Aspects of Modeling Piezoelectric Active Thin-walled Structures

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.The objective of this article is to reconsider some important aspects of modeling piezoelectric active thin-walled structures. Hence, it is dealt here with thin-walled laminated structures involving piezoelectric patches. A recently developed shell type finite element is used for the purpose. The first aspect is adequate modeling of electric field within the piezoelectric patches polarized in the thickness direction. The influence of higher order functions for the electric field on the accuracy of the model is discussed. The second aspect is related to modeling geometrical non-linearities in the behavior of the considered structures and their significance on the accuracy of the predicted behavior. Both aspects are considered with respect to static and dynamic cases

COMPUTATIONAL MECHANICS – GRUNDLAGE FÜR DIE ENTWICKLUNG INTELLIGENTER PRODUKTE

Für die Entwicklung neuer Produkte des Maschinenbaus, der Elektrotechnik, der Verfahrenstechnik, der Fahrzeugtechnik, des Bauwesens, der Medizintechnik und vieler weiterer Industriezweige werden zunehmend computergestützte Methoden genutzt, die es auf der Grundlage virtueller Modelle ermöglichen, die Produkteigenschaften wirklichkeitsnah nachzubilden, zu analysieren und zu optimieren. Derartige computergestützte Entwicklungsprozesse sind für die Industrie von großer Bedeutung, weil zum einen Entwicklungszeiten reduziert und Kosten eingespart und zum anderen wertvolle Informationen über das zukünftige Produkt- und Systemverhalten bei unterschiedlichsten Betriebsbedingungen bereits zu einem sehr frühen Zeitpunkt gewonnen werden können. Der Entwicklung und industriellen Anwendung von leistungsfähigen computerorientierten Methoden kommt daher eine große wirtschaftliche Bedeutung zu. Im vorliegenden Beitrag wird zunächst ein Einblick in die Methoden- und Softwareentwicklungen auf dem Gebiet der computerorientierten Mechanik gegeben und danach an Hand von Anwendungsfällen exemplarisch gezeigt, welche Vorteile und Möglichkeiten sich durch den Einsatz dieser Methoden für die Entwicklung neuer „intelligenter“ Produkte ergeben können

COSAR - Ein bewährtes System für die Forschung und Praxis

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Das universelle Finite-Elemente-Programmsystem COSAR - Gegenwärtiger Stand und Entwicklungstendenzen

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Anisotropic hierarchic finite elements for the simulation of piezoelectric smart structures

Abstract Purpose -Piezoelectric actuators and sensors are an invaluable part of lightweight designs for several reasons. They can either be used in noise cancellation devices as thin-walled structures are prone to acoustic emissions, or in shape control approaches to suppress unwanted vibrations. Also in Lamb wave based health monitoring systems piezoelectric patches are applied to excite and to receive ultrasonic waves. The purpose of this paper is to develop a higher order finite element with piezoelectric capabilities in order to simulate smart structures efficiently. Design/methodology/approach -In the paper the development of a new fully three-dimensional piezoelectric hexahedral finite element based on the p-version of the finite element method (FEM) is presented. Hierarchic Legendre polynomials in combination with an anisotropic ansatz space are utilized to derive an electro-mechanically coupled element. This results in a reduced numerical effort. The suitability of the proposed element is demonstrated using various static and dynamic test examples. Findings -In the current contribution it is shown that higher order coupled-field finite elements hold several advantages for smart structure applications. All numerical examples have been found to agree well with previously published results. Furthermore, it is demonstrated that accurate results can be obtained with far fewer degrees of freedom compared to conventional low order finite element approaches. Thus, the proposed finite element can lead to a significant reduction in the overall numerical costs. Originality/value -To the best of the author's knowledge, no piezoelectric finite element based on the hierarchical-finite-element-method has yet been published in the literature. Thus, the proposed finite element is a step towards a holistic numerical treatment of structural health monitoring (SHM) related problems using p-version finite elements

