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A computational framework for making early design decisions in deep space habitats 深空栖息地早期设计决策的计算框架
IF 4.8 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-10 DOI: 10.1016/j.advengsoft.2024.103690
Amir Behjat , Xiaoyu Liu , Oscar Forero , Roman Ibrahimov , Shirley Dyke , Ilias Bilionis , Julio Ramirez , Dawn Whitaker

The dynamics of systems of systems often involve complex interactions among the individual systems, making the implications of design choices challenging to predict. Design features in such systems may trigger unexpected behaviors or result in large variations in safety, performance or resilience. To provide a means of simulating such systems for aiding in these decisions, we have developed a prototype tool, the control-oriented dynamic computational modeling tool (CDCM). The CDCM provides rapid simulation capabilities to perform trade studies in systems of systems. The general class of systems of systems that we aim to examine involve multiple hazards, damage, cascading consequences, repair and recovery. We especially focus on systems-of-systems that incorporate a health management system (HMS) that can monitor the state of the habitat and make decisions about actions to take. In this paper we describe the features of the CDCM, the architecture we devised for simulation of systems-of-systems, the unique functionalities of this tool, and we provide a demonstration of the capabilities by performing two illustrative examples. We articulate the use of this tool for making early design decisions and demonstrate its use for trade studies that consider a model of a deep space habitat. We also share some experiences and lessons that may be useful for others seeking to address similar problems.

系统之系统的动态往往涉及单个系统之间复杂的相互作用,使得设计选择的影响难以预测。此类系统中的设计特征可能会引发意想不到的行为,或导致安全、性能或弹性方面的巨大变化。为了提供一种模拟此类系统的方法,以帮助做出这些决策,我们开发了一种原型工具,即面向控制的动态计算建模工具(CDCM)。CDCM 具备快速模拟能力,可对系统进行贸易研究。我们要研究的系统之系统的一般类别涉及多重危害、损害、连锁后果、修复和恢复。我们尤其关注包含健康管理系统(HMS)的系统之系统,该系统可监控栖息地的状态,并就应采取的行动做出决策。在本文中,我们介绍了 CDCM 的特点、我们为模拟系统而设计的架构、该工具的独特功能,并通过两个示例演示了其功能。我们阐述了该工具在早期设计决策中的应用,并演示了它在考虑深空栖息地模型的贸易研究中的应用。我们还分享了一些经验和教训,这些经验和教训可能对其他寻求解决类似问题的人有用。
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引用次数: 0
Real-time detection of concrete cracks via enhanced You Only Look Once Network: Algorithm and software 通过增强型 "只看一次 "网络实时检测混凝土裂缝:算法和软件
IF 4.8 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-10 DOI: 10.1016/j.advengsoft.2024.103691
Ronghua Fu , Yufeng Zhang , Kai Zhu , Alfred Strauss , Maosen Cao

Deep learning algorithms have been employed for real-time concrete crack detection. However, many algorithms are not specifically tailored for this purpose. Moreover, their lightweight iterations are generally optimized at the macro-model level, leaving room for further lightweight enhancements at the block level. Therefore, this study developed an enhanced YOLOv3 (You Only Look Once Network v3) model, named YOLO-Crack. The structural optimization of the model takes into consideration the shapes of concrete cracks in the dataset. Meanwhile, two multiple branch-shaped blocks based on dilated convolutions, convolutions and pooling operations were proposed. The two blocks, incorporating depthwise separable convolutions and attention mechanisms, were used to rebuild the model at the block level. These enhancements significantly reduce the size and improve the detection performance of YOLO-Crack. Furthermore, YOLO-Crack was softwareized for real-time detection of concrete cracks. The software was designed to support parallel computing, allowing for real-time detection of concrete cracks even on laptops with limited computing power. It was utilized to detect cracks on concrete roads at a university in Nanjing, China, enabling real-time detection at a frame rate of 30 frames per second with satisfactory accuracy.

