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

Authors

  • A Muliana Department of Mechanical Engineering, Texas A&M University, College Station
  • J.N Reddy Department of Mechanical Engineering, Texas A&M University, College Station
  • S Doshi Department of Civil Engineering, Texas A&M University, College Station
Abstract:

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.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Finite Element Analysis of Functionally Graded‎ ‎Piezoelectric Beams

In this paper‎, ‎the static bending‎, ‎free vibration‎, ‎and dynamic response of functionally graded‎ ‎piezoelectric beams have been carried out by finite element method‎‎under different sets of mechanical‎, ‎thermal‎, ‎and electrical‎ ‎loadings‎. ‎The beam with functionally graded piezoelectric material‎ ‎(FGPM) is assumed to be graded across the thickness with a simple‎ ‎power law distributio...

full text

Dynamic Stability of Functionally Graded Beams with Piezoelectric Layers Located on a Continuous Elastic Foundation

This paper studies dynamic stability of functionally graded beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The Young’s modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton’s principle, the governing dynamic equation is established. The eff...

full text

Free Vibration of Functionally Graded Beams with Piezoelectric Layers Subjected to Axial Load

This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers subjected to axial compressive loads. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton’s principle, the governing equation is established. Resulting equation is solved using the Euler’s Equation. The effects of the constituent...

full text

An Efficient Finite Element Formulation Based on Deformation Approach for Bending of Functionally Graded Beams

Finite element formulations based generally on classical beam theories such as Euler-Bernoulli or Timoshenko. Sometimes, these two formulations could be problematic expressed in terms of restrictions of Euler-Bernoulli beam theory, in case of thicker beams due to non-consideration of transverse shear; phenomenon that is known as shear locking characterized the Timoshenko beam theory, in case of...

full text

Stability of Functionally Graded Beams with Piezoelectric Layers Based on the First Order Shear Deformation Theory

Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical par...

full text

Nonlinear Vibration Analysis of Piezoelectric Functionally Graded Porous Timoshenko Beams

In this paper, nonlinear vibration analysis of functionally graded piezoelectric (FGP) beam with porosities material is investigated based on the Timoshenko beam theory. Material properties of FG porous beam are described according to the rule of mixture which modified to approximate material properties with porosity phases. The Ritz method is used to obtain the governing equation which is then...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 3  issue 4

pages  332- 345

publication date 2011-12-30

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023