| Περίληψη: | The aim of the current dissertation is the development of novel laminate mechanics and finite element methods capable of predicting the guided wave propagation in laminated composite strips and plates, excited by physically modeled piezoelectric actuators. The present thesis is subdivided into three main parts; the first one addresses the development of high order and layerwise laminate theories which can effectively model the propagation of guided waves in laminated or/and sandwich composite strips and plates; the second part describes the formulation of novel time domain spectral finite elements, while the third part describes the adopted experimental procedures and the laboratory tests that were performed in order to validate the developed time domain spectral finite element models.
The developed laminate mechanics theories presented in the first part, were inspired by the Rayleigh-Lamb wave solution, which assumes the axial and the transverse displacements as a summation of sines and cosines. Consequently, high-order approximations and additional degrees of freedom were considered in the kinematic assumptions of both axial and transverse displacements, enabling the prediction of symmetric and anti-symmetric type guided waves. Thereafter, while proving that polynomials up to the third degree were adequate for the simulation of fundamental and modes, a new high order laminate theory was proposed using for the through thickness interpolation functions third order cubic Hermite splines. The newly developed theory for strips and plates, further facilitates the approximation of the displacements and their respective rotations at the interfaces of the strip or the plate. In addition, enables the efficient layerwise expansion for multiple applications, such as the modeling of thick sandwich laminates, the prediction of higher order guided wave modes and the physical representation of piezoelectric actuators and sensors.
The second part describes the combination of the aforementioned laminate theories into a time domain spectral finite element formulation. The time domain spectral finite elements have as a basis the high order polynomial Lagrange shape functions which ensure efficient spatial approximation of very small wavelengths in the length of the strip or in the plane of the plate. More importantly, the integration points are collocated with the element’s nodes using the Gauss-Lobbato-Legendre quadrature, which gives rise to multi-node strip and plate elements with diagonal consistent mass matrices. Thus, a substantial boost of the computational speed of a central-difference explicit time integration scheme is presented while at the same time, improved accuracy compared to the explicit finite element using lumped mass matrices is observed.
At the third part, the TFSDEs were evaluated and validated against well-established semi-analytical methods, commercial FE algorithms and experimental results. The outcome of the evaluation proved that the numerical tool developed within the framework of the present thesis improves the already stated works at the scientific sector of wave propagation in composite laminates. Improvements were observed both in the prediction accuracy and the required analysis time. Finally, a layerwise explicit integration scheme was presented for the coupled electromechanical system.
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