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Thermoelastic Plates with Arc-Shaped Cracks

  • I. Chudinovich
  • C. Constanda

Abstract

Bending theories of elastic plates describe the behavior of thin structures under external mechanical and thermal influences. Among the most accurate ones, Mindlin-type models provide information not only on the bending and twisting moments generated in the body, but also on the transverse shear forces acting across the thickness. In what follows we use a combination of variational and boundary integral equation techniques to study the mathematical properties and solution of the theory proposed in (Schiavone and Tait 1993), when the plate is weakened by an arc-shaped crack. The corresponding results in the absence of the temperature factor can be found in (Chudinovich and Constanda 2006), (Chudinovich and Constanda 2000), and (Chudinovich and Constanda 2005).

Keywords

Elastic Plate Equivalent Norm Exterior Domain Trace Operator Thin Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [Co90]
    Constanda, C.: A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation, Longman, Harlow (1990). MATHGoogle Scholar
  2. [ScTa93]
    Schiavone, P., Tait, R.J.: Thermal effects in Mindlin-type plates. Quart. J. Mech. Appl. Math., 46, 27–39 (1993). MathSciNetMATHCrossRefGoogle Scholar
  3. [ChCo06]
    Chudinovich, I., Constanda, C.: Potential representations of solutions for dynamic bending of elastic plates weakened by cracks. Math. Mech. Solids, 11, 494–512 (2006). MathSciNetMATHCrossRefGoogle Scholar
  4. [ChCo00]
    Chudinovich, I., Constanda, C.: Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation, Chapman & Hall/CRC, Boca Raton, FL (2000). MATHGoogle Scholar
  5. [ChCo05]
    Chudinovich, I., Constanda, C.: Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes, Springer, London (2005). MATHGoogle Scholar
  6. [ChCoVe04]
    Chudinovich, I., Constanda, C., Colín Venegas, J.: The Cauchy problem in the theory of thermoelastic plates with transverse shear deformation. J. Integral Equations Appl., 16, 321–342 (2004). MathSciNetMATHCrossRefGoogle Scholar
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    Lions, J.-L., Magenes, E.: Non-homogeneous Boundary Value Problems and Applications, vol. 1, Springer, Berlin (1972). Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.The University of TulsaTulsaUSA

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