Engineering Analysis with Boundary Elements最新文献

英文中文

Boundary element method for hypersingular integral equations: Implementation and applications in potential theory 超积分方程的边界元方法：势理论中的实施与应用

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-30 DOI: 10.1016/j.enganabound.2024.105999

E. Strelnikova , N. Choudhary , K. Degtyariov , D. Kriutchenko , I. Vierushkin

The main objective of this paper is to develop effective numerical methods to solve hypersingular integral equations arising in various physical and mechanical applications. Both surface and contour integrals are considered. The novelty of the proposed approach lies in the exact formulas obtained for an arbitrary planar polygon in hypersingular integral estimations. A one-dimensional hypersingular integral equation is derived for axially symmetrical configurations, and analytical formulas are established for calculating the hypersingular parts. It is proved that the hypersingular component of the surface integral is equal to its hypersingular component along the tangent plane. These exact formulas enable the development of an effective numerical method based on boundary element implementation. Benchmark tests are considered, and the convergence of the proposed methods is demonstrated. Problems in crack analysis are formulated and solved using both surface and contour hypersingular integral equations. A comparison of the results is made between boundary element methods and finite element methods for penny-shaped cracks. Boundary value problems in fluid-structure interaction are considered, and numerical simulations are performed. An estimation of modes and frequencies of panel and blade vibrations when interacting with liquids is carried out.

本文的主要目的是开发有效的数值方法，以求解各种物理和机械应用中出现的超积分方程。本文同时考虑了曲面积分和轮廓积分。所提方法的新颖之处在于在超积分估算中为任意平面多边形获得精确公式。针对轴对称配置推导出了一维超积分方程，并建立了计算超积分部分的解析公式。证明了曲面积分的超星部分等于其沿切线平面的超星部分。有了这些精确的公式，就可以根据边界元素的实施情况开发有效的数值方法。对基准测试进行了考虑，并证明了所提出方法的收敛性。使用曲面和轮廓超积分方程对裂缝分析中的问题进行了表述和求解。比较了边界元方法和有限元方法对笔形裂缝的处理结果。考虑了流固相互作用中的边界值问题，并进行了数值模拟。对面板和叶片与液体相互作用时的振动模式和频率进行了估算。

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引用次数: 0

A hybrid PSO-WO algorithm for identification of irregular inner wall defects of a body in a thermal environment 用于识别热环境中不规则人体内壁缺陷的 PSO-WO 混合算法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-30 DOI: 10.1016/j.enganabound.2024.106011

Wenchao Ji , Guojun Li , Chunguang Zhao , Zhi Yi , Linyang Wei , Shuangcheng Sun , Cunhai Wang

Accurate knowledge of the inner wall defect shape of industrial thermal equipment (ITE) plays a crucial role in safety inspections. However, direct observation and measurement are challenging due to the high-temperature environment within ITE. To address this issue, the identification of irregular inner wall defect shape based inverse technology is studied in this work. A novel particle swarm optimization (PSO) coupled with the whale optimization (WO) algorithm (HPWA) is developed as solver for inverse problems to identify the inner wall defect irregular shape. This hybrid approach enhanced the late-stage convergence efficiency of WO while avoiding the local optima issue commonly faced by PSO. The radial integral boundary element method (RIBEM) is used for solving the transient heat transfer problem and obtain transient temperature data at measurement points for inverse problem simulations. It was chosen for its capability to effectively handle complex boundary shapes by discretizing only the domain boundaries. Additionally, the effect of the distance between outer and inner boundaries and measurement duration on the inverse results are thoroughly analyzed. Results show that the PSO-WO algorithm is robust to measurement errors and becomes more accurate with measurement points closer to the actual inner boundary position. Extending the measurement time has little effect on inversion results when the measurement period is long enough.

准确了解工业热力设备（ITE）的内壁缺陷形状在安全检查中起着至关重要的作用。然而，由于 ITE 内的高温环境，直接观察和测量具有挑战性。为解决这一问题，本工作研究了基于逆技术的不规则内壁缺陷形状识别。开发了一种新型粒子群优化（PSO）与鲸鱼优化（WO）算法（HPWA）相结合的逆问题求解器，用于识别内壁缺陷的不规则形状。这种混合方法提高了 WO 的后期收敛效率，同时避免了 PSO 通常面临的局部最优问题。径向积分边界元法（RIBEM）用于求解瞬态传热问题，并获取测量点的瞬态温度数据用于逆问题模拟。之所以选择 RIBEM，是因为该方法只对域边界进行离散化处理，能够有效地处理复杂的边界形状。此外，还深入分析了内外边界之间的距离和测量持续时间对反演结果的影响。结果表明，PSO-WO 算法对测量误差具有很强的鲁棒性，测量点越接近实际内边界位置，其精度就越高。当测量时间足够长时，延长测量时间对反演结果影响不大。

