On the Reconstruction of Inhomogeneous Initial Stresses in Plates

  • Rostislav D. NedinEmail author
  • Alexander O. Vatulyan
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)


The direct problem formulation of the steady-state vibration of a thin elastic isotropic plate with non-homogeneous prestress field is described using the variational principle of Lagrange. The solving calculations of the model direct problems were made using finite element method. The investigation of the prestress level influence on the frequency response functions of the plate points was made. The operator relation of the inverse problem is constructed, which binds together the unknown prestress components and the given displacement field functions in the frequency set. The series of computation experiments on the identification of the smooth laws of the uniaxial pretension in the rectangular plate was conducted. On the base of these experiments, the conclusion about the efficiency of the proposed scheme of solving the important inverse problems class was drawn. The preferable frequency ranges are given for that the reconstruction of the initial stresses is most efficient.


Thin plates Inhomogeneous initial stresses Inverse problem Identification 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics, Mechanics and Computer SciencesSouthern Federal UniversityRostov-on-DonRussia

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