How to impose essential and natural boundary conditions has been the key issue of mesh-free methods because the nodes are not located along a boundary in arbitrary geometry in general unlike conventional finite elemen...
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How to impose essential and natural boundary conditions has been the key issue of mesh-free methods because the nodes are not located along a boundary in arbitrary geometry in general unlike conventional finite element method(FEM). The extended finite element method(X-FEM), one of the mesh-free methods is suitable to deal with geometric discontinuity inside an element in fixed mesh such as crack or hole, but has the same problem. In this paper we introduce a method of constructing nodal constraint equations and distributing loading into element nodes for essential or natural boundary conditions imposed along boundaries in the X-FEM problems.
This paper discusses a design procedure for general composite materials. A two-scale analysis is carried out by using homogenization method coupled with X-FEM. A brief review of homogenization method and X-FEM is summ...
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This paper discusses a design procedure for general composite materials. A two-scale analysis is carried out by using homogenization method coupled with X-FEM. A brief review of homogenization method and X-FEM is summarized and illustrated by examples. Material property designs by a micro-structural model as a one-scale optimization and a two scale optimization involving the macro-structure and the micro-structure are implemented and examples shown to demonstrate practicality of the procedure. A new micro-structural pattern not known until now is also obtained in addition to some existing patterns.
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