On numerical evaluation of effective material properties for composite structures with rhombic fiber arrangements

a b s t r a c t This paper deals with unidirectional fiber reinforced composites with rhombic fiber arrangements. It is assumed, that there is a periodic structure on micro level, which can be taken by homogenization as a representative volume element (RVE) for the composite, where the composite phases have isotropic or transversely isotropic material characterizations. A special procedure is developed to handle the primary non-rectangular periodicity with common numerical homogenization techniques based on FE-models. Due to appropriate boundary conditions applied to the RVE elastic effective macroscopic coefficients are derived. Results are listed and compared with other publications and good agreements are shown. Furthermore new results are presented, which exhibit the special orthotropic behavior of such composites caused by the rhombic fiber arrangement

Numerical simulation of the Lamb wave propagation in honeycomb sandwich panels: A parametric study

a b s t r a c t The paper aims to describe the guided Lamb wave propagation in honeycomb sandwich panels. The application of Lamb waves is a well-known method in modern online structural health monitoring techniques. To analyze the wave propagation in such a complicated geometry with an analytical solution is hardly possible; therefore a dimensional finite element simulation is used. A piezoelectric actuator is used to excite the waves on the sandwich panel surface. The extended model of the honeycomb sandwich panel is consisting of two plate layers and a mid-core layer. In addition, a simplified model is used to reduce the computing costs, where the mid-core of the sandwich panel is replaced by a homogeneous layer. The results from the extended model and the simplified model are in most cases in a good agreement; however the limitations of using the simplified model are discussed. A parametric study is used to show the influence of the geometrical properties of honeycomb plates, the material properties of the skin plates and the loading frequency on the group velocity, the wave length and the energy transmission. Each of these properties provides valuable information to design an efficient health monitoring system. Finally, an experimental test is presented

A FEM-PD coupling based on Arlequin approach to impose boundary conditions in peridynamics

The peridynamic approach (PD) is a continuous theory that is well suited for solving damage problems. Because of the nonlocal formulation, PD can predict the response of a material and fracture patterns with high probability in high dynamic processes. In PD, some parameters differ from the continuum formulation and have some deviation in discretized PD systems, such as a horizon. A material constant becomes a parameter dependent on the mesh size. A sticking point, which has to be considered, is that an incomplete horizon at the boundaries results in an unphysical variation of the material's stiffness in these regions. Material points at the boundaries do not have an entire nonlocal neighborhood, meaning the points have fewer bonds and are softer than points within the domain. This leads to the so-called surface effect. The difficulties in applying the classical local initial and boundary conditions happen because of the nonlocal character of the PD. To overcome this problem, several correction techniques have been developed. Nevertheless, a standard method to describe them is not available yet. An alternative approach is the application of the earlier proposed FEM-PD coupling, which can be seen as a local-nonlocal coupling method. The damage-free zones are analyzed by the FEM as classical local theory, while the domain where the fracture is expected is modeled with the PD as a nonlocal theory. Consequently, the reduction of the computational effort as well as the imposing of the conventional local boundary conditions, is achieved. The coupling method is based on the Arlequin method-an energy-based procedure where the energy of a system is found as a weighted average of both systems. The mechanical compatibility in the overlapping zone of both domains is reached by implementing constraints with the help of the penalty method. In the paper at hand, the focus is on imposing BCs. The proposed method is applied to both static and dynamic applications. The accuracy and convergence behavior is evaluated by analyzing test examples

Why develop twice? Integration of continuum mechanical models in Peridynamics

To harvest the full potential of the peridynamic approach the state-of-the-art material models should be usable without redeveloping or reimplementing them from classical continuum mechanics theory. User materials (UMAT) in finite element codes allow the researchers or engineers to apply their own material routines. Simple interfaces are specified to allow the utilization of material behaviors in software. In order to use these already existing and often validated models with Peridynamics, a UMAT interface is presented. It allows the simplified use of already existing material routines in the peridynamic framework Peridigm. The interface is based on the finite element (FE) software Abaqus UMAT definition and allows the integration of Fortran routines directly into Peridigm. In addition, the same material model implementations are applicable in finite element applications as well as peridynamic simulations. In the presentation the interface is presented and various material models are utilized and compared between Peridynamics and FE methods. The effect of the horizon and non-local boundaries are analyzed and discussed