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Dynamic modeling of gears: An innovative hybrid FEM–analytical approach 齿轮动力学建模:一种创新的混合有限元分析方法
Q4 Engineering Pub Date : 2021-06-17 DOI: 10.2495/CMEM-V9-N2-117-125
F. Concli, Concli Gorla
Gearboxes are widely used in several applications ranging from the automotive to the industrial and robotic sectors. A planetary gearbox is a special kinematic gear arrangement that, taking advantage of a planet carrier, ensures high reduction ratios together with a very small design. Therefore, they are widely employed for transmissions which require a high power density. There are several fields of applications including, but not limited to, mechatronic, automation and wind power generation. To improve the design of new solutions, for performing monitoring activities on actual gearboxes and for the definition of maintenance schedules, the availability of physical models able to accurately describe the behavior of the system, both in healthy and damaged conditions, would represent a great support. Experimental and numerical studies of the behavior of gearboxes are already available in the literature. Nevertheless, while the experimental approaches are valid only for the specific configuration tested, the numerical techniques show limitations related to the computational effort required. This paper presents an innovative approach for the characterization of the behavior of two different geared transmissions. It is based on a hybrid approach that combines finite elements (FE) with analytical formulations. In detail, the solver computes separately the macro deformation of the bodies (numerical solution based on a coarse grid) and the contacts (solved analytically avoiding the need of mesh refinements). The computational effort is reduced significantly without affecting the accuracy of the results significantly. This approach was used to investigate and understand the vibro-dynamical behavior of a back-to-back test rig (typically used for the characterization of the surface fatigue strength of gears) and of an indus- trial planetary gearbox. The results obtained for the healthy – not damaged – gearboxes were compared with experimental measurements for both configurations in order to validate the hybrid approach. Once the models were validated, the same methodology was eventually used to study the effects of typical gear failures and in specifically surface fatigue (pitting), on the vibrational response. The capability to reproduce the effect of damages with the model of a gearbox represents the first indispensable step of a Structural Health Monitoring strategy. State-of-art and challenges are analyzed and discussed in the paper.
变速箱广泛应用于从汽车到工业和机器人领域的几个应用中。行星齿轮箱是一种特殊的运动齿轮装置,利用行星载体,确保高减速比和非常小的设计。因此,它们被广泛应用于需要高功率密度的传输。有几个领域的应用,包括但不限于,机电一体化,自动化和风力发电。为了改进新解决方案的设计、对实际齿轮箱执行监测活动以及定义维护计划,能够准确描述系统在健康和损坏状态下行为的物理模型的可用性将是一个很大的支持。实验和数值研究的行为的齿轮箱已经在文献中可用。然而,虽然实验方法仅对测试的特定配置有效,但数值技术显示出与所需计算量相关的局限性。本文提出了一种创新的方法来表征两种不同齿轮传动的行为。它基于将有限元(FE)与解析公式相结合的混合方法。具体来说,求解器分别计算了物体的宏观变形(基于粗网格的数值解)和接触(解析解,避免了网格细化的需要)。在不显著影响结果准确性的情况下,大大减少了计算量。该方法被用于研究和理解背靠背试验台(通常用于表征齿轮表面疲劳强度)和工业行星齿轮箱的振动动力学行为。为了验证混合方法的有效性,将健康非损坏齿轮箱的结果与两种结构的实验测量结果进行了比较。一旦模型得到验证,同样的方法最终被用于研究典型齿轮失效的影响,特别是表面疲劳(点蚀),对振动响应。用齿轮箱模型再现损伤效应的能力是结构健康监测策略不可缺少的第一步。本文对目前的研究现状和面临的挑战进行了分析和讨论。
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引用次数: 4
Energy balance relations for flow through thick porous structures 厚多孔结构流动的能量平衡关系
Q4 Engineering Pub Date : 2021-03-04 DOI: 10.2495/CMEM-V9-N1-28-37
S. Koley, K. Panduranga
In wave–structure interaction problems, energy balance relations are often derived and used to check the accuracy of the computational results obtained using numerical methods. These energy identities are also used to get qualitative information about various physical quantities of interest. It is well known that for rigid structures, the energy identity is K K r t 2 2 1 + = , where Kr and Kt are the reflection and transmission coefficients, respectively. Even if we take flexible barriers, then also the aforementioned energy identity will hold. Now, for wave past a thick porous structure, often a major portion of the incoming wave energy is dissipated due to the structural porosity. So, the aforementioned energy identity will be modified into K K K r t D 2 2 1 + + = , where KD takes into account the amount of dissipative wave energy. These energy identities are available in the literature for thin porous barriers. But derivation of the energy identity is complicated for thick porous structures due to complex momentum equation and boundary conditions. In the present paper, an appropriate energy identity will be derived for water waves past a thick rectangular porous structure. In this regard, Green’s second identity is used in multi-domain regions with the arguments velocity potential and its complex conjugate. With the help of complex function theory, the final form of the same is written in a compact form. Now, to compute each quantity associated with the energy identity, the associated boundary value problem is converted into a system of Fredholm integral equations. Finally, using the boundary element method, the components present in the energy identity are obtained and checked for validation.
