In this paper, a kind of second-order two-scale(SOTS) computation is developed for conductive–radiative heat transfer problem in periodic porous materials. First of all, by the asymptotic expansion of the temperature field, the cell problem,homogenization problem, and second-order correctors are obtained successively. Then, the corresponding finite element algorithms are proposed. Finally, some numerical results are presented and compared with theoretical results. The numerical results of the proposed algorithm conform with those of the FE algorithm well, demonstrating the accuracy of the present method and its potential applications in thermal engineering of porous materials.
This paper considers the bending behaviors of composite plate with 3-D periodic configuration.A second-order two-scale(SOTS)computational method is designed by means of construction way.First,by 3-D elastic composite plate model,the cell functions which are defined on the reference cell are constructed.Then the effective homogenization parameters of composites are calculated,and the homogenized plate problem on original domain is defined.Based on the Reissner-Mindlin deformation pattern,the homogenization solution is obtained.And then the SOTS’s approximate solution is obtained by the cell functions and the homogenization solution.Second,the approximation of the SOTS’s solution in energy norm is analyzed and the residual of SOTS’s solution for 3-D original in the pointwise sense is investigated.Finally,the procedure of SOTS’s method is given.A set of numerical results are demonstrated for predicting the effective parameters and the displacement and strains of composite plate.It shows that SOTS’s method can capture the 3-D local behaviors caused by3-D micro-structures well.
