New method for nonlinear creep analysis of beam structures

Abstract

Some concepts and practical applications relating to determination of the nonlinear creep behaviour of beam and bar structures are presented. Utilization of creep experimental results as a direct source of the material constitutive law is made without approximation to any analytic law and the consequent inherent error. A general discrete equation for strain difference calculation is presented. The equation components can be determined directly from experimental results. With the new approach, the strain history at each point on the structure is taken into account. The strain difference Δϵ depends on the original material properties, and is a function of time, stress, and temperature at time t and ( t− Δt). The new approach is applicable to the general discrete equation and gives better results for materials with a ‘short’ memory. A new finite beam element with creep consideration is presented. The element takes into account the relation between stress and strain and the history of the phenomenon at each point. The stiffness matrix and the internal reaction vector are determined by integration at many points, which is essential as a consequence of the different material properties at each point. Although the structure can be divided into fewer ‘multi-point elements’, more accurate results can be obtained. The creep determination of the structure is made at each time interval Δ t by the Newton-Raphson iterative method. Some examples of creep analysis of frame and truss structures (made of nonlinear viscoelastic material) under constant load are presented. The effect of the nonlinear material, in general, and the ‘creep threshold’, in particular, is emphasized by the results. The reaction of the structure to temperature and load changes can be determined by the same method utilizing simple creep experimental sets of data, which are determined in the relevant range of temperature.