在波-结构相互作用问题中,经常推导能量平衡关系,并用来检验数值方法计算结果的准确性。这些能量恒等式也被用来获得各种感兴趣的物理量的定性信息。众所周知,对于刚性结构,能量恒等式为K Kr t 2 2 1 + =,其中Kr和Kt分别为反射系数和透射系数。即使我们采取灵活的屏障,那么前面提到的能量同一性也会成立。现在,对于波浪通过厚多孔结构时,由于结构孔隙性,通常入射波能的大部分被耗散。因此,将上述能量恒等式修改为K K K r t D 2 21 1 + + =,其中KD考虑的是耗散波能的大小。这些能量恒等式在薄多孔势垒的文献中是可用的。但由于复杂的动量方程和边界条件,厚孔结构的能量恒等式推导比较复杂。本文将推导出水波通过厚矩形多孔结构时的能量恒等式。在这方面,格林的第二恒等式被用于多域区域,其参数是速度势及其复共轭。借助复变函数理论,将其最终形式写成紧化形式。现在,为了计算与能量恒等式相关的每一个量,相关的边值问题被转换成一个Fredholm积分方程系统。最后,利用边界元法,得到了能量恒等式中存在的分量,并进行了验证。
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引用次数: 2
Spherical particle migration evaluation in low reynolds number couette flow using smooth profile method 用光滑剖面法评价低雷诺数couette流中球形颗粒的迁移
Q4 Engineering Pub Date : 2021-01-01 DOI: 10.2495/cmem-v9-n3-261-275
M. Pourghasemi, N. Fathi, P. Vorobieff, G. Ahmadi, Seyed Sobhan Aleyasin, L. Eça
An Eulerian–Lagrangian model is developed to investigate the solid particle migration in low Reynolds number shear flows between two parallel plates. A continuous kernel function with a predefined thickness is applied in the implemented numerical model to smooth the discontinuity at the interface between primary and secondary phases. At each time step, the solid particle’s rotation and displacement are calculated to directly capture the interaction between the solid particle and primary liquid phase without simplification. Solution verification is performed using the global deviation grid convergence index approach. The observed order of accuracy for the primary phase solver approaches 2, consistent with the formal order of accuracy of the applied discretization scheme. The obtained velocity profiles from the implemented numerical approach show a good agreement with the analytical solution, confirming the single-phase flow solver’s reliability. The obtained numerical results from the applied Eulerian–Lagrangian multiphase model are also compared with experimental data from a linear shear flow apparatus with suspended buoyant particles, and good agreement was found.
