Quasi-static analysis for viscoelastic Timoshenko beams with damage

Abstract

Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain. The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.

An Incremental Constituve Law for Damaging Viscoelastic Materials

“…[1]. From a general point of view, the viscoelastic behaviour can take different forms, including creep under constant load, stress relaxation under constant deformation, time-dependent recovery of deformation following load removal, time-dependent creep rupture [2].…”

Nonlinear dynamic behaviors of viscoelastic shallow arches

“…Therefore, many studies [1][2][3][4][5][6][7][8][9][10][11][12][13] have been performed on the nonlinear dynamics of viscoelastic structures. Chen et al [2][3][4][5] investigated the dynamic stability and chaotic motion of a nonlinear viscoelastic beam and column by applying the Leaderman constitutive relation with Galerkin numerical integration.…”

“…Chen et al [2][3][4][5] investigated the dynamic stability and chaotic motion of a nonlinear viscoelastic beam and column by applying the Leaderman constitutive relation with Galerkin numerical integration. Also, other constitutive relations [6][7][8] are adopted to investigate the dynamics of the viscoelastic structures. Moreover, there has been considerable interest in the study of the nonlinear dynamics of the beam [2][3][6][7][8] , column [4][5] , pile [9][10] , plate [11] , shell [12] , and string [13] etc.…”

“…Also, other constitutive relations [6][7][8] are adopted to investigate the dynamics of the viscoelastic structures. Moreover, there has been considerable interest in the study of the nonlinear dynamics of the beam [2][3][6][7][8] , column [4][5] , pile [9][10] , plate [11] , shell [12] , and string [13] etc. However, few studies are focused on the nonlinear dynamic behavior of a viscoelastic shallow arch.…”

A nonlinear model of thermoelastic beams with voids, with applications

“…In [Sheng and Cheng 2004;Cheng et al 2006], the Gurtin-type variational principles of viscoelastic Timoshenko beams and thick plates with damage were established, damage being regarded as voids in materials. These works also studied quasistatic problems of viscoelastic beams and dynamical behaviors of viscoelastic plates.…”