Nonlinear quasi-static finite element formulations for viscoelastic Euler-Bernoulli and Timoshenko beams
Academic Article
Overview
Research
Identity
Additional Document Info
Other
View All
Overview
abstract
AbstractWeak form finite element models for the nonlinear quasistatic bending and extension of initially straight viscoelastic EulerBernoulli and Timoshenko beams are developed using the principle of virtual work. The mechanical properties of the beams are considered to be linear viscoelastic. However, large transverse displacements, moderate rotations and small strains are allowed by retaining the von Krmn strain components of the GreenLagrange strain tensor in the formulation. The fully discretized finite element equations are developed using the trapezoidal rule in conjunction with a twopoint recurrence relation. The resulting finite element equations, therefore, necessitate data storage from the previous time step only, and not the entire deformation history. Membrane locking is eliminated from the EulerBernoulli formulation through the use of selective reduced GaussLegendre quadrature. Membrane and shear locking are both circumvented in the Timoshenko beam finite element by employing a family of highorder Lagrange polynomials. A NewtonRaphson iterative scheme is used to solve the nonlinear finite element equations. Copyright 2009 John Wiley & Sons, Ltd.
