Multiphysics simulations of smart structures using isogeometric finite elements

Abstract

Active piezoelectric materials are widely used for noise-cancelation devices, to suppress unwanted vibrations, or to control the shape of high precision devices, such as optical instruments and measuring devices. Piezoelectric ceramics, e.g. made of lead-zirconate-titanate (PZT), serve both as actuators and sensors to fulfil the aforementioned goals. Nowadays, another important area of application of piezoelectric materials is the development of structural health monitoring (SHM) systems. One common approach uses a network of piezoelectric ceramics. These ceramics are surface-mounted on or embedded into the structure to excite and to receive ultrasonic guided waves. In thin-walled structures these waves are called Lamb waves and have complex physical properties. In order to gain a deeper insight into the underlying physics efficient and powerful numerical tools are needed. A viable means are finite element schemes based on higher order polynomial shape functions. Consequently, the objective of the paper is the development and the evaluation of isogeometric finite elements (electro-mechanical coupling). They are capable of reducing the computational effort noticeably and at the same time they offer very accurate results. The advantages of this higher order finite element is demonstrated using different numerical examples, highlighting the static as well as dynamic properties of higher order finite element methods. In the case of a wave propagation analysis the authors focus on three different higher order methods. Therefore, the spectral element method (SEM), the p-version of the finite element method (p-FEM) and isogeometric analysis is scrutinized and compared with standard elements.