Derivation of constitutive equations for a viscoelastic Timoshenko beam

Viscoelastic materials have a prevalent application in several different scientific and popular fields such as artificial tissues, airplane industries, astronavigation, earthquake isolation systems, asphalt binders and mixtures etc. It is so important to model such materials considering their real conditions and behavior. Generally, their properties are dependent to time, temperature and loading rate. The Timoshenko beam theory is a well-known theorem for explaining behavior of beams which their depth is significant and cannot be neglected in comparison with their length. In this paper, implementing fundamental equations of viscoelastic theorem, constitutive equations of a viscoelastic Timoshenko beam is derived based on Boltzmann’s superposition integral. The hereditary approach of viscoelastic modeling is used to develop main equations of a viscoelastic Timoshenko beam. These equations can be used in all numerical frameworks such as finite element method, boundary element method and extended finite element method. The final differential equation can be simply solved to obtain accurate answers considering main viscoelastic parameters and boundary conditions of each problem.

Keywords:

Timoshenko beam , Viscoelasticity , Hereditary approach , constitutive equation