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Three‐Dimensional Analysis of Some Symmetric Hybrid Piezoelectric Laminates
Author(s) -
He L.H.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(200005)80:5<307::aid-zamm307>3.0.co;2-p
Subject(s) - piezoelectricity , boundary value problem , traction (geology) , electric field , mathematical analysis , enhanced data rates for gsm evolution , transverse plane , shear (geology) , electrostatics , strips , geometry , materials science , mathematics , physics , structural engineering , composite material , computer science , engineering , telecommunications , quantum mechanics , mechanical engineering
Abstract The present paper studies 3D responses of a kind of hybrid laminates. The laminates consist of a nonpiezoelectric layer with a number of symmetrically covered piezoelectric layers possessing 6mm material symmetry. The top and bottom surfaces of the laminates are traction free, and the edge boundary is free of any transverse shear forces. In the first place, an approximate 2D model including the charge equation of electrostatics is proposed on the basis of the classical Kirchhoff hypothesis. Then, it is shown that the corresponding 3D solution can be generated immediately, provided the solution of the 2D model is obtained. The 3D solution satisfies all field equations and surface or interlayer conditions; the only restriction is that the mechanical and electric edge boundary conditions are generally fulfilled in an average manner. As examples, explicit solutions are given for infinite long laminated strips and for arbitrarily shaped laminates with free boundaries. In both cases, however, the electric boundary condition is satisfied exactly, and therefore, the solutions are exact in Saint Venant's sense.