建立了欧拉-拉格朗日模型,研究了两平行板间低雷诺数剪切流动中固体颗粒的迁移问题。在实现的数值模型中,采用具有预定义厚度的连续核函数来平滑主次相界面处的不连续。在每个时间步,计算固体颗粒的旋转和位移,直接捕捉固体颗粒与初级液相之间的相互作用,而不简化。采用全局偏差网格收敛指标法对解进行验证。观测到的初级相求解器的精度阶数接近于2,与所应用的离散化方案的形式精度阶数一致。数值计算得到的速度分布与解析解吻合较好,验证了求解器的可靠性。应用欧拉-拉格朗日多相模型得到的数值结果与悬浮悬浮颗粒线性剪切流实验数据进行了比较,两者吻合较好。
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引用次数: 0
An approac h for adaptive model performance validation within digital twinning 数字孪生中自适应模型性能验证方法
Q4 Engineering Pub Date : 2021-01-01 DOI: 10.2495/cmem-v9-n3-213-225
Madhu Sudan Sapkota, E. Apeh, M. Hadfield, R. Haratian, R. Adey, J. Baynham
The validation of the operationality of models is considered a crucial step in the model development process. Recent developments in Digital Twinning (DT) enable the online availability of operational data from the physical asset required for operational validation. The benefits of DT in situations where operational validation has formed a basis for model adaptation has also been demonstrated. However, these benefits within DT have not been fully utilized due to the lack of an approach for benchmarking the required quantity, quality and diversity of validation data and performance metrics for online model validation and adaptation. Therefore, there is a need for a framework for benchmarking validation data and metrics requirements during model validation in different domains. An approach for benchmarking the required quantity, quality and variability of validation data and performance metric(s) for online model adaptation within DT is proposed. The approach is focused on addressing the problem of parameter(s) uncertainty of a predictive model within its uncertainty boundary. It involves generating virtual test models, a primary and another reference model for the performance evaluation of one compared to the another with the benchmarked validating data and metrics within DT. This process is repeated until the dataset and/or metric(s) are promising enough to validate primary model against the reference model. The proposed approach is demonstrated using BEASY – a simulator designed to predict protection provided by a cathodic protection system to an asset. In this case, a marine structure is the focus of the study, where the protection potentials to prevent corrosion are predicted over the life of the structure. The algorithm(s) for the approach are provided within a Scientific Software (MATLAB) and integrated to the simulator-based cathodic-protection model.
模型可操作性的验证被认为是模型开发过程中的关键步骤。数字孪生(DT)的最新发展使操作验证所需的物理资产的操作数据能够在线可用。在操作验证已经形成模型适应基础的情况下,DT的好处也得到了证明。然而,由于缺乏对在线模型验证和适应所需的验证数据和性能指标的数量、质量和多样性进行基准测试的方法,DT中的这些优势尚未得到充分利用。因此,在不同领域的模型验证期间,需要一个框架来对验证数据和度量需求进行基准测试。提出了一种对DT内在线模型适应所需的验证数据和性能指标的数量、质量和可变性进行基准测试的方法。该方法主要解决预测模型在其不确定性边界内参数的不确定性问题。它包括生成虚拟测试模型,一个主要的和另一个参考模型,用于与DT内的基准验证数据和度量进行比较的性能评估。这个过程不断重复,直到数据集和/或度量足够有希望,可以根据参考模型验证主模型。该方法使用BEASY进行了演示,BEASY是一种用于预测阴极保护系统对资产提供保护的模拟器。在这种情况下,海洋结构是研究的重点,在结构的整个生命周期内预测防止腐蚀的保护潜力。该方法的算法在科学软件(MATLAB)中提供,并集成到基于模拟器的阴极保护模型中。
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引用次数: 3
Phantom -based lumbar spine experimental investigation and validation of a multibody model 基于幻影的腰椎多体模型实验研究与验证
Q4 Engineering Pub Date : 2021-01-01 DOI: 10.2495/cmem-v9-n3-226-238
Simone Borrelli, A. Formaggio, Vittoria Civilini, A. Lugas
The study of the biomechanics of the human spine is not yet developed extensively. Recent developments in this field have heightened the need for observing the spine from a comprehensive perspective to understand the complex biomechanical patterns, which underlie the kinematic and dynamic responses of this multiple-joint column. Within this frame of exigence, a joint study embracing experimental tests and multibody modelling was designed. This study provides novel insights to the segmental contribution profiles in flexion and extension, analysing different forms of sagittal-plane angles. Moreover, the validation of the multibody model contributes to defining the key aspects for a consistent spine modelling as well as it introduces the basis for simulating pathological conditions and post-orthopaedic surgical outcomes.
