3次元圧電問題に対するベクトル電気ポテンシャル型の有限要素解析手法  [in Japanese] Vector-Electric-Potential Finite Element Procedure for Three-Dimensional Piezoelectric Problems  [in Japanese]

Alternative three-dimensional finite element for piezoelectric problems is formulated with three restrictions: no volumetric charge, equipotential electrodes, and no surface charge except for the electrodes. In the conventional formulation, independent variables are mechanical displacement and scalar electric potential so-called voltage but in the present formulation they are mechanical displacement and vector potential that derives electric displacement. From thermodynamic viewpoint, the present formulation is better for nonlinear ferroelectric problems and the resulting global stiffness matrix is at lest semi-positive definite. For descritization, nodal-edge finite element is used to keep the arbitrainess of vector potential in null-space of the matrix. Numerical examples of three-dimensional piezoelectric problem are demonstrated. For solving the linear systems, direct method with tree-cotree decomposition gauge and conjugate gradient iterative method are used.