On the Analysis of FGM Beams: FEM with Innovative Element

Journal of Solid Mechanics

مقاله 9، دوره 8، شماره 2، شهریور 2016، صفحه 348-364   

نوع مقاله: Research Paper

نویسندگان

M Zakeri^{* 1}؛ A Modarakar Haghighi²؛ R Attarnejad¹

¹School of Civil Engineering, College of Engineering, University of Tehran

²School of Civil Engineering, College of Engineering, University of Tehran----Centre of Numerical Methods in Engineering, University of Tehran

چکیده

This paper aims at presenting a new efficient element for free vibration and instability analysis of Axially Functionally Graded Materials (FGMs) non-prismatic beams using Finite Element Method (FEM). Using concept of Basic Displacement Functions (BDFs), two- node element extends  to three-node element for obtaining much more exact results using FEM. First, BDFs are introduced and computed using energy method such as unit-dummy load method. Afterward, new efficient shape functions are developed in terms of BDFs during the procedure based on the mechanical behavior of the element in which presented shape functions benefit generality and accuracy from stiffness and force method, respectively. Finally, deriving structural matrices of the beam with respect to new shape functions; free vibration and instability analysis of the FGM beam are studied using finite element method for all types of AFGM beams and the convergence of FEM has been studied. The results from both free vibration and instability analysis are in perfect agreement with those of previously published.

کلیدواژه‌ها

Axially functionally graded materials (AFGM)؛ Finite element method (FEM)؛ Basic displacement functions (BDFs)؛ Free vibration؛ Instability analysis

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