Yue’s solution of classical elasticity in n-layered solids: Part 2, mathematical verification

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• 作者：Zhong-qi Quentin Yue
• 关键词：elasticity ; boundary element method ; elastodynamics ; poroelasticity ; thermoelasticity
• 刊名：Frontiers of Architecture and Civil Engineering in China
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：9
• 期：3
• 页码：250-285
• 全文大小：484 KB
• 参考文献：1.Yue Z Q. Yue’s solution of classical elasticity in n-layered solids: Part 1, mathematical formulation. Frontiers of Structural and Civil Engineering, 2015, 9(3): 215-49CrossRef
  2.Yue Z Q. Elastic fields in two joined transversely isotropic solids due to concentrated forces. International Journal of Engineering Science, 1995, 33(3): 351-69MATH MathSciNet CrossRef
  3.Xiao H T, Yue Z Q. Elastic fields in two joined transversely isotropic media of infinite extent as a result of rectangular loading. International Journal for Numerical & Analytical Methods in Geomechanics, 2013, 37(3): 247-77CrossRef
  4.Yue Z Q. Closed-form Green’s functions for transversely isotropic bi-solids with a slipping interface. Structural Engineering and Mechanics. An International Journal, 1996, 4(5): 469-84CrossRef
  5.Yue Z Q, Yin J H. Closed-form fundamental solutions for transversely isotropic bi-materials with inextensible interface. Journal of Engineering Mechanics, ASCE, 1996, 122(11): 1052-059CrossRef
  6.Yue Z Q, Xiao H T, Tham L G, Lee C F, Yin J H. Stresses and displacements of a transversely isotropic elastic halfspace due to rectangular loadings. Engineering Analysis with Boundary Elements, 2005, 29(6): 647-71MATH CrossRef
  7.Yue Z Q. On generalized Kelvin solutions in multilayered elastic media. Journal of Elasticity, 1995, 40(1): 1-4MATH MathSciNet CrossRef
  8.Yue Z Q. On elastostatics of multilayered solids subjected to general surface traction. Quarterly Journal of Mechanics and Applied Mathematics, 1996, 49(3): 471-99MATH MathSciNet CrossRef
  9.Yue Z Q. 1996. Elastic field for an eccentrically loaded rigid plate on multilayered solids. International Journal of Solids and Structures, 33(27): 4019-049MATH CrossRef
  10.Yue Z Q, Svec O C. Effect of tire-pavement contact pressure distribution on the response of asphalt concrete pavements. Canadian Journal of Civil Engineering, 1995, 22(5): 849-60CrossRef
  11.Yue Z Q, Yin J H. Backward transfer-matrix method for elastic analysis of layered solid with imperfect bonding. Journal of Elasticity, 1998, 50(2): 109-28MATH CrossRef
  12.Yue Z Q, Yin J H. Layered elastic model for analysis of cone penetration testing. International Journal for Numerical & Analytical Methods in Geomechanics, 1999, 23(8): 829-43MATH CrossRef
  13.Yue Z Q, Yin J H, Zhang S Y. Computation of point load solutions for geo-materials exhibiting elastic non-homogeneity with depth. Computers and Geotechnics, 1999, 25(2): 75-05CrossRef
  14.Yue Z Q, Xiao H T, 2002. Generalized Kelvin solution based boundary element method for crack problems in multilayered solids. Engineering Analysis with Boundary Elements, 26(8): 691-05MATH CrossRef
  15.Yue Z Q, Xiao H T, Tham L G. Boundary element analysis of crack problems in functionally graded materials. International Journal of Solids and Structures, 2003, 40(13-4): 3273-291MATH CrossRef
  16.Yue Z Q, Xiao H T, Tham L G. Elliptical crack normal to functionally graded interface of bonded solids. Theoretical and Applied Fracture Mechanics. 2004, 42: 227-48CrossRef
  17.Yue Z Q, Xiao H T, Tham L G, Lee C F, Pan E. Boundary element analysis of three-dimensional crack problems in two joined transversely isotropic solids. Computational Mechanics, 2005, 36(6): 459-74MATH CrossRef
  18.Yue Z Q, Xiao H T, Pan E. Stress intensity factors of square crack inclined to interface of transversely isotropic bi-material. Engineering Analysis with Boundary Elements, 007, 31(1): 50-5
  19.Xiao H T, Yue Z Q. Fracture Mechanics in Layered and Graded Solids: Analysis Using Boundary Element Methods. Berlin: De Gruyter & Higher Education Press, 2014, 305
  20.Yue Z Q. Solutions of transversely isotropic elastodynamics in a vertically heterogeneous halfspace. In: Proceedings of the 2nd Chinese Congress of Earthquake Engineering. Wuhan, China, 1987 (in Chinese)
  21.Yue Z Q, Selvadurai A P S. The role of Poisson’s ratios on the consolidation response of soils. In: Proceedings of the 45th Conference of Canadian Geotechnical Engineering. Toronto, Canada, October 1992, 11- to 11-1
  22.Yue Z Q, Selvadurai A P S. Eccentric settlement of a rigid foundation on a consolidating thin layer. Vertical and Horizontal Deformation of Foundation and Embankments, ASCE Geotechnical Special Publication, 1994, 40(2): 612-27
  23.Yue Z Q, Selvadurai A P S. On the asymmetric indentation of a consolidating poroelastic halfspace. International Journal of Applied Mathematical Modeling, 1994, 18: 170-85MATH CrossRef
  24.Yue Z Q, Selvadurai A P S, Law K T. Excess pore pressure in a poroelastic seabed saturated with a compressible fluid. Canadian Geotechnical Journal, 1994, 31: 989-003CrossRef
  25.Selvadurai A P S, Yue Z Q. On the indentation of a poroelastic layer. International Journal of Numerical & Analytical Methods for Geomechanics, 1994, 18: 161-75MATH CrossRef
  26.Yue Z Q, Selvadurai A P S. On the mechanics of a rigid disc inclusio
• 作者单位：Zhong-qi Quentin Yue (1)
  
  1. Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
  
• 刊物类别：Engineering
• 刊物主题：Civil Engineering
  Cities, Countries and Regions
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-7512

文摘

This paper presents a detailed and rigorous mathematical verification of Yue’s approach, Yue’s treatment, Yue’s method and Yue’s solution in the companion paper for the classical theory of elasticity in n-layered solid. It involves three levels of the mathematical verifications. The first level is to show that Yue’s solution can be automatically and uniformly degenerated into these classical solutions in closed-form such as Kelvin’s, Boussinesq’s, Mindlin’s and bimaterial’s solutions when the material properties and boundary conditions are the same. This mathematical verification also gives and serves a clear and concrete understanding on the mathematical properties and singularities of Yue’s solution in n-layered solids. The second level is to analytically and rigorously show the convergence and singularity of the solution and the satisfaction of the solution to the governing partial differential equations, the interface conditions, the external boundary conditions and the body force loading conditions. This verification also provides the easy and executable means and results for the solutions in n-layered or graded solids to be calculated with any controlled accuracy in association with classical numerical integration techniques. The third level is to demonstrate the applicability and suitability of Yue’s approach, Yue’s treatment, Yue’s method and Yue’s solution to uniformly and systematically derive and formulate exact and complete solutions for other boundary-value problems, mixed-boundary value problems, and initial-boundary value problems in layered solids in the frameworks of classical elasticity, boundary element methods, elastodynamics, Biot’s theory of poroelasticity and thermoelasticity. All of such applications are substantiated by peerreviewed journal publications made by the author and his collaborators over the past 30 years. Keywords elasticity boundary element method elastodynamics poroelasticity thermoelasticity