人体脊柱的生物力学研究尚未广泛开展。该领域的最新发展提高了从综合角度观察脊柱的需求,以理解复杂的生物力学模式,这是多关节柱的运动学和动力学响应的基础。在这种紧急情况下,设计了一个包括实验测试和多体建模的联合研究。本研究分析了不同形式的矢状面角度,为屈伸节段贡献剖面提供了新的见解。此外,多体模型的验证有助于确定一致脊柱建模的关键方面,并为模拟病理状况和骨科后手术结果提供基础。
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引用次数: 3
Ductile damage model of an alluminum alloy: experimental and numerical validation on a punch test 铝合金韧性损伤模型:冲压试验的实验与数值验证
Q4 Engineering Pub Date : 2021-01-01 DOI: 10.2495/cmem-v9-n3-249-260
M. Mastrone, L. Fraccaroli, F. Concli
The correct prediction of ductile fracture of mechanical components requires the knowledge of physical quantities that are in the plastic field. This region is characterized by non-linearities, and the classical yield criteria cannot be applied since they work only in the elastic field. It has been observed that parameters such as stress triaxiality and plastic strain play a determinant role in failure mechanisms. Thanks to simulation software, it is possible to implement the virtual models capable of calculating these parameters numerically by solving partial differential equations. These parameters can then be used to describe the fracture locus of a material that, in turn, allows to predict failure of a component. In this work, the Rice and Tracey damage model was calibrated for an aluminum alloy and validated on a punch test exploiting Finite Element Analysis. Good agreement between experimental observations and numerical results was obtained, demonstrating the capability of the considered model to predict failure on a real test case.
正确预测机械部件的韧性断裂需要塑性领域的物理量知识。该区域具有非线性特征,经典屈服准则仅适用于弹性场,不能应用。应力三轴性和塑性应变等参数在破坏机制中起决定性作用。借助仿真软件,可以通过求解偏微分方程实现能够数值计算这些参数的虚拟模型。这些参数可以用来描述材料的断裂轨迹,进而预测部件的失效。在这项工作中,Rice和Tracey损伤模型针对铝合金进行了校准,并利用有限元分析在冲压试验中进行了验证。实验结果与数值结果吻合较好,证明了所考虑的模型在实际测试用例中预测故障的能力。
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引用次数: 2
Field test and numerical modelling of RC slabs at different scaled distances with two types of external reinforcement 两种外配筋的RC板在不同比例距离下的现场试验与数值模拟
Q4 Engineering Pub Date : 2021-01-01 DOI: 10.2495/cmem-v9-n3-201-212
S. Martínez-Almajano, R. Castedo, Lina Ma López, Anastasio P. Santos, M. Chiquito, A. Alañón, C. Reifarth
This work deals with the response of eight reinforced concrete (RC) slabs, made at full-scale, some of them with the addition of externally bonded fibre reinforced polymer (FRP). The reinforcements were placed in all cases on the face opposite to the explosive detonation. Three scaled distances have been used from 0.83 m/kg1/3, in one test with no extra reinforcement; four tests were made with a scaled distance of 0.42 m/kg1/3: one without extra reinforcement, two with carbon fibre reinforcement (CFRP) and one with the E-glass fibre reinforcement (GFRP); finally, 0.21 m/kg1/3, in three trials, one without extra reinforcement, one with carbon fibre reinforcement and one with the E-GFRP. The first slab, used for calibration of the numerical models, was instrumented with pressure and acceleration sensors. For the validation of the other seven slabs, the damage surfaces on both sides of the slabs are used. In terms of numerical simulation performed with LS-DYNA, several models covering different solutions such as smooth particle hydrodynamics (SPH) or load blast enhanced have been performed for the description of the explosive, as well as the use of CSCM material models for concrete to analyse the best available solutions. The steel was modelled with the piecewise linear plasticity material, while the material laminated composite fabric was used for the FRP. Reinforcement with CFRP resulted in a generally reduced damage area on both surfaces. All models show a good correlation, including nonspherical charges made with SPH models, with the test results when comparing them with respect to acceleration and surface damage. SPH models work well for the high and medium scaled distance, but not so good for the shorter scaled distance.
