IST contribution to WP 3 WP 3: Adaptive composites modeling (Leader – TUT / Italy)

1. IST contribution to WP 3 • WP 3: Adaptive composites modeling • (Leader – TUT / Italy) • Task 3.1: Modeling composites with piezoelectric sensors/actuators • (TL: TUT, IST, LPMM) • IST is developing a mixed finite element formulation for the static analysis of composite plates based on least-squares variational principles. The formulation considers both thin and thick plates using finite element models for the classical laminated plate theory and the first-order shear deformation theory. • The use of least-squares principles leads to a variational unconstrained minimization problem where compatibility conditions present in the traditional weak form Galerkin mixed finite element models no longer arise. Furthermore, the resulting linear algebraic problem will have a symmetric positive definite stiffness matrix, allowing the use of robust solvers.

2. IST contribution to WP 3 • Task 3.1: Modeling composites with piezoelectric sensors/actuators • (TL: TUT, IST, LPMM) • The formulation uses the generalized displacements and stress resultants as independent variables for both the CLPT and FSDT. The plate equations are used in their first-order form to allow the use of C0 Lagrange interpolation functions in the finite element model (presently, fourth and sixth order). • Specifically, high-order nodal expansions and full integration are used to develop the discrete finite element model as they have been proved to be beneficial for least-squares based finite element models. It follows that the mixed plate elements based on this formulation are expected to be insensitive to shear-locking.

3. IST contribution to WP 3 • Task 3.1: Modeling composites with piezoelectric sensors/actuators • (TL: TUT, IST, LPMM) • The finite element models are currently under testing and are soon to be extended to piezoelectric layers or patches. • Preliminary results are being compared with HSDT and FSDT coupled piezoelectric finite element models for plates (based on displacement approach, shown below). • Generic displacement field: • Basic equilibrium equation:

4. IST contribution to WP 3 • Task 3.1: Modeling composites with piezoelectric sensors/actuators • (TL: TUT, IST, LPMM) • Comparisons will also be carried out with layerwise mixed and displacement models (Garção et. al. 2004, Lage et. al. 2004 a, b) and with closed form solutions and also with CASSEM partners alternative models when available.