深度学习算法已被用于实时混凝土裂缝检测。然而,许多算法并不是专门为此目的定制的。此外,这些算法的轻量级迭代一般都是在宏观模型层面上进行优化的,这就为在区块层面上进行进一步的轻量级增强留下了空间。因此,本研究开发了一个增强型 YOLOv3(You Only Look Once Network v3)模型,命名为 YOLO-Crack。该模型的结构优化考虑了数据集中混凝土裂缝的形状。同时,提出了两个基于扩张卷积、卷积和池化操作的多分支形状块。这两个块结合了深度可分离卷积和关注机制,用于在块级重建模型。这些改进大大缩小了 YOLO-Crack 的体积,提高了其检测性能。此外,YOLO-Crack 还被软件化,用于实时检测混凝土裂缝。该软件的设计支持并行计算,即使在计算能力有限的笔记本电脑上也能实时检测混凝土裂缝。该软件被用于检测中国南京某大学混凝土道路上的裂缝,以每秒 30 帧的帧速率进行实时检测,检测精度令人满意。
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引用次数: 0
Pre-tension design and research of cable net structure for space modular deployable antenna 用于空间模块化可部署天线的索网结构的预拉伸设计与研究
IF 4.8 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-07 DOI: 10.1016/j.advengsoft.2024.103685
Dake Tian , Zuwei Shi , Lu Jin , Xihua Yang , Rongqiang Liu , Chuang Shi

Modular deployable antennas represent an ideal structural form for the development of large-aperture antennas because of their flexibility, adaptability, and high versatility. To enhance the surface accuracy of the antenna after deployment, a comprehensive pre-tension design method that considers truss deformation and tension uniformity is proposed. First, the configuration design of the antenna cable net is constructed, and the mathematical models for cable length under surface accuracy requirements and boundary nodes are established considering catenary effects. Second, the distribution patterns of cable net structure nodes and segments are analyzed, leading to the creation of node coordinate matrices and cable net connection matrices. A basic model for cable net pre-tension design is developed based on the fundamental principles of force density. Furthermore, a multi-objective optimization of cable net pre-tension is performed using a genetic algorithm, considering truss structure deformation and tension uniformity as dual factors. Finally, the developed model is applied to design a single-module cable net structure, and numerical simulation is used for validation. Research results show that the overall surface form error is 0.32 mm, and the maximum tension ratio of cable net on the front cable net surface is 1.54, whereas the maximum tension ratio of tension ties is 2.28, thereby meeting the design requirements. Numerical simulation shows that the maximum deformation of the cable net structure is 0.16 mm, validating the correctness of the model. This research can provide valuable insights and references for the pre-tension design and research of cable net structures in other antennas.

模块化可展开天线具有灵活性、适应性和多功能性,是开发大孔径天线的理想结构形式。为了提高天线展开后的表面精度,本文提出了一种综合考虑桁架变形和张力均匀性的预张力设计方法。首先,构建了天线缆网的配置设计,并建立了表面精度要求和边界节点下的缆长数学模型,考虑了悬臂效应。其次,分析了缆网结构节点和线段的分布模式,从而建立了节点坐标矩阵和缆网连接矩阵。根据力密度的基本原理,建立了索网预张拉设计的基本模型。此外,考虑到桁架结构变形和张力均匀性这两个因素,使用遗传算法对索网预张力进行了多目标优化。最后,将所建立的模型用于设计单模块索网结构,并进行了数值模拟验证。研究结果表明,整体表面形状误差为 0.32 毫米,前索网表面的索网最大张力比为 1.54,而拉索的最大张力比为 2.28,从而满足了设计要求。数值模拟表明,索网结构的最大变形量为 0.16 毫米,验证了模型的正确性。这项研究可为其他天线的预张拉设计和索网结构研究提供有价值的启示和参考。
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引用次数: 0
Structural topology optimization considering casting and stress constraints under uniform dimensional shrinkage 考虑均匀尺寸收缩下的铸造和应力约束的结构拓扑优化
IF 4.8 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-05 DOI: 10.1016/j.advengsoft.2024.103692
Chao Wang , Wenzhe Han , Wenfeng Du , Yongqiang Yu , Bin Xu , Jianhua Rong

