Abstract.
The Laplace transform\(\hat D(x,p)\) of a matrix D(x,t) of fundamental solutions for the partial differential operator describing the time-dependent bending of thermoelastic plates with transverse shear deformation is constructed, and its asymptotic behavior near the origin is investigated. The differential system is reduced to an algebraic one through the application of the Laplace and then Fourier transformations, and all possible cases of roots of the determinant of the latter system are considered. It is shown that in every case, the asymptotic expansion of \(\hat D(x,p)\) near the origin has the same dominant term. This is an important step in the construction of boundary-element methods for the above time-dependent model because it determines the nature of the singularity of the kernel of the boundary-integral-equations associated with various initial-boundary-value problems for the governing system.
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G. Kirchhoff (1850) ArticleTitleÜber das Gleichgewicht und die Bewegung einer elastischen Scheibe J.Reine Angew. Math. 40 51–58
E. Reissner (1944) ArticleTitleOn the theory of bending of elastic plates. J. Math Phys. 23 189–191
E. Reissner (1945) ArticleTitleThe effect of transverse shear deformation on the bending of elastic plates. J. Appl Mech. 12 A69–A77
E. Reissner (1947) ArticleTitleOn bending of elastic plates. Q.Appl Math. 5 55–68
R.D. Mindlin (1951) ArticleTitleInfluence of rotatory inertia and shear on flexural motions of isotropic elastic plates. J. Appl Mech. 18 31–38
C. Constanda (1990) A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation Longman/Wiley Harlow-New York 169
P. Schiavone R.J. Tait (1993) ArticleTitleThermal effects in Mindlin-type plates. Quart J. Mech. Appl. Math. 46 27–39
Ch. Lubich (1994) ArticleTitleOn the multistep time discretization of linear initial-boundary value problems and their boundary-integral equations. Numer Math. 67 364–389
I. Chudinovich C. Constanda (2000) ArticleTitleThe Cauchy problem in the theory of plates with transverse shear deformation. Math Models Meth. Appl. Sci. 10 463–477
M. Abramowitz I. Stegun (1964) Handbook of Mathematical Functions Dover New York 1046
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Chudinovich, I., Constanda, C. & Dolberg, O. On the Laplace transform of a matrix of fundamental solutions for thermoelastic plates. J Eng Math 51, 199–209 (2005). https://doi.org/10.1007/s10665-004-3066-5
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DOI: https://doi.org/10.1007/s10665-004-3066-5