We study the thermoelectric field for an electrically and thermally insulated coated hole of arbitrary shape embedded in an infinite nonlinearly coupled thermoelectric material subject to uniform remote electric curre...We study the thermoelectric field for an electrically and thermally insulated coated hole of arbitrary shape embedded in an infinite nonlinearly coupled thermoelectric material subject to uniform remote electric current density and uniform remote energy flux.A conformal mapping function for the coating and matrix is introduced,which simultaneously maps the hole boundary and the coating-matrix interface onto two concentric circles in the image plane.Using analytic continuation,we derive a general solution in terms of two auxiliary functions.The general solution satisfies the insulating conditions along the hole boundary and all of the continuity conditions across the perfect coating-matrix interface.Once the two auxiliary functions have been obtained in the elementary-form,the four original analytic functions in the coating and matrix characterizing the thermoelectric fields are completely and explicitly determined.The design of a neutral coated circular hole that does not disturb the prescribed thermoelectric field in the thermoelectric matrix is achieved when the relative thickness parameter and the two mismatch parameters satisfy a simple condition.Finally,the neutrality of a coated circular thermoelectric inhomogeneity is also accomplished.展开更多
By using Schwarz alternating method, this paper presents asimplified alternating algorithm for the problems of two holes having arbitrary shapes and arrangements in an isotropic homogeneous linear elastic infinite reg...By using Schwarz alternating method, this paper presents asimplified alternating algorithm for the problems of two holes having arbitrary shapes and arrangements in an isotropic homogeneous linear elastic infinite region, and obtains stress and displacement fields for random times of iteration. After precision analysis it is found that the results for twenty times of iteration are of very high precision, and those with higher precision can be acquired if the iteration solving is further conducted. The comparison of the results from FEM further proves the reliability of the simplified alternating algorithm presented by this paper.展开更多
基金supported by the Discovery Grant from the Natural Sciences and Engineering Research Council of Canada(No.RGPIN-2017-03716115112)。
文摘We study the thermoelectric field for an electrically and thermally insulated coated hole of arbitrary shape embedded in an infinite nonlinearly coupled thermoelectric material subject to uniform remote electric current density and uniform remote energy flux.A conformal mapping function for the coating and matrix is introduced,which simultaneously maps the hole boundary and the coating-matrix interface onto two concentric circles in the image plane.Using analytic continuation,we derive a general solution in terms of two auxiliary functions.The general solution satisfies the insulating conditions along the hole boundary and all of the continuity conditions across the perfect coating-matrix interface.Once the two auxiliary functions have been obtained in the elementary-form,the four original analytic functions in the coating and matrix characterizing the thermoelectric fields are completely and explicitly determined.The design of a neutral coated circular hole that does not disturb the prescribed thermoelectric field in the thermoelectric matrix is achieved when the relative thickness parameter and the two mismatch parameters satisfy a simple condition.Finally,the neutrality of a coated circular thermoelectric inhomogeneity is also accomplished.
基金the National Natural Science Foundation of China (Grant No. 49772166).
文摘By using Schwarz alternating method, this paper presents asimplified alternating algorithm for the problems of two holes having arbitrary shapes and arrangements in an isotropic homogeneous linear elastic infinite region, and obtains stress and displacement fields for random times of iteration. After precision analysis it is found that the results for twenty times of iteration are of very high precision, and those with higher precision can be acquired if the iteration solving is further conducted. The comparison of the results from FEM further proves the reliability of the simplified alternating algorithm presented by this paper.
