Large Displacement Analysis of Viscoelastic Beams and Frames by the Finite-Element Method

Abstract

A finite-element displacement formulation and solution procedure are developed for the analysis of large displacement problems of viscoelastic beams and frames. The displacements considered are of the same order as the length of the beam member. The geometrical nonlinearity is accounted for by a midpoint-tangent incremental approach together with coordinate transformation at every step. The linear viscoelastic stress-strain relation in the form of hereditary integral is accounted for by the numerical integration with trapezoidal rule. Results are given for the displacements of a variety of beam and frame problems. For the simple case of cantilever beams, some alternative approximate solutions are available for comparison and reasonable agreement is indicated.