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Influence functions, integral formulas, and explicit solutions for thermoelastic spherical wedges

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Abstract

In this study, new exact Green’s functions and a new exact Green-type integral formula for a boundary value problem (BVP) in thermoelasticity for some spherical wedges with mixed homogeneous mechanical boundary conditions are derived. The thermoelastic displacements are subjected to a heat source applied in the inner points of the spherical wedges and to a mixed non-homogeneous boundary heat conditions. When the thermoelastic Green’s function is derived, the thermoelastic displacements are generated by an inner unit point heat source, described by Dirac’s δ-function. All results are obtained in elementary functions that are formulated in a special theorem. Exact solutions in elementary functions for two particular BVPs of thermoelasticity for spherical wedges also are included. In these particular BVPs, the thermoelastic displacements are subjected to a constant temperature (in the first particular BVP) or to a constant heat source (in the second particular BVP). In both BVPs, the constant temperature or the constant heat source is given on the segment of the radius of the quarter-space. On the boundary half-planes of the quarter-space zero temperature and zero heat flux are prescribed.

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Authors and Affiliations

  1. Laboratory of Green’s Functions, Agrarian State University of Moldova, Mircesti Street 44, 2049, Chişinău, Moldova

    Victor Şeremet

  2. Laboratory of Mathematical Modeling, Academy of Science of Moldova, Institute of Mathematics and Computer Science, str. Academiei, 5, 2028, Chişinău, Moldova

    Victor Şeremet

  3. Department of Construction and Structural Mechanics, Technical University of Moldova, Chisinău Bd. Dacia 41, 2060, Chişinău, Moldova

    Ion Creţu

Authors
  1. Victor Şeremet
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  2. Ion Creţu
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Correspondence to Victor Şeremet.

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Şeremet, V., Creţu, I. Influence functions, integral formulas, and explicit solutions for thermoelastic spherical wedges. Acta Mech 224, 893–918 (2013). https://doi.org/10.1007/s00707-012-0782-1

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  • DOI: https://doi.org/10.1007/s00707-012-0782-1

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