zbMATH — the first resource for mathematics

A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures. (English) Zbl 1232.74108
Summary: We report on a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated. Numerical results and comparative studies with other existing solutions in the literature suggest that the present element is robust, computationally inexpensive and easy to implement.

74S05 Finite element methods applied to problems in solid mechanics
74F15 Electromagnetic effects in solid mechanics
Full Text: DOI