DIRECT CONSTRUCTION METHOD OF FINITE ELEMENT SHAPE FUNCTION IN GLOBAL COORDINATE SYSTEM
Cui Menglei1,2, Li Chunguang1,2, Zhuang Xinshan1
1. School of Civil Engineering and Architecture, Hubei University of Technology, Wuhan 430068 China;
2. Institute of Rock and Soil Mechanics, The Chinese Academy of Science, State Key Laboratory of Geotechnical Mechanics and Engineering, Wuhan 430071, China
In the finite element analysis, when calculating the field variables of a coordinate point (x,y) in the global coordinates, we often get the local coordinates of the point (ξ,η) by solving the inverse isoparametric transformation firstly,and then receive the size of the field variables of the point through the interpolation function. However, solving the inverse isoparametric transformation is equivalent to solve a set of nonlinear equations. The article constructes the interpolation shape function in the global coordinate systemis based on the Lagrange interpolation principal and the characteristics of the shape function, numerical examples show that solving the shape function of in this paper is easy, and the accuracy is equal to the conventional inverse transformation.
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