This work proposes and investigates a new multi-field-multi-constraint coupled topology optimization problem, in which stress control, design castability, and geometry dimensional shrinkage issues that are of concern to practical engineering are simultaneously considered. In the optimization proposal considered, a pair of special twin designs are generated using a two-projected-field scheme, which maintains a consistent topological configuration and uniform dimensional shrinkage variations during the optimization process. The implicit correlation between these twin designs poses major challenges to their independent stress and castability control. To this end, an appropriate formulation is presented by reasonably integrating stress and casting constraints into the optimization proposal with dimensional shrinkage. And, special numerical techniques including stress penalization, aggregation approximation, approximation correction, and regional regularization are appropriately introduced to construct an effective solution strategy. Typical numerical examples are operated to demonstrate the validity of the proposed method and systematically evaluate its numerical properties. The results indicate that in the absence of necessary stress control measures, the obtained twin designs cannot avoid local high-stress concentration under uniform dimensional shrinkage. In contrast, the proposed method can effectively address this issue, but at the cost of the design stiffness under a given material volume limit. As a result, twin designs used for blueprint and model designs that simultaneously meet stress, castability, and uniform dimensional shrinkage requirements are now readily available.

这项工作提出并研究了一个新的多场-多约束耦合拓扑优化问题,其中同时考虑了实际工程中关注的应力控制、设计铸造性和几何尺寸收缩问题。在所考虑的优化方案中,使用双投影场方案生成了一对特殊的孪生设计,在优化过程中保持了一致的拓扑结构和均匀的尺寸收缩变化。这些孪生设计之间的隐含相关性对其独立的应力和可铸性控制提出了重大挑战。为此,通过将应力和铸造约束合理地整合到带有尺寸收缩的优化方案中,提出了一个合适的方案。此外,还适当引入了包括应力惩罚、聚集近似、近似修正和区域正则化在内的特殊数值技术,以构建有效的求解策略。通过典型的数值计算实例,证明了所提方法的有效性,并系统地评估了其数值特性。结果表明,在缺乏必要的应力控制措施的情况下,所得到的孪生设计无法避免均匀尺寸收缩下的局部高应力集中。相比之下,所提出的方法可以有效解决这一问题,但代价是在给定材料体积限制下的设计刚度。因此,用于蓝图和模型设计、同时满足应力、可铸性和均匀尺寸收缩要求的孪晶设计现在很容易获得。
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引用次数: 0
A method of combined metamodel and subset simulation for reliability analysis of rare events 用于罕见事件可靠性分析的元模型与子集模拟相结合的方法
IF 4.8 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-04 DOI: 10.1016/j.advengsoft.2024.103693
Yuming Zhang , Juan Ma

Reliability analysis of large, complex structures with high reliability has always been a challenging task. The Subset Simulation (SUS) has proven highly effective for high-dimensional and small failure probability problems. However, the computational demands of time-consuming numerical simulations in the field of mechanical engineering remain substantial. Metamodeling techniques provide an effective means to reduce simulation computational costs. This paper introduces a novel approach, termed SUSAK, which combines the Subset Simulation with Kriging metamodels to address the challenge of small failure probability calculations. By using the original distribution of input variables representing the structural system, the SUSAK method establishes an adaptive metamodel and iteratively optimizes it with intermediate failure domain samples corresponding to the intermediate events. By replacing the performance function in subsequent calculations of the probability associated with intermediate events with metamodels, the enhanced method significantly reduces the computational burden compared to using the SUS method. This approach does not rely on solving for the design point, is not constrained by the shape of the failure domain, and retains the advantages of the SUS method in high-dimensional small failure probability calculations. As a result, it is well-suited for calculating small failure probabilities in nonlinear, discontinuous failure domains, multiple failure domains, and high-dimensional problems.

对具有高可靠性的大型复杂结构进行可靠性分析一直是一项具有挑战性的任务。子集模拟(SUS)已被证明对高维和小失效概率问题非常有效。然而,在机械工程领域,耗时的数值模拟对计算量的要求仍然很高。元建模技术是降低仿真计算成本的有效手段。本文介绍了一种名为 SUSAK 的新方法,它结合了子集模拟与克里金元模型,以应对小故障概率计算的挑战。通过使用代表结构系统的输入变量的原始分布,SUSAK 方法建立了一个自适应元模型,并利用与中间事件相对应的中间失效域样本对其进行迭代优化。通过在后续计算与中间事件相关的概率时用元模型替代性能函数,与使用 SUS 方法相比,增强型方法大大减轻了计算负担。这种方法不依赖于对设计点的求解,不受失效域形状的限制,并保留了 SUS 方法在高维小失效概率计算中的优势。因此,它非常适合计算非线性、不连续失效域、多失效域和高维问题中的小失效概率。
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引用次数: 0
A new concurrent optimization method of structural topologies and continuous fiber orientations for minimum structural compliance under stress constraints 结构拓扑和连续纤维取向的并行优化新方法,实现应力约束下的最小结构顺应性
IF 4.8 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-03 DOI: 10.1016/j.advengsoft.2024.103688
Liangbing Guo , Zeng Meng , Xuan Wang

