Article

# A linear quadrilateral shell element with fast stiffness computation

Institut für Werkstoffe und Mechanik im Bauwesen, Technische Universität Darmstadt, Petersenstraße 12, Darmstadt D-64287, Germany; Institut für Baustatik, Universität Karlsruhe (TH), Kaiserstraße 12, Karlsruhe D-76131, Germany

Computer Methods in Applied Mechanics and Engineering (Impact Factor: 2.62). 01/2005; DOI: 10.1016/j.cma.2004.11.005 - [Show abstract] [Hide abstract]

**ABSTRACT:**Since many piezoelectric components are thin rod-like structures, a piezoelectric finite beam element can be utilized to analyse a wide range of piezoelectric devices effectively. The mechanical strains and the electric field are coupled by the constitutive relations. Finite element formulations using lower order functions to interpolate mechanical and electrical fields lead to unbalances within the numerical approximation. As a consequence incorrect computational results occur, especially for bending dominated problems. The present contribution proposes a concept to avoid these errors. Therefore, a mixed multi-field variational approach is introduced. The element employs the Timoshenko beam theory and considers strains throughout the width and the thickness enabling to directly use 3D constitutive relations. By means of several numerical examples it is shown that the element formulation allows to analyse piezoelectric beam structures for all typical load cases without parasitically affected results.Computational Mechanics 12/2013; 52(6). · 2.43 Impact Factor - ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik 03/2012; 92(3):236-252. · 0.95 Impact Factor
- International Journal for Numerical Methods in Engineering 07/2013; 95(2):145-180. · 2.06 Impact Factor

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.