Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of tw...Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem 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 effect 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.展开更多
In this paper a second-order two-scale(SOTS)analysismethod is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities.By using asympto...In this paper a second-order two-scale(SOTS)analysismethod is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities.By using asymptotic expansion for the temperature field and a proper regularity assumption on the macroscopic scale,the cell problem,effective material coefficients,homogenization problem,first-order correctors and second-order correctors are obtained successively.The characteristics of the asymptotic model is the coupling of the cell problems with the homogenization temperature field due to the nonlinearity and nonlocality of the radiation boundary condition.The error estimation is also obtained for the original solution and the SOTS’s approximation solution.Finally the corresponding finite element algorithms are developed and a simple numerical example is presented.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.10801042,11126132,and 11171257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20104410120001)San Diego supported by China Scholarship Council from July 2012 to July 2013
文摘Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem 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 effect 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.
基金supported by the National Natural Science Foundation of China(90916027)the Special Funds for National Basic Research Program of China(973 Program 2010CB832702)supported by the State Key Laboratory of Science and Engineering Computing.
文摘In this paper a second-order two-scale(SOTS)analysismethod is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities.By using asymptotic expansion for the temperature field and a proper regularity assumption on the macroscopic scale,the cell problem,effective material coefficients,homogenization problem,first-order correctors and second-order correctors are obtained successively.The characteristics of the asymptotic model is the coupling of the cell problems with the homogenization temperature field due to the nonlinearity and nonlocality of the radiation boundary condition.The error estimation is also obtained for the original solution and the SOTS’s approximation solution.Finally the corresponding finite element algorithms are developed and a simple numerical example is presented.
