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Abstract There are a large number of structures with discontinuities such as holes and inclusions in engineering, the existence of voids and other defects plays an important role in the integrity and stability of the structure, and affects the macro mechanical property of the material. Therefore, developing numerical simulation methods for such structure has great directive significance for engineering application. At present, the main numerical simulation methods for such structure mainly include FEM, XFEM and meshless methods, each of these methods has its advantages and disadvantages such as blending elements in XFEM and displacement boundary condition in meshless methods. This paper proposes a new kind of numerical simulation method based on entire displacement mode for plain hole structure. In the paper, we introduce level set functions for hole boundary and force boundary by level set method, construct boundary trial function with the aid of boundary level set function, and express the trial space as the linear combination of power series and boundary trial functions. Meanwhile, this paper also presents a new displacement boundary processing method based on level set method, which can be hopefully applied in other existing meshless methods. In the method, we involve the displacement boundary condition into the of approximate displacement field, the displacement boundary level set function is introduced to construct the approximate displacement field satisfying displacement boundary condition, and consequently we obtain the formula of balanced equation, stiffness matrix and load matrix. Comparing with FEM, XFEM and element free methods, this method doesn’t need to scatter the solution area, it can obtain the reversible stiffness matrix directly, avoid the ill condition problem of stiffness matrix, and decrease the difficulty of solving the linear equations, furthermore it is also suitable for hole structure with more complicated shape. Finally a numerical case is presented to testify the validity of the method.
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Received: 16 February 2017
Published: 28 October 2017
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2017, Vol. 38 
