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      KCI등재 SCIE SCOPUS

      Concerning the tensor-based flexural formulation: Theory

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      https://www.riss.kr/link?id=A106225757

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      다국어 초록 (Multilingual Abstract)

      Since the days of yore, plate\'s flexural analysis and formulation were dependent on the assumed coordinate system. In uncovering the coordinates-independent flexural interpretation, in this study, the plate bending analysis has been interpreted in terms of the tensor\'s components of curvatures and bending moments, in accordance with the continuum mechanics. The paper herein presents the theoretical formulations and conceptual perspectives of the Hydrostatic Method of Analysis (HM) that combines the continuum mechanics with the elasticity theory; the graphical statics and analysis; the theory of thin isotropic and orthotropic plates.
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      Since the days of yore, plate\'s flexural analysis and formulation were dependent on the assumed coordinate system. In uncovering the coordinates-independent flexural interpretation, in this study, the plate bending analysis has been interpreted in te...

      Since the days of yore, plate\'s flexural analysis and formulation were dependent on the assumed coordinate system. In uncovering the coordinates-independent flexural interpretation, in this study, the plate bending analysis has been interpreted in terms of the tensor\'s components of curvatures and bending moments, in accordance with the continuum mechanics. The paper herein presents the theoretical formulations and conceptual perspectives of the Hydrostatic Method of Analysis (HM) that combines the continuum mechanics with the elasticity theory; the graphical statics and analysis; the theory of thin isotropic and orthotropic plates.

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      참고문헌 (Reference)

      1 Kirchhoff, G., "Über das Gleichgewicht und die Bewegung einer elastischen Scheibe" 51-88, 1850

      2 Gray, M., "Women of Mathmatics" Greenwood Press 1978

      3 Föppl, A., "Vorlesungen über Technische Mechanik" Teubner 1900

      4 Kirchhoff, G., "Vorlesungen über mechanic" Teubner 1897

      5 Ventsel, E., "Thin Plates and Shells: Theory: Analysis, and Applications" CRC Press 2001

      6 Szilard, R., "Theories and Applications of Plate Analysis: Classical, Numerical and Engineering Methods" John Wiley and Sons 2004

      7 Love, A., "The small free vibrations and deformation of a thin elastic shell" 179 : 491-546, 1888

      8 Kurrer, K. E., "The history of the theory of structures : From arch analysis to computational mechanics" 23 (23): 193-197, 2008

      9 Einstein, A., "The foundation of the generalised theory of relativity" The University of Calcutta 89-163, 1920

      10 Richard J. Lisle, "The Mohr circle for curvature and its application to fold description" Elsevier BV 17 (17): 739-750, 1995

      1 Kirchhoff, G., "Über das Gleichgewicht und die Bewegung einer elastischen Scheibe" 51-88, 1850

      2 Gray, M., "Women of Mathmatics" Greenwood Press 1978

      3 Föppl, A., "Vorlesungen über Technische Mechanik" Teubner 1900

      4 Kirchhoff, G., "Vorlesungen über mechanic" Teubner 1897

      5 Ventsel, E., "Thin Plates and Shells: Theory: Analysis, and Applications" CRC Press 2001

      6 Szilard, R., "Theories and Applications of Plate Analysis: Classical, Numerical and Engineering Methods" John Wiley and Sons 2004

      7 Love, A., "The small free vibrations and deformation of a thin elastic shell" 179 : 491-546, 1888

      8 Kurrer, K. E., "The history of the theory of structures : From arch analysis to computational mechanics" 23 (23): 193-197, 2008

      9 Einstein, A., "The foundation of the generalised theory of relativity" The University of Calcutta 89-163, 1920

      10 Richard J. Lisle, "The Mohr circle for curvature and its application to fold description" Elsevier BV 17 (17): 739-750, 1995

      11 Ugural, A. C., "Stresses in Beams, Plates, and Shells" CRC Press 2010

      12 A. Behravan Rad, "Static analysis of non-uniform heterogeneous circular plate with porous material resting on a gradient hybrid foundation involving friction force" 국제구조공학회 64 (64): 591-610, 2017

      13 J. H. Bramble, "Some uniqueness theorems in the theory of elasticity" Springer Science and Business Media LLC 9 (9): 319-328, 1962

      14 Navier, C. L. M. H., "Remarques sur l’article de M. Poisson, inséré dans le cahier d’août" 39 (39): 145-151, 1828

      15 Germain, S., "Remarques sur la nature, les bornes et l’étendue de la question des surfaces élastiques et équation générale de ces surfaces" Huzard-Courcier 1826

      16 Germain, S., "Recherches sur la théorie des surfaces élastiques" Mme. Ve. Courcier 1821

      17 George E. Backus, "Potentials for tangent tensor fields on spheroids" Springer Science and Business Media LLC 22 (22): 210-252, 1966

      18 Cauchy, A., "Oeuvres complètes d’Augustin Cauchy, Série 2, Tome 1"

      19 Wu-Hsiung Huang, "Negatively Curved Sets on Surfaces of Constant Mean Curvature in ℝ 3 are Large" Springer Science and Business Media LLC 141 (141): 105-116, 1998

      20 Parry, R. H. G., "Mohr Circles, Stress Paths and Geothechnics" CRC Press 2005

      21 Adim Belkacem, "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions" 국제구조공학회 66 (66): 761-769, 2018

      22 Lamé, G., "Leçons sur la théorie mathématique de l’élasticité des corps solides" Gauthier-Villars 1866

      23 Murat Altekin, "Large deflection analysis of point supported super-elliptical plates" 국제구조공학회 51 (51): 333-347, 2014

      24 Timoshenko, S. P., "History of Strength of Materials: With a Brief Account of the History of Theory of Elasticity and Theory of Structures" McGraw-Hill 1953

      25 Norton, J. D., "General covariance and the foundations of general relativity: Eight decades of dispute" 56 (56): 791-, 1993

      26 Davit Harutyunyan, "Gaussian Curvature as an Identifier of Shell Rigidity" Springer Science and Business Media LLC 226 (226): 743-766, 2017

      27 Navier, C. L. M. H., "Extrait des recherches sur la flexion des planes élastiques" 10 : 92-102, 1823

      28 Sihame Ait Yahia, "Effect of homogenization models on stress analysis of functionally graded plates" 국제구조공학회 67 (67): 527-544, 2018

      29 Kühnel, W., "Differential Geometry: Curves-Surfaces-Manifolds" American Mathematical Society 2015

      30 Euler, L., "De motu vibratorio tympanorum" 10 : 243-260, 1766

      31 Quinn, V., "Continuum and Solid Mechanics: Concepts and Applications" 2012

      32 Capaldi, F. M., "Continuum Mechanics: Constitutive Modeling of Structural and Biological Materials" Cambridge University Press 2012

      33 Tran Minh Tu, "Bending analysis of functionally graded plates using new eight-unknown higher order shear deformation theory" 국제구조공학회 62 (62): 311-324, 2017

      34 Ugural, A. C., "Advanced Strength and Applied Elasticity" Prentice Hall 2008

      35 Poisson, S. D., "Académie des sciences" Gauthier-Villars 1829

      36 Mohr, O., "Abhandlungen aus dem Gebiete der technischen Mechanik mit zahlreichen textabbildungen" Wilhelm Ernst & Sohn 1906

      37 Navier, C. L. M. H., "1er partie: Leçons sur la résistance des materiaux et sur l’établissement des constructions en terre" Firmin Didot père et fils 1826

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