Numerical analysis of creep problems

Abstract

Introduction of computers several decades ago was a quantum jump in what is feasible in creep structural analysis. It made possible efficient step-by-step evaluation of history integrals or integration of differential equations for both frame-type and finite element creep analysis of structures. Closer to the first principles is the numerical analysis based on history integrals. We discuss it first and point out its limitations due to excessive computer demands. Then, we present the rate-type conversion of creep analysis with aging, which represents a generalization of the Kelvin chain model of classical viscoelasticity, leads to far more efficient calculations, and makes it easy to take into account the effects of drying, variable environment, and cracking. We examine the accuracy and numerical stability of various numerical integration schemes and emphasize the exponential algorithm, which is unconditionally stable, allowing arbitrarily increasing time steps as the stress changes fade out. The algorithm is first presented for a nonaging Kelvin chain and then extended to a solidifying chain and to a chain with general aging.