Mechanic-electric coupling cell-based smoothed isogeometric analysis for the static behaviors of piezoelectric structures

In order to improve the accuracy and efficiency of piezoelectric structure design, the static mechanic-electric coupling of two-dimensional piezoelectric material problems are investigated by a cell-based smoothed isogeometric analysis (CS-IGA) in this work. The CS-IGA was developed on the basis of the isogeometric analysis by using strain smoothing technology. Based on the generalized Galerkin weak form and the constitutive equation of piezoelectric structures, the equilibrium equation of piezoelectric material in the problem of mechanic-electric coupling is obtained. For further improving the calculation precision of the algorithm, average strain is defined in the element domains. It completely avoids the gradient calculation of rational NURBS basis function in the stiffness matrix formula and further improves the computational efficiency. Besides, numerical example results can verify the precision, correctness and reliability of the proposed method in comparison with the finite element method in the analysis of piezoelectric material problems. Overall, this work can provide a help for analyzing the problems of piezoelectric structures.