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

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Abstract

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.

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Authors and Affiliations

  1. Department of Civil Engineering, The University of Hong Kong, Hong Kong, China

    Zhong-qi Quentin Yue

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  1. Zhong-qi Quentin Yue
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Correspondence to Zhong-qi Quentin Yue.

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Professor Zhong-qi Quentin Yue obtained his BSc and MSc degrees’ education in earthquake and geology from Peking University in Beijing (1979 to 1986). He obtained his Ph.D. degree’s education in geotechnical engineering from Carleton University in Ottawa (1988 to 1992). Prior to joining HKU on December 1, 1999, Professor Yue had a total of ten years professional working experience in Beijing, Ottawa, and Hong Kong. He chartered as a geotechnical engineer in Ontario in 1995 and in Hong Kong in 1998.

Professor Yue’s research interests include the following six areas: 1) Formulations and applications of new analytical solutions for predicting mechanical behavior of layered elastic and poroelastic solids under various conditions; 2) Quantifying, analyzing and predicting the mechanical behavior of non-homogeneous geomaterials with numerical and digital image processing techniques; 3) Prevention and mitigation of landslide hazards in complex slope grounds from coastal soft soils to mountainous rock masses; 4) Development and invention of automatic drilling process monitor (DPM) for in-situ continuously measuring and recording the strength and distribution of rock masses at depth in real time; 5) Design methods for tunnels and caverns in both saturated soft soils and soft or hard rocks, and their long-term stability and integrity; 6) Gas cause and mechanism of earthquakes, volcanos, landslides, tsunamis, and rock bursts. Most importantly, Professor Yue has discovered the existence of a thin spherical methane gas layer between the crust and the mantle of the Earth and has developed a more realistic model for the Earth.

Professor Yue has published 3 books, 187 journal articles, 133 conference papers and two USA/China patents. He has given more than 430 invited lectures/seminars at more than 100 conferences and more than 100 institutions worldwide. He has received some prestigious awards including the Excellent Contributions Award from International Association for Computer Methods and Advances in Geomechanics in 2008.

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Yue, Zq.Q. Yue’s solution of classical elasticity in n-layered solids: Part 2, mathematical verification. Front. Struct. Civ. Eng. 9, 250–285 (2015). https://doi.org/10.1007/s11709-015-0299-5

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  • DOI: https://doi.org/10.1007/s11709-015-0299-5

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