The concurrent optimization of structural topologies and fiber orientations offers an effective way for improving the mechanical performance of fiber-reinforced composite structures. However, its local optimal solution problem under stress constraints remains extremely challenging. To tackle this problem, this paper presents an orientation variable corrected principal stress direction (OVCPSD) method, which is composed by a two-step optimization strategy. In the first step, the fiber orientation for the shear-weak materials is roughly distributed along the principal stress direction, and the principal stress direction of the previous iteration step is used as the initial fiber orientation. In the second step, the principal stress direction is further modified by an orientation variable in a small subinterval. Finally, a new optimization model of structural topologies and fiber orientations for minimum structural compliance under stress constraints is established, and the sensitivities of the objective and constraint functions with respect to both the pseudo-density and orientation variable are derived. Three numerical examples are presented to verify the effectiveness of the OVCPSD method. The complete code is available from the website: https://github.com/TopOpt-lbg/OVCPSD_L-shaped-beam.

同时优化结构拓扑和纤维取向为提高纤维增强复合材料结构的机械性能提供了有效途径。然而,其在应力约束下的局部最优解问题仍然极具挑战性。为解决这一问题,本文提出了一种由两步优化策略组成的取向可变校正主应力方向(OVCPSD)方法。第一步,剪切弱材料的纤维取向大致沿主应力方向分布,并将上一步迭代的主应力方向作为初始纤维取向。第二步,在一个小的子区间内通过取向变量进一步修正主应力方向。最后,建立了应力约束下最小结构顺应性的结构拓扑和纤维取向的新优化模型,并得出了目标函数和约束函数对伪密度和取向变量的敏感性。通过三个数值示例验证了 OVCPSD 方法的有效性。完整代码可从以下网站获取:https://github.com/TopOpt-lbg/OVCPSD_L-shaped-beam。
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引用次数: 0
A novel approach for reliable pedestrian trajectory collection with behavior-based trajectory reconstruction for urban surveillance systems 为城市监控系统提供可靠的行人轨迹收集和基于行为的轨迹重建的新方法
IF 4.8 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-31 DOI: 10.1016/j.advengsoft.2024.103687
Wonjun No , Byeongjoon Noh , Youngchul Kim

Collecting reliable pedestrian trajectories in pedestrian behavior analysis, trajectories broken by frame sampling and trajectories crossing in multi-object conditions often hinder their performance of existing pedestrian tracking models. Despite attempts to address these issues by performing detection and tracking simultaneously using deep learning algorithms, previous methods still struggle with errors such as mistaking a single pedestrian for multiple pedestrians. We propose a novel approach to efficiently collect and correct pedestrian trajectories with minimized practical errors in multi-object conditions for urban surveillance systems. Our system utilizes a single vision sensor to automatically collects trajectories of multiple pedestrians and employ simple, low-computational algorithms, particularly the Deep simple online real-time tracking (Deep SORT) method, to calibrate the trajectories from tracking-by-detection models. Additionally, our system identifies and merges broken pedestrian trajectories, treating them as potential single trajectories, while considering their spatiotemporal ranges. We evaluate the proposed system by implementing it on real testbed video footage. Our method significantly improves practical errors and achieves more accurate pedestrian trajectories compared to existing models, and exhibits robust characteristics, effectively handling complex situations such as occlusions and crowds.

