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Article: Yue’s solution of classical elasticity in nlayered solids: Part 1, mathematical formulation
Title  Yue’s solution of classical elasticity in nlayered solids: Part 1, mathematical formulation 

Authors  
Issue Date  2015 
Publisher  Springer Verlag, copublished with Higher Education Press. The Journal's web site is located at http://link.springer.com/journal/11709 
Citation  Frontiers of Structural and Civil Engineering, 2015, v. 9 n. 3, p. 215249 How to Cite? 
Abstract  This paper presents the exact and complete fundamental singular solutions for the boundary value problem of a nlayered elastic solid of either transverse isotropy or isotropy subject to body force vector at the interior of the solid. The layer number n is an arbitrary nonnegative integer. The mathematical theory of linear elasticity is one of the most classical field theories in mechanics and physics. It was developed and established by many wellknown scientists and mathematicians over 200 years from 1638 to 1838. For more than 150 years from 1838 to present, one of the remaining key tasks in classical elasticity has been the mathematical derivation and formulation of exact solutions for various boundary value problems of interesting in science and engineering. However, exact solutions and/or fundamental singular solutions in closed form are still very limited in literature. The boundaryvalue problems of classical elasticity in nlayered and graded solids are also one of the classical problems challenging many researchers. Since 1984, the author has analytically and rigorously examined the solutions of such classical problems using the classical mathematical tools such as Fourier integral transforms. In particular, he has derived the exact and complete fundamental singular solutions for elasticity of either isotropic or transversely isotropic layered solids subject to concentrated loadings. The solutions in nlayered or graded solids can be calculated with any controlled accuracy in association with classical numerical integration techniques. Findings of this solution formulation are further used in the companion paper for mathematical verification of the solutions and further applications for exact and complete solutions of other problems in elasticity, elastodynamics, poroelasticty and thermoelasticity. The mathematical formulations and solutions have been named by other researchers as Yue’s approach, Yue’s treatment, Yue’s method and Yue’s solution. 
Persistent Identifier  http://hdl.handle.net/10722/231708 
ISSN  2015 SCImago Journal Rankings: 0.411 
DC Field  Value  Language 

dc.contributor.author  Yue, QZQ   
dc.date.accessioned  20160920T05:24:59Z   
dc.date.available  20160920T05:24:59Z   
dc.date.issued  2015   
dc.identifier.citation  Frontiers of Structural and Civil Engineering, 2015, v. 9 n. 3, p. 215249   
dc.identifier.issn  20952430   
dc.identifier.uri  http://hdl.handle.net/10722/231708   
dc.description.abstract  This paper presents the exact and complete fundamental singular solutions for the boundary value problem of a nlayered elastic solid of either transverse isotropy or isotropy subject to body force vector at the interior of the solid. The layer number n is an arbitrary nonnegative integer. The mathematical theory of linear elasticity is one of the most classical field theories in mechanics and physics. It was developed and established by many wellknown scientists and mathematicians over 200 years from 1638 to 1838. For more than 150 years from 1838 to present, one of the remaining key tasks in classical elasticity has been the mathematical derivation and formulation of exact solutions for various boundary value problems of interesting in science and engineering. However, exact solutions and/or fundamental singular solutions in closed form are still very limited in literature. The boundaryvalue problems of classical elasticity in nlayered and graded solids are also one of the classical problems challenging many researchers. Since 1984, the author has analytically and rigorously examined the solutions of such classical problems using the classical mathematical tools such as Fourier integral transforms. In particular, he has derived the exact and complete fundamental singular solutions for elasticity of either isotropic or transversely isotropic layered solids subject to concentrated loadings. The solutions in nlayered or graded solids can be calculated with any controlled accuracy in association with classical numerical integration techniques. Findings of this solution formulation are further used in the companion paper for mathematical verification of the solutions and further applications for exact and complete solutions of other problems in elasticity, elastodynamics, poroelasticty and thermoelasticity. The mathematical formulations and solutions have been named by other researchers as Yue’s approach, Yue’s treatment, Yue’s method and Yue’s solution.   
dc.language  eng   
dc.publisher  Springer Verlag, copublished with Higher Education Press. The Journal's web site is located at http://link.springer.com/journal/11709   
dc.relation.ispartof  Frontiers of Structural and Civil Engineering   
dc.rights  The final publication is available at Springer via http://dx.doi.org/10.1007/s1170901502986   
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.title  Yue’s solution of classical elasticity in nlayered solids: Part 1, mathematical formulation   
dc.type  Article   
dc.identifier.email  Yue, QZQ: yueqzq@hku.hk   
dc.identifier.authority  Yue, QZQ=rp00209   
dc.description.nature  postprint   
dc.identifier.doi  10.1007/s1170901502986   
dc.identifier.hkuros  266317   
dc.identifier.volume  9   
dc.identifier.issue  3   
dc.identifier.spage  215   
dc.identifier.epage  249   
dc.publisher.place  Germany and China   