• Title/Summary/Keyword: Numerical integration

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The Expressions of Vector Gravity and Gravity Gradient Tensor due to an Elliptical Cylinder (타원 기둥에 의한 벡터 중력 및 중력 변화율 텐서 반응식)

  • Hyoungrea Rim
    • Geophysics and Geophysical Exploration
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    • v.26 no.1
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    • pp.1-7
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    • 2023
  • This study derives the expressions of vector gravity and gravity gradient tensor due to an elliptical cylinder. The vector gravity for an arbitrary three-dimensional (3D) body is obtained by differentiating the gravitational potential, including the triple integral, according to the shape of the body in each axis direction. The vector gravity of the 3D body with axial symmetry is integrated along the axial direction and reduced to a double integral. The complex Green's theorem using complex conjugates subsequently converts the double integral into a one-dimensional (1D) closed-line integral. Finally, the vector gravity due to the elliptical cylinder is derived using 1D numerical integration by parameterizing a boundary of the elliptical cross-section as a closed line. Similarly, the gravity gradient tensor due to the elliptical cylinder is second-order differentiated from the gravitational potential, including the triple integral, and integrated along the vertical axis direction reducing it to a double integral. Consequently, all the components of the gravity gradient tensor due to an elliptical cylinder are derived using complex Green's theorem as used in the case of vector gravity.

Formulation and evaluation a finite element model for free vibration and buckling behaviours of functionally graded porous (FGP) beams

  • Abdelhak Mesbah;Zakaria Belabed;Khaled Amara;Abdelouahed Tounsi;Abdelmoumen A. Bousahla;Fouad Bourada
    • Structural Engineering and Mechanics
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    • v.86 no.3
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    • pp.291-309
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    • 2023
  • This paper addresses the finite element modeling of functionally graded porous (FGP) beams for free vibration and buckling behaviour cases. The formulated finite element is based on simple and efficient higher order shear deformation theory. The key feature of this formulation is that it deals with Euler-Bernoulli beam theory with only three unknowns without requiring any shear correction factor. In fact, the presented two-noded beam element has three degrees of freedom per node, and the discrete model guarantees the interelement continuity by using both C0 and C1 continuities for the displacement field and its first derivative shape functions, respectively. The weak form of the governing equations is obtained from the Hamilton principle of FGP beams to generate the elementary stiffness, geometric, and mass matrices. By deploying the isoparametric coordinate system, the derived elementary matrices are computed using the Gauss quadrature rule. To overcome the shear-locking phenomenon, the reduced integration technique is used for the shear strain energy. Furthermore, the effect of porosity distribution patterns on the free vibration and buckling behaviours of porous functionally graded beams in various parameters is investigated. The obtained results extend and improve those predicted previously by alternative existing theories, in which significant parameters such as material distribution, geometrical configuration, boundary conditions, and porosity distributions are considered and discussed in detailed numerical comparisons. Determining the impacts of these parameters on natural frequencies and critical buckling loads play an essential role in the manufacturing process of such materials and their related mechanical modeling in aerospace, nuclear, civil, and other structures.

Concrete Reinforcement Modeling with IFC for Automated Rebar Fabrication

  • LIU, Yuhan;AFZAL, Muhammad;CHENG, Jack C.P.;GAN, Vincent J.L.
    • International conference on construction engineering and project management
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    • 2020.12a
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    • pp.157-166
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    • 2020
  • Automated rebar fabrication, which requires effective information exchange between model designers and fabricators, has brought the integration and interoperability of data from different sources to the notice of both academics and industry practitioners. Industry Foundation Classes (IFC) was one of the most commonly used data formats to represent the semantic information of prefabricated components in buildings, whereas the data format utilized by rebar fabrication machine is BundesVereinigung der Bausoftware (BVBS), which is a numerical data structure exchanging reinforcement information through ASCII encoded files. Seamless transformation between IFC and BVBS empowers the automated rebar fabrication and improve the construction productivity. In order to improve data interoperability between IFC and BVBS, this study presents an IFC extension based on the attributes required by automated rebar fabrication machines with the help of Information Delivery Manual (IDM) and Model View Definition (MVD). IDM is applied to describe and display the information needed for the design, construction and operation of projects, whereas MVD is a subset of IFC schema used to describe the automated rebar fabrication workflow. Firstly, with a rich pool of vocabularies practitioners, OmniClass is used in information exchange between IFC and BVBS, providing a hierarchy classification structure for reinforcing elements. Then, using International Framework for Dictionaries (IFD), the usage of each attribute is defined in a more consistent manner to assist the data mapping process. Besides, in order to address missing information within automated fabrication process, a schematic data mapping diagram has been made to deliver IFC information from BIM models to BVBS format for better data interoperability among different software agents. A case study based on the data mapping will be presented to demonstrate the proposed IFC extension and how it could assist/facilitate the information management.

