The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.
The extended linear complementarity problem(denoted by ELCP) can be reformulated as the solution of a nonsmooth system of equations. By the symmetrically perturbed CHKS smoothing function, the ELCP is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is designed for solving the ELCP. The proposed algorithm is proved to be globally convergent under suitable assumptions.
Applications for piezoelectric efect have grown rapidly,and piezoelectric materials play important roles in countless areas of modern life.By means of twoscale method and coupled boundary layer,some new kinds of twoscale asymptotic expansions for solutions to the electrical potential and the displacement in quasi-periodic structure under coupled piezoelectric efect are derived,and the homogenization constants of piezoelectric materials are presented.The coupled twoscale relation between the electrical potential and the displacement is set up,and some improved asymptotic error estimates are analyzed.
