Non-linear analysis of functionally graded microbeams using Eringens non-local differential model

J. N. Reddy, Sami El-Borgi, Jani Romanoff

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

The primary objective of this paper is two-fold: (1) to formulate the governing equations of the Euler-Bernoulli and Timoshenko beams that account for (a) two-constituent material variation through beam thickness, (b) small strains but moderate displacements and rotations, and (c) material length scales based on Eringens non-local differential model; and (2) develop the non-linear finite element models of beam theories with aforementioned features and obtain numerical results for static bending. The principle of virtual displacements is used to derive the non-linear equations governing functionally graded beams with Eringens non-local constitutive models for both the Euler-Bernoulli and Timoshenko beam theories. A power-law model is used for the variation of the material properties of the two constituent materials. Finite element models of the resulting equations are developed and numerical results are presented for pinned-pinned and clamped-clamped boundary conditions, showing the effect of the non-local parameter and the power-law index on deflections and stresses.

Original languageEnglish
Pages (from-to)308-318
Number of pages11
JournalInternational Journal of Non-Linear Mechanics
Volume67
DOIs
Publication statusPublished - 2014

Fingerprint

Nonlinear analysis
Nonlinear Analysis
Euler-Bernoulli Beam
Timoshenko Beam
Finite Element Model
Power Law
Numerical Results
Nonlinear Finite Element
Constitutive Model
Length Scale
Deflection
Material Properties
Governing equation
Nonlinear Equations
Fold
Constitutive models
Nonlinear equations
Model
Boundary conditions
Materials properties

Keywords

  • Eringens differential model
  • Finite element models
  • Functionally graded material
  • Microbeams
  • Static analysis

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Applied Mathematics

Cite this

Non-linear analysis of functionally graded microbeams using Eringens non-local differential model. / Reddy, J. N.; El-Borgi, Sami; Romanoff, Jani.

In: International Journal of Non-Linear Mechanics, Vol. 67, 2014, p. 308-318.

Research output: Contribution to journalArticle

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