The level set method is used for representing the location of random inclusions. Numerical examples are presented to demonstrate the accuracy and potential of this technique. The obtained results are compared with available refered results and COMSOL, the finite element method software. | Tạp chí Phát triển Khoa học và Công nghệ, tập 20, số K3-2017 119 Extended finite-element method for modeling the mechanical behavior of functionally graded material plates with multiple random inclusions Kim Bang Tran, The Huy Tran, Quoc Tinh Bui and Tich Thien Truong Abstract— Functionally graded material is of great importance in many engineering problems. Here the effect of multiple random inclusions in functionally graded material (FGM) is investigated in this paper. Since the geometry of entire model becomes complicated when many inclusions with different sizes appearing in the body, a methodology to model those inclusions without meshing the internal boundaries is proposed. The numerical method couples the level set method to the extended finite-element method (X-FEM). In the X-FEM, the finite-element approximation is enriched by additional functions through the notion of partition of unity. The level set method is used for representing the location of random inclusions. Numerical examples are presented to demonstrate the accuracy and potential of this technique. The obtained results are compared with available refered results and COMSOL, the finite element method software. Index Terms— Extended finite-element method; multiple; random; inclusions, functionally graded material. Manuscript Received on March 15th, 2017, Manuscript Revised on November 01st, 2017. This research is funded by Ho Chi Minh City University of Technology –VNU-HCM, under grant number T-KHUD2016-69. Kim Bang Tran, Ho Chi Minh City University of Technology, VNU-HCM, Vietnam (e-mail: tkbang@). The Huy Tran, Ho Chi Minh city University of Technology, VNU-HCM, Vietnam. (e-mail: thehuydhbk@). Tinh Quoc Bui, Department of Civil and Environmental Engineering, Tokyo Institute of Technology, Japan (email:). Tich Thien Truong, Ho Chi Minh city University of Technology, VNU-HCM, Vietnam (e-mail: tttruong@). 1 .