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引用次数: 0

A new method to solve the forward and inverse problems for the spatial Solow model by using Physics Informed Neural Networks (PINNs) 利用物理信息神经网络 (PINN) 解决空间索洛模型正演和反演问题的新方法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-30 DOI: 10.1016/j.enganabound.2024.106013

Wanjuan Hu

The spatial Solow model can take into account the geographical interdependence and the spatial organization of economic activities, and offers a better understanding of economic growth. In this work, governing equations of the spatial Solow model were solved by using the Physics Informed Neural Networks (PINNs) method, and both the forward and inverse problems were considered. For the forward problems, the conditions with and without considering the technology progress were solved, and the results were validated against the existing ones and good agreement can be found. For the inverse problems, the parameter identification of the production function was conducted by using very sparse data points. For the data without noise, two parameters of the production function can be estimated by using only 2 data points, where the errors can be below 3 %. For the low level noisy data, the parameters can also be inversed with 30 data points, and the errors for the two parameters were both less than 1 %.

空间索洛模型可以考虑地理上的相互依存性和经济活动的空间组织，并能更好地理解经济增长。在这项工作中，利用物理信息神经网络（PINNs）方法求解了空间索洛模型的支配方程，并考虑了正向和反向问题。在正向问题中，求解了考虑和不考虑技术进步的条件，并将结果与现有结果进行了验证，结果一致。对于逆向问题，利用非常稀疏的数据点进行了生产函数的参数识别。对于无噪声数据，只需使用 2 个数据点即可估计生产函数的两个参数，误差可低于 3%。对于低水平噪声数据，也可以用 30 个数据点对参数进行反演，两个参数的误差均小于 1%。

引用次数: 0

An efficient scheme of calculating nearly singular integrals for the 3D BEM modeling of thin media 用于薄介质三维 BEM 建模的近奇异积分高效计算方案

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-30 DOI: 10.1016/j.enganabound.2024.106005

Y.C. Shiah , Jin-Jia Zhan , M.R. Hematiyan

For engineering analysis of 3D problems, common difficulty to apply the boundary element method (BEM) is the so called “nearly singular integrals” that arise when the object is thin or the internal points of analysis are close to the boundary. In the present work, the local integration domain is sub-divided into 4 quadrants at the projection of the source point. By use of the FG-Squircular Mapping, the four quadrants are transformed to 4 quarter-discs for the integrations to be performed under the polar coordinates. As such, the singularity strength is reduced by one order. Thus, the Gauss points can be reasonably increased solely for the integration of the radial distance, while the other integration for the angular parameter remains regular. Such treatment greatly enhances the efficiency of the integration computation. To demonstrate the validity of all presented formulations, a few typical examples are presented to calculate the nearly singular boundary integrals for treating 3D problems of heat transfer as well as elastostatics.

在三维问题的工程分析中，应用边界元法（BEM）的常见困难是所谓的 "近奇异积分"，当物体较薄或内部分析点靠近边界时会出现这种情况。在本研究中，局部积分域在源点投影处被细分为 4 个象限。通过使用 FG-Squircular Mapping，四个象限被转换为 4 个四分之一圆盘，以便在极坐标下进行积分。因此，奇异性强度降低了一个等级。因此，只需对径向距离进行积分，就可以合理地增加高斯点，而对角度参数的其他积分则保持规则。这种处理方法大大提高了积分计算的效率。为了证明所有公式的有效性，本文列举了几个典型的例子来计算近奇异边界积分，用于处理三维传热和弹性问题。

引用次数: 0

Modeling variably saturated flows in porous media using the numerical manifold method 利用数值流形法模拟多孔介质中的可变饱和流动

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-28 DOI: 10.1016/j.enganabound.2024.106016

Yuanqiang Chen , Hong Zheng , Xiaocheng Huang , Shunkai Liu

Robust and reliable numerical models are vital to solve the Richards’ equation, which depicts the variably saturated flows in porous media. In this study, the Richards’ equation is discretized spatially with the numerical manifold method (NMM) and temporally with the backward Euler scheme, in which the under-relaxation and mass lumping techniques are introduced to keep the numerical stability and mass balance. Several examples are performed to validate the correctness and accuracy of the proposed model. The numerical results demonstrate the potential applicability of the proposed model to solve saturated-unsaturated seepage problems.

