Mục đích của tác phẩm này trình bày một ứng dụng của vấn đề ngược gãy xương cơ học theo truyền nhiệt. Các phương pháp ranh giới thành phần được sử dụng để xác định sự truyền nhiệt trong các vấn đề hai chiều, có và không có vết nứt. Crack vị trí trong vật liệu được phát hiện dựa trên dự toán năng lượng mất tại hai lời khuyên của các vết nứt. Kết quả số cho thấy rằng phương pháp trình bày có được độ tin cậy cao | An inverse problem in linear crack media under heat transfer using boundary element method Toan Cao-Duc and Hung Nguyen-Dang European Master in Engineering Science of Mechanics of Construction EMMC Centre d Excellence Belgo-Vietnamien en Sciences Appliquées Programme de Coopération Universitaire Institutionnelle L université de Polytechnique de Ho Chi Minh ville - L universités Liege de Belgique . Full professor of Fracture Mechanics Department University of Liege Chemin des chevreuils 1 B-4000 liege Belgium. Abstract The purpose of this work presents an application of the inverse problem to fracture mechanics under heat transfer. The boundary element method is used to determine the heat transfer in two-dimensional problems with and without crack. Crack location in the material is detected based on the estimation of the energy loss at two tips of a crack. Numerical results show that the presented method obtains high reliability. 1 Introduction The boundary element method BEM is a numerical method for obtaining approximate solutions by solving boundary integral equations. Equations provide a determined formulation of boundary-value problems in different fields of engineering elasticity plasticity fracture mechanics wave propagation and electromagnetic field problems 6 . Basically finite element method FEM require the subdivision of the region into small elements but BEM on the other hand only requires the subdivision of the boundary of the region Figure 1a b . BEM consists of two different approaches the indirect and the direct approach Figure 2a b . For D-BEM at least one closed boundary is required and one side of the surface can be regarded. Using I-BEM both sides of a surface can be considered. I-BEM can also deal with open boundary problems 12 . 1 Vietnam National Commission On Large Dams Figure 1 a Finite element mesh b Boundary element mesh Figure 2 a Direct BEM b Indirect BEM Nowadays BEM is used in many fields of fracture mechanics as it .
