• Title/Summary/Keyword: Laplace

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Stress Analysis of Orthogonally Stiffened Rectangular Plates by the Laplace Transformation (직교보강재(直交補强材)가 붙은 구형평판(矩形平板)에 있어서의 응력해석(應力解析))

  • S.J.,Yim;J.D.,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.13 no.3
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    • pp.11-19
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    • 1976

  • Grillages are abundant in ship structures and in many other types of structures such as bridges and building floors. Clarkson has shown that plated grillages can be satisfactorily analyzed as gridworks if an appropriate effective breadth is taken into account. Also, it has previously been pointed out, by Nielsen, that grillage calculations could be simplified by use of the Laplace transformation. In this paper, it is assumed that the torsional rigidity of the members and axial load are negligible, also that girders have the same scantling and spacing each other and so stiffeners do. Then the grillages composed of both-end-fixed girders and both-end-hinged stiffeners, which are subjected only to uniform normal loads are investigated. The calculus of variation is used to set up the differential equations and the Laplace transformation is applied to solve the differential equations. The program has been tested by FACOM 28 and the results show good agreements with those by the STRESS, which was developed in M.I.T.. The amount of the data input and computing time are much less than those of the STRESS. But this program has so much restrictions that it is urgent to extend the program to the grillage problems of arbitrary loading and boundary conditions.

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IMPLEMENTATION OF LAPLACE ADOMIAN DECOMPOSITION AND DIFFERENTIAL TRANSFORM METHODS FOR SARS-COV-2 MODEL

  • N. JEEVA;K.M. DHARMALINGAM;S.E. FADUGBA;M.C. KEKANA;A.A. ADENIJI
    • Journal of applied mathematics & informatics
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    • v.42 no.4
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    • pp.945-968
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    • 2024

  • This study focuses on SIR model for SARS-CoV-2. The SIR model classifies a population into three compartments: susceptible S(t), infected I(t), and recovered R(t) individuals. The SARS-CoV-2 model considers various factors, such as immigration, birth rate, death rate, contact rate, recovery rate, and interactions between infected and healthy individuals to explore their impact on population dynamics during the pandemic. To analyze this model, we employed two powerful semi-analytical methods: the Laplace Adomian decomposition method (LADM) and the differential transform method (DTM). Both techniques demonstrated their efficacy by providing highly accurate approximate solutions with minimal iterations. Furthermore, to gain a comprehensive understanding of the system behavior, we conducted a comparison with the numerical simulations. This comparative analysis enabled us to validate the results and to gain valuable understanding of the responses of SARS-CoV-2 model across different scenarios.

  • https://doi.org/10.14317/jami.2024.945 인용 PDF

Deep-Learning Seismic Inversion using Laplace-domain wavefields (라플라스 영역 파동장을 이용한 딥러닝 탄성파 역산)

  • Jun Hyeon Jo;Wansoo Ha
    • Geophysics and Geophysical Exploration
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    • v.26 no.2
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    • pp.84-93
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    • 2023

  • The supervised learning-based deep-learning seismic inversion techniques have demonstrated successful performance in synthetic data examples targeting small-scale areas. The supervised learning-based deep-learning seismic inversion uses time-domain wavefields as input and subsurface velocity models as output. Because the time-domain wavefields contain various types of wave information, the data size is considerably large. Therefore, research applying supervised learning-based deep-learning seismic inversion trained with a significant amount of field-scale data has not yet been conducted. In this study, we predict subsurface velocity models using Laplace-domain wavefields as input instead of time-domain wavefields to apply a supervised learning-based deep-learning seismic inversion technique to field-scale data. Using Laplace-domain wavefields instead of time-domain wavefields significantly reduces the size of the input data, thereby accelerating the neural network training, although the resolution of the results is reduced. Additionally, a large grid interval can be used to efficiently predict the velocity model of the field data size, and the results obtained can be used as the initial model for subsequent inversions. The neural network is trained using only synthetic data by generating a massive synthetic velocity model and Laplace-domain wavefields of the same size as the field-scale data. In addition, we adopt a towed-streamer acquisition geometry to simulate a marine seismic survey. Testing the trained network on numerical examples using the test data and a benchmark model yielded appropriate background velocity models.

  • https://doi.org/10.7582/GGE.2023.26.2.084 인용 PDF