这项工作涉及8块钢筋混凝土(RC)板的响应,按全尺寸制作,其中一些添加了外部粘合纤维增强聚合物(FRP)。增援部队在所有情况下都部署在爆炸地点对面。在一次试验中,从0.83 m/kg1/3开始使用了三个缩放距离,没有额外的加固;在0.42 m/kg1/3的比例距离下进行了4次试验:1次不加筋,2次碳纤维增强(CFRP), 1次e -玻璃纤维增强(GFRP);最后,0.21 m/kg1/3,在三个试验中,一个没有额外的加固,一个碳纤维加固和一个E-GFRP。第一块板子上装有压力和加速度传感器,用于数值模型的校准。对于其他7块板的验证,使用板的两侧损伤面。在LS-DYNA进行的数值模拟方面,几个模型涵盖了不同的解决方案,如光滑颗粒流体动力学(SPH)或负载爆炸增强,已经执行了炸药的描述,以及使用CSCM材料模型的混凝土来分析最佳可行的解决方案。钢材采用分段线性塑性材料建模,而材料层压复合织物用于FRP。用CFRP加固导致两个表面的损伤面积普遍减少。所有模型,包括SPH模型产生的非球形电荷,在比较加速度和表面损伤时,都显示出与试验结果的良好相关性。SPH模型对中高比例尺距离效果较好,但对较短比例尺距离效果不佳。
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引用次数: 0
Multiscale viscoelastic analysis of plain weave textile composites 平纹织物复合材料的多尺度粘弹性分析
Q4 Engineering Pub Date : 2021-01-01 DOI: 10.2495/cmem-v9-n3-189-200
M. Šejnoha, J. Vorel, S. Valentová, G. Marseglia
This paper outlines the prediction of a macroscopic viscoelastic response of plain weave textile composites made either from basalt or carbon fiber tows impregnated by polymeric matrix. Owing to a natural orthotropic response at the level of yarns, the calibration of a simple meso-scale constitutive model from virtual laboratory tests is precluded and a fully coupled analysis is needed instead. One option is solving the problem in the framework of FE analysis when both the microand meso-scale problems are solved with the help of the finite element method. This requires formulation of a suitable computational model most often represented by a statistically equivalent periodic unit cell on both scales. However, such an approach may prove computationally expensive particularly at stages of initial design where a large parametric study is often needed to test various material and geometrical configurations. A suitable method of attack then arises from the application of computationally efficient classical micromechanical models such as the Mori-Tanaka (MT) method. This approach is examined in the present study. While the present work is mostly computational, it requires an extensive experimental program to tune the generalized Leonov constitutive model describing the behavior of the matrix phase. Additionally, a series of virtual laboratory tests is carried out at the level of yarns to improve the predictive capability of the MT method.
本文概述了玄武岩或碳纤维纤维束经聚合物基体浸渍制成的平纹织物复合材料的宏观粘弹性响应预测。由于纱线水平上的自然正交各向异性响应,排除了从虚拟实验室测试中校准简单的中观尺度本构模型,而需要进行完全耦合分析。一种选择是在有限元分析的框架下解决微观和中观问题,并借助于有限元方法。这需要制定一个合适的计算模型,通常由两个尺度上的统计等效周期单元格表示。然而,这种方法可能在计算上很昂贵,特别是在初始设计阶段,通常需要进行大型参数研究来测试各种材料和几何结构。一种合适的攻击方法是应用计算效率高的经典微力学模型,如Mori-Tanaka (MT)方法。本研究对这种方法进行了检验。虽然目前的工作主要是计算性的,但它需要一个广泛的实验程序来调整描述矩阵相行为的广义列昂诺夫本构模型。此外,在纱线水平上进行了一系列虚拟实验室测试,以提高MT方法的预测能力。
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引用次数: 0
A validation study for a new erosion model to predict erosive airfoil defouling 一种新的侵蚀模型预测侵蚀型去污的验证研究
Q4 Engineering Pub Date : 2020-01-01 DOI: 10.2495/CMEM-V8-N1-13-26
A. Rudek, D. Muckenhaupt, T. Zitzmann, G. Russ, B. Duignan
A new defouling erosion model for Lagrangian particle tracking is used to predict defouling of amorphous, heterogeneous coatings such as those typically found in aircraft compressors. The main problem description, the mathematical formulation and the underpinning experiment of the model are presented in a previous communication by the authors. In this work, the Ansys CFX implementation of the model is described and an experiment is presented for the validation of the model. Air flows laden with a number of dry-ice particles are observed in an optically accessible stream channel containing a flat plate target. The defouling process of these particles is recorded with HSCs and the main parameters, such as indentation size in fouling layers, are processed and compared to corresponding numerical results. The model parameters considered are particle impact velocity and angle as well as particle and fouling material. Typical coatings which are relevant to commercial aircraft defouling processes are investigated. The target plate angle and the air velocity are varied and dry-ice particles of random size and shape are injected into the flow. The experiment is set up in a wind-tunnel test-rig and all recordings are made using two HSCs, a digital camera and Prandtl probe measurement. Experimental and numerical defouling results show good overall agreement for steep target angles but significant deviations for low target angles. Potential improvement to the defouling erosion model is discussed based on these results. The model as presented is used in large-scale compressor defouling simulations in the development process of on-wing aircraft maintenance systems.
