An advanced finite element formulation for piezoelectric beam structures

作者：Legner D^*; Wackerfuss J; Klinkel S; Wagner W

来源：Computational Mechanics, 2013, 52(6): 1331-1349.

DOI：10.1007/s00466-013-0879-y

• Piezoelectric beam element
• Mixed variational formulation
• 3D constitutive equations
• Geometric nonlinearity
• Balanced areas of approximation

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.

• 出版日期2013-12