Nonlinear viscoelastic analysis of orthotropic beams using a general third-order theory

Venkat Vallala, Annie Ruimi, J. N. Reddy

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14 Citations (Scopus)


The displacement based finite element model of a general third-order beam theory is developed to study the quasi-static behavior of viscoelastic rectangular orthotropic beams. The mechanical properties are considered to be linear viscoelastic in nature with a scope to undergo . von Kármán nonlinear geometric deformations. A differential constitutive law is developed for an orthotropic linear viscoelastic beam under the assumptions of plane-stress. The fully discretized finite element equations are obtained by approximating the convolution integrals using a trapezoidal rule. A two-point recurrence scheme is developed that necessitates storage of data from the previous time step only, and not from the entire deformation history. Full integration is used to evaluate all the stiffness terms using spectral/. hp lagrange polynomials. The Newton iterative scheme is employed to enhance the rate of convergence of the nonlinear finite element equations. Numerical examples are presented to study the viscoelastic phenomena like creep, cyclic creep and recovery for thick and thin beams using classical mechanical analogues like generalized . n-parameter Kelvin-Voigt solids and Maxwell solids.

Original languageEnglish
Pages (from-to)3759-3768
Number of pages10
JournalComposite Structures
Issue number12
Publication statusPublished - Dec 2012



  • Finite element model
  • General third-order beam theory
  • Spectral/hp approximations
  • Viscoelastic behavior
  • Von Kármán nonlinearity

ASJC Scopus subject areas

  • Ceramics and Composites
  • Civil and Structural Engineering

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