Theoretical Formulations for Finite Element Models of Functionally Graded Beams with Piezoelectric Layers

Journal of Solid Mechanics

مقاله 3، دوره 3، شماره 4، اسفند 2011، صفحه 332-345   

نوع مقاله: Research Paper

نویسندگان

J.N Reddy^{* 1}؛ S Doshi²؛ A Muliana¹

¹Department of Mechanical Engineering, Texas A&M University, College Station

²Department of Civil Engineering, Texas A&M University, College Station

چکیده

In this paper an overview of functionally graded materials and constitutive relations of electro elasticity for three-dimensional deformable  solids is presented, and  governing equations of the Bernoulli–Euler and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material and piezoelectric layers are developed  using the  principle  of virtual  displacements. The formulation is based on a power-law variation of the material in the core with piezoelectric layers at the top and bottom. Virtual work statements of the two theories are also developed and their finite element models are presented. The theoretical formulations and finite element models presented herein can be used in the analysis of piezolaminated and adaptive structures such as beams and plates.

کلیدواژه‌ها

Bending؛ Bernoulli–Euler beam theory؛ Functionally graded material؛ Piezoelectricity؛ PZT؛ Timoshenko Beam Theory

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