在行人行为分析中收集可靠的行人轨迹、因帧采样而中断的轨迹以及在多目标条件下交叉的轨迹往往会阻碍现有行人跟踪模型的性能。尽管有人试图通过使用深度学习算法同时执行检测和跟踪来解决这些问题,但以往的方法仍然难以解决诸如将单个行人误认为多个行人等错误。我们提出了一种新方法,在多目标条件下有效地收集和纠正行人轨迹,最大限度地减少城市监控系统的实际误差。我们的系统利用单个视觉传感器自动收集多个行人的轨迹,并采用简单、低运算量的算法,特别是深度简单在线实时跟踪(Deep SORT)方法,根据逐个检测跟踪模型校准轨迹。此外,我们的系统还能识别并合并断裂的行人轨迹,将其视为潜在的单一轨迹,同时考虑其时空范围。我们在真实的测试平台视频片段上对所提出的系统进行了评估。与现有模型相比,我们的方法明显改善了实际误差,获得了更准确的行人轨迹,并表现出鲁棒性特征,能有效处理遮挡和人群等复杂情况。
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引用次数: 0
A high-precision T-spline blade modeling method with 2D and 3D knot adaptive refinement 采用二维和三维节点自适应细化的高精度 T-样条叶片建模方法
IF 4.8 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-29 DOI: 10.1016/j.advengsoft.2024.103684
Kewen Chen , Chan Qiu , Zhengyu Liu , Jianrong Tan

The aerodynamic shape of blades in turbo machinery is a key factor that affects blade efficiency, pressure ratio and other performance indicators. To address the lack of global continuity and difficulty in ensuring fairing quality in blade modeling, this paper proposes a novel blade modeling method that uses curvature constraints and a Mid-Closest Criterion to achieve adaptive knot refinement in 2D profile reconstructing and 3D T-mesh establishing process respectively. To begin with, the proposed Curvature-Constrained Periodic Reconstruction (CCPR) is used to reconstruct discrete sampling points of the section profile into a globally fairing periodic curve, and meets minimal error requirement. Additionally, the distribution of control points matches with curvature variation of the curve itself. Next, the Double Curves-guided Mid-Closest T-spline Surface skinning (DCM-TS) is used to construct a T-mesh from the stacked cross-sectional profile curves automatically, and the control vertices of the T-mesh are in a controllable scale and reasonably distributed. Further, the modeling precision is allocated with the curvature information of the ideal blade contour, and based on that, a T-spline skinning surface is obtained through LSPIA method, which updates the model and realizes blade modeling that considers both the design efficiency and accuracy. Eventually the proposed method is verified and compared with several traditional surface skinning methods in practical modeling cases. The result unveils that the presented method is compatible with traditional aerofoil parameterization methods, generates surface with global continuity and high fairing quality, and has sharply reduced and evenly distributed control vertices.

涡轮机械叶片的气动外形是影响叶片效率、压力比等性能指标的关键因素。针对叶片建模中缺乏全局连续性和难以保证公平性的问题,本文提出了一种新颖的叶片建模方法,在二维剖面重构和三维 T 形网格建立过程中分别使用曲率约束和 Mid-Closest 准则实现自适应节点细化。首先,所提出的曲率约束周期重构(CCPR)用于将断面轮廓的离散采样点重构为全局公平的周期曲线,并满足最小误差要求。此外,控制点的分布与曲线本身的曲率变化相匹配。其次,利用双曲线引导的最宽 T 样条曲面剥皮法(DCM-TS),自动将叠加后的断面曲线构建成 T 样条曲面,且 T 样条曲面的控制顶点尺度可控、分布合理。此外,利用理想叶片轮廓的曲率信息分配建模精度,并在此基础上通过 LSPIA 方法获得 T 型样条蒙皮面,更新模型,实现兼顾设计效率和精度的叶片建模。最后,在实际建模案例中,对所提出的方法进行了验证,并与几种传统的表面蒙皮方法进行了比较。结果表明,所提出的方法与传统的机翼参数化方法兼容,生成的曲面具有全局连续性和较高的整流质量,控制顶点锐减且分布均匀。
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引用次数: 0
A finite element based homogenization code in python: HomPy 基于有限元的 python 均质化代码:HomPy
IF 4.8 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-25 DOI: 10.1016/j.advengsoft.2024.103674
Emin Emre Ozdilek , Egecan Ozcakar , Nitel Muhtaroglu , Ugur Simsek , Orhan Gulcan , Gullu Kiziltas Sendur

