FINITE-ELEMENT MODELING OF ONE-DIMENSIONAL VISCOELASTIC STRUCTURES USING ANELASTIC DISPLACEMENT-FIELDS

A physically motivated approach to modeling the dynamic behavior of vi scoelastic structures using augmenting thermodynamic fields was previo usly reported. Anelastic displacement fields, special kinds of augment ing thermodynamic fields, are now introduced. Instead of addressing ph ysical damping mechanisms directly, as in the earlier approach, their effects on the displacement field are considered. in this approach, th e total displacement field comprises two parts: 1) an elastic part and 2) an anelastic part. The material constitutive equations are develop ed, as well as the governing differential equations and boundary condi tions for a one-dimensional structural member, and are compared to the results developed previously using the augmented thermodynamic fields approach. In addition, a physical interpretation of some of the quant ities involved is advanced in terms of a classical mechanical analogy Because the anelastic displacement field(s) and the total displacement field may be treated similarly in analytical or numerical study, the key practical benefit of this anelastic displacement fields approach i s that it leads to the straightforward development of time-domain fini te element models. Modal analyses and frequency response analyses have been implemented using the matrix manipulation capabilities of a comm ercial finite element code.