Prevention of Stress Relaxation in Viscoelastic Structures

Abstract

This paper presents a new problem in linear viscoelastic structural analysis. Homogeneous structures with rigid restraints, where stress relaxation is prevented at a time after loading, are studied. This restriction produces time‐dependent increments in the initial displacements. In addition, if the structure has more than one initial redundant reaction, a significant stress redistribution also occurs. Assuming the increments of displacement of the cross section where the stress relaxation is prevented as unknown, the equation of equilibrium assumes the form of an integral Volterra equation. This mathematical formulation leads to the definition of an integral function (which only takes into account creep effects) that make resolving the problem by affinity to elastic quantities easy. The problem examined is related by duality to the well‐known problem of delayed restraints (also called change of structural system), in which the additional restraints, introduced after loading, prevent the creep increments of displacements at their points of application. Finally, the relation existing between the relaxation function and the integral function obtained is shown.