We develop a new numerical model based on a precise integration method to investigate the coupled thermo-mechanical performance of layered transversely isotropic media around a cylindrical/tubular heat source. To obtain the relational matrices of the extended precise integration method, we first convert the governing equations of the problem into ordinary differential matrix equations through the Laplace–Hankel transform. Then, the cylindrical heat source is divided into a series of plane heat sources, and the plane temperature load term is added to the state vector between layer elements. By combining the layer elements, we build a layered transversely isotropic numerical model containing a cylindrical heat source in the transformed domain. Finally, we solve the model in the transformed domain and obtain the solution of the problem in the real domain through the Laplace–Hankel transform inversion. The accuracy of this method is verified by comparing the solutions with the results of the analytical method and the finite element method. Then, we study the influence of the anisotropy of thermal parameters, the embedded depth, the length/radius ratio, the type of heat source and the stratification of the medium on the thermo-mechanical coupled performance.
In this paper we introduce a measure of magnetic field discontinuity, MAD, defined as Maximum Angular Difference between two adjacent magnetic field vectors. To examine the characteristics of the MAD, we have considered several active region models having a quadrupolar field configuration and computed MADs over these active regions by approximating the 3-D magnetic fields as an ensemble of charge potential fields or linear force-free fields. The computed MAD fields are studied in comparison with other flare activity indicators such as separators. It is found that (1) the region of high level MAD corresponds well with the separator, or practically the intersection of the separator with the plane of measurement, (2) it singles out local discontinuities of magnetic fields, and (3) the MAD can also be a measure of the evolutionary status of an active region.An observational test has been made for 2-D MADs, using the Yohkoh SXT observation of a flare in AR 6919 and the vector magnetogram taken at the Mees Solar Observatory during this flare activity. The high level contours of 2-D MAD are found to trace well the observed soft X-ray bright points, which indicates that the MAD could serve as a good flare activity indicator. 相似文献