稳健可靠的数值模型对于求解描述多孔介质中可变饱和流动的理查兹方程至关重要。本研究采用数值流形法（NMM）对理查兹方程进行空间离散化，并采用后向欧拉方案对其进行时间离散化，其中引入了欠松弛和质量块技术，以保持数值稳定性和质量平衡。通过几个实例验证了所提模型的正确性和准确性。数值结果证明了所提模型在解决饱和-非饱和渗流问题上的潜在适用性。

引用次数: 0

Boundary Knots Method with ghost points for high-order Helmholtz-type PDEs in multiply connected domains 多连通域中高阶 Helmholtz 型 PDE 的带鬼点的边界结方法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-28 DOI: 10.1016/j.enganabound.2024.105998

T. Li , M. Lei , HongEn. Jia

This paper proposes the Boundary Knot Method with ghost points (BKM-G), which enhances the performance of the BKM for solving 2D (3D) high-order Helmholtz-type partial differential equations in domains with multiple cavities. The BKM-G differs from the conventional BKM by relocating the source points from the boundary collocation nodes to a random region, such as a circle (sphere) encompassing the original domain in 2D (3D). Compared with classical BKM, this modification improves accuracy without sacrificing simplicity and efficiency. Moreover, this paper investigates and analyzes the effect of the ghost circle/sphere’s radius

R

in BKM-G for solving various high-order Helmholtz-type PDEs. Numerous 2D and 3D numerical examples illustrate that the BKM-G outperforms the BKM for a wide range of

R

. The effectiveness of the proposed effective condition number (ECN) approach in finding the optimal

R

has also been demonstrated. Furthermore, the economic ECN (EECN) is studied to significantly improve the efficiency of ECN.

本文提出了带鬼点的边界结方法（BKM-G），它提高了 BKM 在求解具有多个空腔的域中的二维（三维）高阶 Helmholtz 型偏微分方程时的性能。BKM-G 与传统的 BKM 不同，它将源点从边界配准节点迁移到一个随机区域，如一个环绕原始二维（三维）域的圆（球）。与经典 BKM 相比，这种修改在不牺牲简单性和效率的前提下提高了精度。此外，本文还研究和分析了 BKM-G 中幽灵圆/球半径 R 对求解各种高阶 Helmholtz 型 PDE 的影响。大量二维和三维数值示例表明，BKM-G 在很大的 R 范围内都优于 BKM。此外，还研究了经济 ECN（EECN），以显著提高 ECN 的效率。

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引用次数: 0

Discussion on “2.5D prediction of soil vibrations due to railway loads by the isogeometric analysis with scaled boundary” by Yang Y.B. and Li. J 就 Yang Y.B. 和 Li.J. 所著 "利用等值边界分析法对铁路荷载引起的土壤振动进行 2.5D 预测 "的讨论J

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-28 DOI: 10.1016/j.enganabound.2024.106006

Alireza Yaseri

引用次数: 0

An online interactive physics-informed adversarial network for solving mean field games 用于解决均值场博弈的在线交互式物理信息对抗网络

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-25 DOI: 10.1016/j.enganabound.2024.106002

Weishi Yin , Zhengxuan Shen , Pinchao Meng , Hongyu Liu

We propose an online interactive physics-informed adversarial network (IPIAN) to address mean field games (MFGs) from the perspective of physics-informed interaction. In this study, we model the interaction between agents as a physics-informed exchange process, quantifying the evolution and distribution of individual strategy choices. We utilize the variational dyadic structure of MFGs to transform the dynamic game problem into a static optimization problem, subsequently employing the adversarial network to solve the mean field games. Based on the generative adversarial framework, two online physics-informed networks solve the value and density functions. These networks are trained to approximate the solution of MFGs through adversarial means. Additionally, a self-attention mechanism is introduced to enhance the focus on strategic physics-informed, thereby improving the expressiveness of IPIAN. Numerical experiments validate the effectiveness of IPIAN in solving high-dimensional mean field game models, as demonstrated by obstacle avoidance experiments with a quadrotor in various scenarios.

