates as well as the shear stresses variations along the thickness direction. The framework is validated using various laminated plate configurations and loading conditions, with results showing excellent agreement with the meshless radial point interpolation method (RPIM), as well as other published solutions. These results highlight the potential of the PINN framework to enhance the predictive bending analysis of laminated composite plates, positioning it as a promising alternative for laminated composite structures.

介绍了一种将物理信息神经网络（PINN）与广义分层理论（LW）相结合的新型计算框架，用于层合复合材料板的弯曲分析。该框架利用深度神经网络的近似能力，同时结合LW理论的物理约束，准确捕获层合复合材料板的位移场以及沿厚度方向的剪切应力变化。该框架在各种层合板结构和加载条件下进行了验证，结果与无网格径向点插值方法（RPIM）以及其他已发表的解决方案非常吻合。这些结果突出了PINN框架在增强层压复合材料板的预测弯曲分析方面的潜力，将其定位为层压复合材料结构的有前途的替代品。

引用次数: 0