The ability to predict the effective material property of composites with periodic micro-structures based on homogenization theory has been an effective method to analyze structures with complex heterogeneities. Homogenization codes have been made available for educational purposes including the homogenization code for the prediction of effective elasticity and thermal material properties in MATLAB. The aim of this educational paper is to present a Python version of the existing homogenization code and provide detailed diagrams of its key modules extending its ability to conduct analysis and design studies possibly via integration into commercial FEM software. Python has become a popular programming language due to its wide applicability to several disciplines, its portability, its flexibility by means of programming paradigms, its open-source nature, its well-documented libraries, and its easy-to-learn syntax. To increase the applicability and community reach of the homogenization algorithm presented, we provide a Python translation of the well-known MATLAB implementation. By doing so, we aim to increase the integration potential and adaptability of the homogenization approach to other computing packages and target adoption by a wider audience by leveraging the advantages of basing the solution on a free and open-source platform.

根据均质化理论预测具有周期性微结构的复合材料的有效材料特性,是分析具有复杂异质性结构的有效方法。均质化代码已可用于教学目的,包括在 MATLAB 中预测有效弹性和热材料特性的均质化代码。本教育论文的目的是介绍现有均质化代码的 Python 版本,并提供其关键模块的详细图示,通过与商业有限元软件的集成,扩展其进行分析和设计研究的能力。Python 因其在多个学科的广泛适用性、可移植性、编程范式的灵活性、开源性、文档齐全的库以及易于学习的语法而成为一种流行的编程语言。为了提高所介绍的均质化算法的适用性和社区影响力,我们对著名的 MATLAB 实现进行了 Python 翻译。通过这样做,我们旨在提高同质化方法的集成潜力和对其他计算软件包的适应性,并利用基于免费开源平台的解决方案的优势,让更多人采用。
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引用次数: 0
Enrichment terms for line singularities in second-order elliptic boundary value problems in 3D heterogeneous media: Application to heat conduction problems 三维异质介质中二阶椭圆边界值问题中线奇点的丰富项:热传导问题的应用
IF 4.8 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-24 DOI: 10.1016/j.advengsoft.2024.103683
Omid Bateniparvar , Danial Afifi , Nima Noormohammadi , Bijan Boroomand

A novel enrichment technique is proposed for the solution quality enhancement near weak singularities along straight lines in second-order elliptic boundary value problems. The considered 3D media can generally be heterogeneous. Enrichment is applied through construction of proper 3D singular functions for heterogeneous media. An advantage over similar approaches is that the singular bases are constructed without any knowledge of the analytical singularity order. To this end, the governing PDE is considered in a cylindrical fictitious domain whose axis lies along the singular line, over which the 3D equilibrated singular basis functions are developed. Combined with the smooth solution, the total solution undergoes imposition of the boundary conditions, so that the proper singular functions are automatically built. The singular solution series is primarily made by a combination of first kind Chebyshev polynomials and trigonometric functions, subjected to weighted residual imposition of the PDE to extract the equilibrated singular functions. Meanwhile, the cumbersome 3D integrals break into algebraic combinations of 1D predefined integrals, so that no numerical quadrature will be needed. The bases are tested as a boundary method in the solution of multiple 3D problems including weak singularities, to show their accuracy and efficiency. The proposed singular bases may be implemented in enriched techniques such as XFEM.

针对二阶椭圆边界值问题中沿直线的弱奇点附近的解质量提升,提出了一种新颖的增强技术。所考虑的三维介质一般可能是异质的。富集技术是通过为异质介质构建适当的三维奇异函数来实现的。与类似方法相比,其优势在于奇异基的构建无需任何分析奇异阶的知识。为此,在一个轴线沿奇异线的圆柱形虚构域中考虑支配 PDE,并在该虚构域上开发三维平衡奇异基函数。结合平滑解法,对总解法施加边界条件,从而自动建立适当的奇异函数。奇异解序列主要由第一类切比雪夫多项式和三角函数组合而成,并对 PDE 进行加权残差强加,以提取平衡奇异函数。同时,将繁琐的三维积分分解为一维预定义积分的代数组合,这样就不需要数值正交了。在解决包括弱奇点在内的多个三维问题时,这些基作为边界方法进行了测试,以显示其准确性和效率。提出的奇异基可以在 XFEM 等丰富的技术中实现。
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引用次数: 0
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