• Smart Structures and Systems
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• 제9권5호
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• pp.411-426
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• 2012

Thin-walled adaptive structures render a large and important group of adaptive structures. Typical material system used for them is a composite laminate that includes piezoelectric material based sensors and actuators. The piezoelectric active elements are in the form of thin patches bonded onto or embedded into the structure. Among different types of patches, the paper considers those polarized in the thickness direction. The finite element method (FEM) imposed itself as an essential technical support for the needs of structural design. This paper gives a brief description of a developed shell type finite element for active/adaptive thin-walled structures and the element is, furthermore, used as a tool to consider the aspect of mesh distortion over the surface of actuators and sensors. The aspect is of significance for simulation of behavior of adaptive structures and implementation of control algorithms.

• Smart Structures and Systems
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• 제13권4호
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• pp.587-614
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• 2014

In recent years the interest in online monitoring of lightweight structures with ultrasonic guided waves is steadily growing. Especially the aircraft industry is a driving force in the development of structural health monitoring (SHM) systems. In order to optimally design SHM systems powerful and efficient numerical simulation tools to predict the behaviour of ultrasonic elastic waves in thin-walled structures are required. It has been shown that in real industrial applications, such as airplane wings or fuselages, conventional linear and quadratic pure displacement finite elements commonly used to model ultrasonic elastic waves quickly reach their limits. The required mesh density, to obtain good quality solutions, results in enormous computational costs when solving the wave propagation problem in the time domain. To resolve this problem different possibilities are available. Analytical methods and higher order finite element method approaches (HO-FEM), like p-FEM, spectral elements, spectral analysis and isogeometric analysis, are among them. Although analytical approaches offer fast and accurate results, they are limited to rather simple geometries. On the other hand, the application of higher order finite element schemes is a computationally demanding task. The drawbacks of both methods can be circumvented if regions of complex geometry are modelled using a HO-FEM approach while the response of the remaining structure is computed utilizing an analytical approach. The objective of the paper is to present an efficient method to couple different HO-FEM schemes with an analytical description of an undisturbed region. Using this hybrid formulation the numerical effort can be drastically reduced. The functionality of the proposed scheme is demonstrated by studying the propagation of ultrasonic guided waves in plates, excited by a piezoelectric patch actuator. The actuator is modelled utilizing higher order coupled field finite elements, whereas the homogenous, isotropic plate is described analytically. The results of this "semi-analytical" approach highlight the opportunities to reduce the numerical effort if closed-form solutions are partially available.