On the Importance of Viscoelastic Response Consideration in Structural Design Optimization Kai A. James a , Haim Waisman b a University of Illinois at Urbana-Champaign, Department of Aerospace Engineering, Urbana, Illinois, United States; tel: 217-300-3270; fax: 217-244-0720; kaijames@illinois.edu b Columbia University, Department of Civil Engineering and Engineering Mechanics, New York, New York, United States Abstract In this paper we present a series of mathematical proofs that demonstrate the importance of accounting for viscoelastic effects in structural optimiza- tion algorithms. Focusing specifically on mass minimization problems with stiffness and deflection constraints, we show that standard techniques based on linear elastic analysis overestimate the long-term stiffness of the struc- ture, leading to designs that become infeasible after sustained loading due to viscoelastic creep. Conversely, assuming maximum creep deflection, which also allows for linear analysis, leads to an overly conservative design that is unnecessarily heavy and therefore suboptimal. We prove both propositions for both constant and time-varying load histories. We also present proofs for generalized continuum mechanics problems as well as for a finite element for- mulation, which can be applied to any arbitrary geometry. Lastly, we present two numerical examples in which the conclusions derived in the proofs are verified empirically. Keywords: structural optimization; viscoelasticity; creep deformation; finite element analysis 1. Introduction Viscoelasticity is the property by which solid materials exhibit time- dependent responses when subject to sustained loading. While many en- gineering materials are known to have significant and observable viscoelastic behavior, particularly when operating at high temperatures, most structural Preprint submitted to Optimization and Engineering April 28, 2016