A Nonlinear Finite Element Framework for Viscoelastic Beams Based on the High-Order Reddy Beam Theory

Abstract

A weak form Galerkin finite element model for the nonlinear quasi-static and fully transient analysis of initially straight viscoelastic beams is developed using the kinematic assumptions of the third-order Reddy beam theory. The formulation assumes linear viscoelastic material properties and is applicable to problems involving small strains and moderate rotations. The viscoelastic constitutive equations are efficiently discretized using the trapezoidal rule in conjunction with a two-point recurrence formula. Locking is avoided through the use of standard low-order reduced integration elements as well through the employment of a family of elements constructed using high-polynomial order Lagrange and Hermite interpolation functions.