A Bound Method for Creep Analysis of Structures: Direct Use of Solutions in Elasticity and Plasticity

Abstract

A structure of given geometry is made of a material whose stress-strain rate law is of the form

where B_n and n are properties of the material. The authors set out to consider the effects on the load-rate of deflection characteristics of the structure of changes in the index n. A non-dimensional diagram is used to compare the load-rate of deflection characteristics of the structure for different values of n. A recent theorem is quoted which indicates that in this diagram the (closed) curves corresponding to different values of n nest inside each other as n increases. As the curves for n = 1 (which corresponds to linear elasticity) and n=∞ (which corresponds to perfect plasticity) may usually be established without much difficulty, they may therefore be used conveniently to locate the region in which the curves lie for any other intermediate value of n. Inspection of the curves for different values of n for several structures indicates that the theorem may become a useful tool in the study of the steady creep of structures or, by analogy, the study of non-linear elasticity.