我们提出了一种在线交互式物理信息对抗网络（IPIAN），从物理信息交互的角度解决均场博弈（MFGs）问题。在这项研究中，我们将代理之间的互动建模为物理信息交换过程，量化了个体策略选择的演变和分布。我们利用 MFGs 的变式二元结构将动态博弈问题转化为静态优化问题，然后利用对抗网络解决均场博弈。基于生成对抗框架，两个在线物理信息网络解决了值函数和密度函数问题。这些网络经过训练，可通过对抗手段近似求解均值场博弈。此外，还引入了自我关注机制，以加强对战略性物理信息的关注，从而提高 IPIAN 的表现力。数值实验验证了 IPIAN 在求解高维均场博弈模型方面的有效性，四旋翼飞行器在各种场景下的避障实验也证明了这一点。

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引用次数: 0

A coupled scaled boundary finite element and phase-field algorithm for seismic loading 地震加载的耦合比例边界有限元和相场算法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-24 DOI: 10.1016/j.enganabound.2024.106009

Yue Zhuo , Degao Zou , Kai Chen , Jingmao Liu , Yongqian Qu , Guoyang Yi

Seismic-induced damage, integral to the safety evaluations of major engineering projects, persists as a key focus of research worldwide. Based on the Scaled Boundary Finite Element Method (SBFEM) and the Phase-Field Method (PFM), a coupled algorithm tailored for reciprocal loading was introduced in this paper, integrating strategies including "closure constraints," "numerical threshold strategy," and "subdomain block integration." Adopting object-oriented principles, a universal coupling solution framework has been built and seamlessly embedded within GEODYNA, a self-developed finite element software system. The accuracy was validated through rigorous benchmark tests. The entire process of crack initiation, propagation, and dynamic opening-closing cycles in the Koyna concrete gravity dam was reproduced. Furthermore, the effect of mesh size and computational timestep on the structural seismic response, crack localization, and the extent of damage in the dam were explored. The outcomes demonstrated that the SBFEM-PFM coupling algorithm performs effectively and meets the engineering precision criteria for seismic evaluations and reinforcement analyses of crucial structures.

地震诱发的破坏是重大工程项目安全评估不可或缺的一部分，一直是全球研究的重点。本文以比例边界有限元法（SBFEM）和相场法（PFM）为基础，结合 "闭合约束"、"数值阈值策略 "和 "子域分块集成 "等策略，介绍了一种专为往复加载量身定制的耦合算法。采用面向对象的原则，建立了一个通用耦合解决方案框架，并无缝嵌入到自主开发的有限元软件系统 GEODYNA 中。通过严格的基准测试验证了其准确性。Koyna 混凝土重力坝的裂缝萌发、扩展和动态开合循环的整个过程都得到了再现。此外，还探讨了网格大小和计算时间步长对大坝结构地震响应、裂缝定位和损坏程度的影响。结果表明，SBFEM-PFM 耦合算法在关键结构的抗震评估和加固分析中表现有效，符合工程精度标准。

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RIM-IGABEM and DRM-IGABEM in three-dimensional general anisotropic elastic problems with complex-shape cavities 带有复杂形状空腔的三维一般各向异性弹性问题中的 RIM-IGABEM 和 DRM-IGABEM

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-22 DOI: 10.1016/j.enganabound.2024.106000

Fangling Sun , Chunying Dong

The paper establishes the pure boundary integral equations of the isogeometric boundary element method (IGABEM) based on isotropic fundamental solutions to solve three-dimensional (3D) general anisotropic elastic problems including various complex cavities. The residual method is employed which introduces the fictitious body force causing the domain integral. Subsequently, the radial integration method (RIM) and the dual reciprocity method (DRM) are utilized to transform the domain integral to the boundary integral, respectively. Moreover, the Bézier extraction technique are used to facilitate the incorporation of NURBS into boundary element codes. Based on this, a novel scheme to determine the location of the collocation points in NURBS elements is proposed. Finally, the theoretical frameworks of the RIM-IGABEM and the DRM-IGABEM are developed, which retain the advantages of BEM and IGA, i.e. only boundary is discretized and complex geometry is described exactly, and the schemes are adaptable that only require to change pre-processing of a considered anisotropic problems, including the material properties and the geometry. Several numerical examples are used to demonstrate effectiveness of the schemes, and the effects of the material properties and the geometric shape on the distribution of displacements are discussed in detail.

本文建立了基于各向同性基本解的等几何边界元法（IGABEM）纯边界积分方程，用于求解包括各种复杂空腔在内的三维（3D）一般各向异性弹性问题。残差法引入了引起域积分的虚体力。随后，利用径向积分法（RIM）和二元互易法（DRM）分别将域积分转换为边界积分。此外，贝塞尔抽取技术也有助于将 NURBS 纳入边界元代码。在此基础上，提出了一种确定 NURBS 元素中配位点位置的新方案。最后，提出了 RIM-IGABEM 和 DRM-IGABEM 的理论框架，它们保留了 BEM 和 IGA 的优点，即只对边界进行离散化，并精确描述复杂的几何形状，而且方案适应性强，只需改变对所考虑的各向异性问题的预处理，包括材料属性和几何形状。我们使用了几个数值示例来证明这些方案的有效性，并详细讨论了材料属性和几何形状对位移分布的影响。

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