Search

The accurate evaluation of interlaminar stresses is of great significance in the analysis and design of laminated and piezoelectric laminated structures because complex behaviours of these stresses near free edges initiate edge delamination that raises concerns about the structural integrity and reliability. This thesis presented 3D hybrid analyses on the interlaminar stresses to investigate the electromechanical coupling and free edge effects of piezoelectric laminated plates with an emphasis on the realistic distributions of the 3D stress and electric fields near free edges. In this research, the state space equations for simply-supported and free-edge piezoelectric laminates under transverse loads and infinite long free-edge piezoelectric laminates under uniaxial extension were obtained in the framework of 3D piezoelasticity by considering all the independent elastic and piezoelectric constants. The equations satisfy the traction-free and open-circuit boundary conditions at free edges and the continuity conditions across all interfaces. On the basis of the transfer matrix and recursive solution approaches, 3D exact solutions were sought by a novel non-uniform layer refinement technique to evaluate the accuracy of the finite element method (FEM), and realistic gradients of interlaminar stresses and electric fields were captured. The FEM results were in good agreement with those from the present solutions except for the regions near free edges. For simply-supported and free-edge laminates, stress variations with material properties, geometries and stacking sequences were obtained. The interlaminar stress τxz was dominant at corners and τyz also tended to contribute to delamination. In the infinite long free-edge laminates, σz, τyz, Ey and Ez exhibited significant gradients near free edges. Furthermore, the considerable influence of the electromechanical coupling effect on interlaminar stresses revealed that piezoelectric laminates were more susceptible to edge delamination and the application of closed-circuited surface conditions might prevent such edge delamination. The present analytical solution demonstrated an improvement in precision over other 2D analytical and numerical solutions and could serve as a benchmark for the determination of interlaminar stresses and electric fields near the free edges of the piezoelectric laminates.

In recent years, laminated carbon fiber reinforced polymer (CFRP) composites have gained popularity in engineering applications due to their lightweight and strong mechanical properties. One of this material's greatest weaknesses is that it performs poorly in out-of-plane impact resistance. Thus, it was the objective of this research to investigate the effect of bistability on the impact resistance of laminated CFRP composites. Bistable composites have the ability to alternate between two different geometric equilibria through external loading, and when unloaded, do not require external forces to maintain either geometry. An instrumented dropweight tower was designed and constructed according to ASTM standards with modifications to accommodate bistability. Laminated CFRP composite specimens of bistable, flat monostable, and curved monostable configurations were subjected to low velocity impacts of 20 J. The acceleration and force of each impact was recorded using an accelerometer and a load cell mounted on the dropweight tower's impactor. The sensor data was used to analyze the dynamic response and calculate the energy absorption of each impact. Post-impact crack length measurements and damage characterization were used to conduct a damage resistance analysis. The effects of moisture, geometry, stacking sequence, and bistability of the impacted specimens were determined. The results showed that bistability improves the low velocity impact damage resistance of laminated CFRP composites through increased energy absorption and specimen kinetic energy.

This study presents the warpage analysis in thin-walled beams of arbitrary open cross section subjected to dynamic loads. Strength analysis has also been conducted for laminated composite beams under static loading conditions. The beam has seven displacement degrees of freedom at each node and the element formulation is based on Vlasov theory of thin-walled beams. Coupling between the force and moment resultants, and the transverse shear deformation have been accounted in the development of laminated composite beam theory. Hellinger-Reissner mixed variational principle is used in element formulation, with an augmented Lagrangian to impose the constraint condition on the rotational degree of freedom. A lumped mass matrix for the beam element has been derived, and central difference scheme is used for explicit time integration. The convergence of 2-node and 3-node thin-walled beam finite elements is studied and the results presented. An eigenvalue analysis is also performed using the lumped mass matrix. Several examples of dynamic loading are studied, and the time history results are compared with implicit time integration results obtained using 3D shell models in ANSYS. Results are also presented for various laminate stacking sequences.

Many commercial finite element programs support piezoelectric modeling and composite modeling to some extent. The popular program ABAQUS, however, has piezoelectric modeling capabilities only for continuum and one-dimensional truss elements. In situations where aspect ratio constraints and computational inefficiencies become a significant issue, such as modeling very large thin structures, alternate modeling techniques are sometimes required. Much of the focus of this thesis was to introduce equivalent methods for modeling laminated piezoelectric beams and plates. Techniques are derived based on classical beam and plate theory, classical lamination theory, and the linear theory of piezoelectricity. Finite element approximations are used with the principle of minimum potential energy to derive the static equilibrium equations for piezoelectric laminated structures. Equivalent loading techniques are derived based on the constitutive equations of piezoelectricity to simulate actuation forces within the piezoelectric layers. Finite element models using equivalent modeling techniques as well as equivalent loading techniques for piezoelectric laminated structures are developed and compared to ABAQUS models using piezoelectric elements to evaluate the error in theoretical assumptions. The analysis will prove that equivalent structural models and equivalent loading techniques provide excellent means for simplifying the analysis of thin piezoelectric laminated structures.