# On the importance of viscoelastic response consideration in structural design optimization

- 368 Downloads
- 1 Citations

## Abstract

In this paper we present a series of mathematical proofs that demonstrate the importance of accounting for viscoelastic effects in structural optimization 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 structure, 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 formulation, 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## Notes

### Acknowledgments

The authors wish to acknowledge the financial support of the National Science Foundation under grant number CMMI-1334857.

## References

- Andreassen E, Jensen J (2013) Topology optimization of periodic microstructures for enhanced dynamic properties of viscoelastic composite materials. Struct Multidisc Optim 49:695–705MathSciNetCrossRefGoogle Scholar
- Brinson H, Brinson L (2008) Polymer engineering science and viscoelasticity. Springer, BerlinCrossRefMATHGoogle Scholar
- Chen W, Liu S (2014) Topology optimization of microstructures of viscoelastic damping materials for a prescribed shear modulus. Struct Multidisc Optim 50:287–296. doi: 10.1007/s00158-014-1049-3 MathSciNetCrossRefGoogle Scholar
- Deng M, Zhou J (2006) Effects of temperature and strain level on stress relaxation behaviors of polypropylene sutures. J Mater Sci 17:365–369Google Scholar
- El-Sabbagh A, Baz A (2014) Topology opitmization of unconstrained damping treatments for plates. Engrg Optim 46:1153–1168MathSciNetCrossRefGoogle Scholar
- Gutierrez-Lemini D (2014) Engineering viscoelasticity. Springer, BerlinCrossRefMATHGoogle Scholar
- James K, Waisman H (2015) Topology optimization of viscoelastic structures using a time-dependent adjoint method. Comput Methods Appl Mech Engrg 285:166–187MathSciNetCrossRefGoogle Scholar
- Jensen K, Szabo P, Okkels F (2012) Topology optimization of viscoelastic rectifiers. Appl Phys Lett 100:1–4CrossRefGoogle Scholar
- Liu Z, Guan H, Zhen W (2013) Topology optimization of viscoelastic materials distribution of damped sandwich plate composite. Appl Mech Mater 347–350:1182–1186CrossRefGoogle Scholar
- Marques S, Creus G (2012) Computational viscoelasticity. Springer, BerlinCrossRefGoogle Scholar
- Prasad J, Diaz A (2009) Viscoelastic material design with negative stiffness components using topology optimization. Struct Multidisc Optim 38:583–597CrossRefGoogle Scholar
- Sedef M, Samur E, Basdogan C (2006) Real-time finite-element simulation of linear viscoelastic tissue behavior based on experimental data. IEEE Comput Gr Appl 26:28–38Google Scholar
- Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Meth Optim 24:359–373MathSciNetCrossRefMATHGoogle Scholar