一种新的拉格朗日粒子跟踪去污腐蚀模型被用于预测非晶非均相涂层的去污,如飞机压缩机中常见的涂层。该模型的主要问题描述、数学公式和基础实验在作者之前的通信中已经给出。本文介绍了该模型的Ansys CFX实现,并通过实验对模型进行了验证。在包含平板靶的光学可达流通道中观察到载有若干干冰颗粒的气流。用hsc记录了这些颗粒的去污过程,并对主要参数(如污垢层的压痕尺寸)进行了处理,并与相应的数值结果进行了比较。模型参数考虑了颗粒的冲击速度和角度以及颗粒和污垢材料。研究了与商用飞机除污工艺相关的典型涂料。改变靶板角度和气流速度,向流中注入大小和形状各异的干冰颗粒。实验是在风洞试验台进行的,所有的记录都是用两个hsc、一台数码相机和普朗特尔探针测量完成的。实验和数值去污结果表明,大目标角去污结果总体一致,小目标角去污结果偏差较大。在此基础上讨论了对消污侵蚀模型的改进潜力。该模型已应用于飞机维修系统开发过程中的大型压气机去污仿真。
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引用次数: 0
Relative displacements of 3D optical markers for deformations and crack monitoring of a masonry structure under shaking table tests 振动台试验下砌体结构变形与裂缝监测三维光学标记物的相对位移
Q4 Engineering Pub Date : 2019-10-01 DOI: 10.2495/cmem-v7-n4-350-362
I. Roselli, G. Canio, M. Rossi, C. Calderini, S. Lagomarsino
The application of 3D motion capture systems to shaking table testing provides a unique tool for recording relative displacements of a large number of measurement points of the tested structure. The analysis of 3D relative displacements during dynamic tests allows us to evaluate the structure deformations and to monitor the cracks formation and evolution. The present paper focuses on the processing and analysis of 3D motion capture data to extract accurate displacements between markers positioned on a full-scale model of a masonry cross vault representing a vault of the mosque of Dey, Algiers, tested at the ENEA Casaccia Research Centre. The management and processing of the data acquired through 67 markers located on the vault are described, showing the potentialities of the methodology. Moreover, the possible formulation of damage indices based on the structure deformations and cracks aperture detected from markers relative displacements (MRDs) was explored. In particular, cracks could be counted and classifi ed as a function of the detected apertures, following damage thresholds indicated in the Italian regulations. Moreover, the failure mechanism could be easily visualized and analysed by monitoring the cumulative MRDs. In addition, in-plane and out-of-plane deformations of walls could be monitored during each seismic test, providing accurate information on the torsional and bending effects.
三维运动捕捉系统在振动台测试中的应用为记录被测结构的大量测点的相对位移提供了一种独特的工具。动态测试过程中的三维相对位移分析使我们能够评估结构变形并监测裂缝的形成和演变。本文着重于3D动作捕捉数据的处理和分析,以提取位于代表阿尔及尔Dey清真寺拱顶的砖石交叉拱顶全尺寸模型上的标记之间的准确位移,该模型在ENEA Casaccia研究中心进行了测试。描述了通过位于保险库上的67个标记获得的数据的管理和处理,显示了该方法的潜力。此外,还探讨了基于标记相对位移(MRDs)检测到的结构变形和裂缝孔径的损伤指标的可能公式。特别是,裂缝可以被计数和分类为检测到的孔径的函数,按照意大利法规中指出的损伤阈值。此外,通过监测累积mrd,可以很容易地可视化和分析失效机制。此外,在每次地震试验中,可以监测墙体的面内和面外变形,提供有关扭转和弯曲影响的准确信息。
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引用次数: 5
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International Journal of Computational Methods and Experimental Measurements
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