The extended finite element method (XFEM)  originallyproposed in 1999  is very powerful for discontinuous problems inmechanics, such as crack growth, complex fluid, interface, and so on.The major difference between the XFEM and the conventional finite elementmethod (CFEM) is that the mesh  in XFEM is independent of theinternal geometry and physical interfaces, such that meshing and re-meshingdifficulties in discontinuous problems can be overcome. Based on thepartition of unity concept, the XFEM relaxes the prohibitive requirementsfor  meshdensity by improving the shape functions with the basic knowledge ofdiscontinuous problems. The XFEM retains all advantages of the CFEM,such as thesingle-field variational principle, symmetric banded and sparse systemmatrices, the ease of application to non-linear problems, anisotropic materialsand arbitrary geometries. This paper presents an overview and comments onthe XFEM, and is organized as follows. The partition of unity method (PUM) andLevel Set Method (LSM) are briefly introduced in sections 2 and 3,respectively. Basic theory, implementation procedures and formulations ofthe XFEM are described  in detail in sections 4 and 5, together with correction toseveral inaccurated points in literature. The future investigationson XFEM are finally recommended in section 6.

The methods of optimizing structure's topology include two classes, analytical method andnumerical method.  The Michell theory is an analytical method,developed early and having a great influence on structural topologyoptimization study. Thispaper mainly focuses on the numerical methods of optimizing truss, frame and continuumstructures. The ground structure approach is usually used to optimize trusses and frames. Theoptimum topology is achieved by deleting parts of members in trusses or frames. To optimizecontinuum structures, the design region is divided into finite elements. The optimum topologyis achieved by deleting parts of elements to form continuum structures with holes. Three kindsof material models are generally used, isotropic, anisotropic and thatwith microstructures. The numerical instabilities in (0-1) topology optimization ofcontinuum structures are analyzed. The methods in common use to overcomethis difficulty include perimeter control, local gradient constraint, mesh-independence filter methods and topologyanalysis. The singular optimum in topology optimization of structures with stressconstraints is introduced briefly. The main mathematical methods to solve topologyoptimization are discussed.

More and more underground coal and metal mines have been developed intoa deep level. Withincrease of mining depth, a series of engineering catastrophes such as rockburst, coal and gas burst,collapse of roof strata and water burst from floor strata are gettingmore serious and more frequent. In addition,supporting and retaining theory of tunnel and stope in the depths aredifferent from the ones at a shallow levels.Such a difference is caused by the difference of geological environmentsbetween deep and shallow levels.The most distinguished differences between deep and shallow levels arethe  so-called three ``highs'', i.e., highcrustal  stress, high earth temperature and high pore pressure. Underhigh crustal stress, rocks showsome special mechanical behaviors. In this paper, the current state ofunderground mining in the depths,technical difficulties of deep mining and geological environment of highcrustal stress of rocks in the depths areintroduced. Moreover, the developments in researches on mechanicalbehaviors of rocks in the  depths arereviewed, including brittle-ductile transition, time-dependent behavior, strength features and failurebehaviors especially rockburst  under the condition of high crustal stress. At the end of the paper, itis pointed out that the thermal-mechanical-hydrological coupling model under the conditions of deepmining is an attractive topic.