a análise de placas laminadas compostas inteligentes

Abstract
Intelligent structures are systems whose shape and structural and functionals features
may be monitored and modified while in its useful life, allowing to hold the satisfying to
design requirements and improving the performance. In this scope, laminated composite
structures are very adaptable to this technology, favoring the design of components with
sensors and actuators embedded within the laminate or bonded on the surfaces. Allied
to the exceptional performance of the composite materials and to the special properties
of materials with coupled response, control systems consist of the link which complete
the chain that define intelligent systems. Undoubtedly, for the design of such structures,
there exist the demand for methodology and tools for analysis and verification. Hence,
this work presents a tool implemented under the Generalized Finite Element Method
philosophy (GFEM) for numerical analysis of composite laminated plates with piezoelectric
sensors and actuators. The GFEM, as a nonconventional Finite Element Method
(FEM) formulation, employs a finite element mesh to build a Partition of Unity, over
which are added p-hierarchical refinements with the proposal of enlarge the solution approximation
subspace. The enrichment functions are globally defined and, therefore, such
strategy minimize the mesh importance, factor which has motivated the meshfree methods
development. The formulation is based on a Mixed Theory model, and in this case,
it is proposed the approximation of electrical unknowns through of the Reddy’s Layerwise
Theory and the approximation of mechanical unknowns through of the Levinson’s
Higher-Order Shear Deformation Theory, this is, a Equivalent Single Layer Theory. The
complete development was conducted for a dynamic system and computational routines
was implemented with FORTRAN 90 language for the static analysis of some models,
whose solutions obtained by others theories constants in the literature were used for the
formulation verification. Moreover, the influence of the way as the essential boundary
conditions are enforced was analyzed, the approximation capability when of the use of
polynomial enrichment -p for distorted meshes and its influence in the primal and dual
fields approximation was showed. The displacement equations and the consistent boundary
conditions were developed for the mixed model employed in the numerical implementation.
A rectangular laminate was analyzed by the GFEM formulation and its results
were compared to the analytical solution, using trigonometrical series, obtained from the
strong form problem.
Keywords: Generalized Finite Element Method, composite laminated plates, piezoelectricity,
Higher-Order Shear Deformation Theory, Layerwise Theory.