Evaluation of modified finite elements with spatially varying elastic parameters for FGMs

Abstract eng:
This paper represents a new discussion on the contribution of graded elements in providing better estimation in comparison with conventional homogeneous elements. This comparison relies on the stress/strain variation through graded and conventional elements. The piecewise homogeneous modelling of functionally graded materials (FGMs) by normal elements is challenged with specific examples. Static nodal equilibrium equations are derived based on the traditional finite element formulation for a 9-node graded quadrilateral element in which elastic constants change spatially. The superiority of graded elements over conventional elements is proved by producing more accurate results with less efforts. Moreover, it is indicated that errors may happen in the estimation of the local field behaviour of FGMs which are modeled with normal elements. The validity of the solution with graded elements is demonstrated by comparison with analytical works.

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