Analytical solutions for the deformation of anisotropic elastic and piezothermoelastic laminated plates.

摘要

The Eshelby-Stroh formalism is used to analyze the generalized plane strain quasistatic deformations of an anisotropic, linear elastic laminated plate. The formulation admits any set of boundary conditions on the edges and long faces of the laminate. Each lamina may be generally anisotropic with as many as 21 independent elastic constants. The three dimensional governing differential equations are satisfied at every point of the body. The boundary conditions and interface continuity conditions are satisfied in the sense of a Fourier series. Results are presented for three sample problems to illustrate the versatility of the method.The solution methodology is generalized to study the deformation of finite rectangular plates subjected to arbitrary boundary conditions. The effect of truncation of the series on the accuracy of the solution is carefully examined. Results are presented for thick plates with two opposite edges simply supported and the other two subjected to eight different boundary conditions. The results are compared with three different plate theories. The solution exhibits boundary layers at the edges except when they are simply supported. Results are presented in tabular form for different sets of edge boundary conditions to facilitate comparisons with predictions from various plate theories and finite element formulations.The Eshelby-Stroh formalism is also extended to study the generalized plane deformations of piezothermoelastic laminated plates. The method is capable of analyzing laminated plates with embedded piezothermoelastic patches. Results are presented for a thermoelastic problem and laminated elastic plates with piezothermoelastic lamina attached to its top surface. When a PZT actuator patch is attached to an elastic cantilever substrate, it is observed that the transverse shear stress and transverse normal stress are very large at the corners of the PZT-substrate interface.This dissertation is organized in the form of three self-contained chapters each of which will be submitted for possible publication in a journal.This work was parially supported by the NSF grant CMS9713453 and the ARO grant DAAG55-98-1-0030 to Virginia Polytechnic Institute and State University.