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Coupled Dynamic Analyses of Underwater Tracked Vehicle and Long Flexible Pipe (유연관-해저주행차량 연성 동적거동 해석)

  • Hong, Sup;Kim, Hyung-Woo
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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    • v.13 no.3
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    • pp.237-245
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    • 2008
  • We developed a computational method on coupled dynamics of tracked vehicle on seafloor and long flexible pipe. The tracked vehicle is modeled as rigid-body vehicle, and the linked flexible pipe is discretized according to a lumped-parameter model. The equations of motion of the rigid-body vehicle on the soft seafloor are combined with the governing equations of flexible pipe dynamics. Four Euler parameters method is used to express the orientations of the vehicle and the flexible pipe. In order to solve the nonlinear coupled dynamics of vehicle and flexible pipe an incremental-iterative formulation is implemented. For the time-domain integration $Newmark-\beta$ method is adopted. The total Jacobean matrix has been derived based on the incremental-iterative formulation. The interactions between the dynamics of flexible pipe and the mobility of the tracked vehicle on soft seafloor are investigated through numerical simulations in time domain.

Calculation of the Mutual Radiation Impedance by the Spatial Convolution in the Cylindrical Structure (원통 구조에서 공간 콘볼루션을 이용한 상호 방사 임피던스 계산)

  • Bok, Tae-Hoon;Li, Ying;Paeng, Dong-Guk;Lee, Jong-Kil;Shin, Ku-Kyun;Joh, Chee-Yong
    • The Journal of the Acoustical Society of Korea
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    • v.29 no.1
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    • pp.1-9
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    • 2010
  • The mutual radiation impedance was calculated using the spatial convolution in the cylindrical structure. The Cartesian coordinate was transformed into the cylindrical coordinate using the spatial convolution for the cylindrical array structure. This method cannot consider the cylindrical baffle, but can reduce the computation time. The error for not considering the cylindrical baffle was analyzed by the comparison of the spatial convolution method with the quadruple integration method in the cylindrical structure. The mutual radiation resistance in the cylindrical structure was compared with the one in the planar baffle. Based on two kinds of the comparison, we presented the error of the suggesting method in this paper, confirming that the spatial convolution method could be applied to compute the mutual radiation impedance in the cylindrical structure at certain conditions.

Thermal post-buckling measurement of the advanced nanocomposites reinforced concrete systems via both mathematical modeling and machine learning algorithm

  • Minggui Zhou;Gongxing Yan;Danping Hu;Haitham A. Mahmoud
    • Advances in nano research
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    • v.16 no.6
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    • pp.623-638
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    • 2024
  • This study investigates the thermal post-buckling behavior of concrete eccentric annular sector plates reinforced with graphene oxide powders (GOPs). Employing the minimum total potential energy principle, the plates' stability and response under thermal loads are analyzed. The Haber-Schaim foundation model is utilized to account for the support conditions, while the transform differential quadrature method (TDQM) is applied to solve the governing differential equations efficiently. The integration of GOPs significantly enhances the mechanical properties and stability of the plates, making them suitable for advanced engineering applications. Numerical results demonstrate the critical thermal loads and post-buckling paths, providing valuable insights into the design and optimization of such reinforced structures. This study presents a machine learning algorithm designed to predict complex engineering phenomena using datasets derived from presented mathematical modeling. By leveraging advanced data analytics and machine learning techniques, the algorithm effectively captures and learns intricate patterns from the mathematical models, providing accurate and efficient predictions. The methodology involves generating comprehensive datasets from mathematical simulations, which are then used to train the machine learning model. The trained model is capable of predicting various engineering outcomes, such as stress, strain, and thermal responses, with high precision. This approach significantly reduces the computational time and resources required for traditional simulations, enabling rapid and reliable analysis. This comprehensive approach offers a robust framework for predicting the thermal post-buckling behavior of reinforced concrete plates, contributing to the development of resilient and efficient structural components in civil engineering.

The Expressions of Vector Gravity and Gravity Gradient Tensor due to an Elliptical Disk (타원판에 의한 벡터 중력 및 중력 변화율 텐서 반응식)

  • Hyoungrea Rim
    • Geophysics and Geophysical Exploration
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    • v.27 no.1
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    • pp.51-56
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    • 2024
  • In this paper, the vector gravity and gravity gradient tensor of an elliptical disk are derived. The vector gravity of an elliptical disk is defined by differentiating the gravitational potential due to the elliptical disk expressed by a double integral with respect to each axial direction. The vector gravity defined by the double integral is then transformed into a line integral of a closed curve along the elliptical disk boundary using the complex Green's theorem. Finally, vector gravity due to the elliptical disk is derived by 1D parametric numerical integration along the elliptical disk boundary. The xz, yz, zz components of the gravity gradient tensor due to the elliptical disk are obtained by differentiating the vector gravity with respect to vertical direction. The xx, yy, xy components are derived by differentiating the horizontal components of the vector gravity in the form of a double integral with respect to horizontal directions and then using the complex Green's theorem.

Minimum cost design for circular isolated footings with eccentric column taking into account that the surface in contact with the ground works partially in compression

  • Inocencio Luevanos-Soto;Arnulfo Luevanos-Rojas;Victor Manuel Moreno-Landeros;Griselda Santiago-Hurtado
    • Coupled systems mechanics
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    • v.13 no.4
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    • pp.311-335
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    • 2024
  • This work aims to show a model to estimate the minimum cost (Thickness and area of steel in X and Y directions) for design a circular isolated footing with eccentric column that considers that the surface in contact with the ground works partially under compression. The formulation is shown by integration to find the moments, the bending shears and the punching shear using the pressure volume under the footing. Some researchers show the minimum cost design for circular isolated footings for an eccentric column assuming that the contact area works completely in compression, others consider the contact surface with the ground working partially in compression for a column in the center of the base. Three numerical examples are developed to obtain the complete design, which are: Example 1 for a column in the center of the base,Example 2 for a column at a distance of 1.50 m from the center of the base in the X direction, Example 3 for a column at a distance of 1.50 m from the center of the base in both directions. Also, a comparison of the new model against the model proposed by other authors is presented. The comparison shows that the new model generates a great saving of up to 43.74% for minimum area and 48.44% for minimum cost design in a column located in the center of the base, and when the column is located at a distance of radius/2 starting from the center of the base in the X direction generates great savings of up to 45.24% for minimum area and 31.80% for minimum cost design. Therefore, it is advisable to use the model presented in this study.

Comparison of Algorithms for Generating Parametric Image of Cerebral Blood Flow Using ${H_2}^{15}O$ PET Positron Emission Tomography (${H_2}^{15}O$ PET을 이용한 뇌혈류 파라메트릭 영상 구성을 위한 알고리즘 비교)

  • Lee, Jae-Sung;Lee, Dong-Soo;Park, Kwang-Suk;Chung, June-Key;Lee, Myung-Chul
    • The Korean Journal of Nuclear Medicine
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    • v.37 no.5
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    • pp.288-300
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    • 2003
  • Purpose: To obtain regional blood flow and tissue-blood partition coefficient with time-activity curves from ${H_2}^{15}O$ PET, fitting of some parameters in the Kety model is conventionally accomplished by nonlinear least squares (NLS) analysis. However, NLS requires considerable compuation time then is impractical for pixel-by-pixel analysis to generate parametric images of these parameters. In this study, we investigated several fast parameter estimation methods for the parametric image generation and compared their statistical reliability and computational efficiency. Materials and Methods: These methods included linear least squres (LLS), linear weighted least squares (LWLS), linear generalized least squares (GLS), linear generalized weighted least squares (GWLS), weighted Integration (WI), and model-based clustering method (CAKS). ${H_2}^{15}O$ dynamic brain PET with Poisson noise component was simulated using numerical Zubal brain phantom. Error and bias in the estimation of rCBF and partition coefficient, and computation time in various noise environments was estimated and compared. In audition, parametric images from ${H_2}^{15}O$ dynamic brain PET data peformed on 16 healthy volunteers under various physiological conditions was compared to examine the utility of these methods for real human data. Results: These fast algorithms produced parametric images with similar image qualify and statistical reliability. When CAKS and LLS methods were used combinedly, computation time was significantly reduced and less than 30 seconds for $128{\times}128{\times}46$ images on Pentium III processor. Conclusion: Parametric images of rCBF and partition coefficient with good statistical properties can be generated with short computation time which is acceptable in clinical situation.

The Change in Participation Patterns in Play Activities of Children with Autism Spectrum Disorder during COVID-19: A Scoping Review (COVID-19로 인한 자폐스펙트럼 장애아동의 놀이 활동 참여 변화: 주제범위 문헌고찰)

  • Kim, Hyang-Won;Song, Ye-Ji;Kang, Seong-Hyeon;Won, Ha-Eun;Jeong, Yun-Wha
    • The Journal of Korean Academy of Sensory Integration
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    • v.21 no.1
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    • pp.59-73
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    • 2023
  • Objective : To examine changes in participation patterns of children with Autism Spectrum Disorder (ASD) in play activities during COVID-19 by reviewing relevant literature. Methods : This scoping review was conducted via five steps. we created a research question and searched for relevant literature published in English through CINAHL, PubMed, ERIC, MEDLINE, Google Scholar and Google search engine. After selecting the literature based on inclusion criteria, data were charted based on 10 items (i.e., author name, journal name, publication year, nation, authors' majors, research method, participant' age and gender as well as quantitative and qualitative results of study). The results were analyzed using descriptive numerical and thematic analyses. Results : After reviewing 437 articles and 152 websites, six articles were included. Theses articles were conducted by experts from various fields and countries. Five themes were highlighted in selected articles: COVID-19 resulted in (1) decreased time of outdoor play, (2) increased play time on screen, (3) increased time spent with family, (4) increased sensory difficulties, and (5) recommendations for services for children with disabilities and during COVID-19. Conclusion : This study suggests telerehabilitation programs about parental behavior strategies in order to solve difficulties in which children with ASD may experience when participating in play activities during disasters. Study results can be used as fundamental evidence to emphasize importance of play activities and to systematize role of occupational therapists and service guidelines for supporting play activities of children with disabilities in disasters.