# Material nonlinear topology optimization using the ground structure method with a discrete filtering scheme

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## Abstract

Topology optimization of truss lattices, using the ground structure method, is a practical engineering tool that allows for improved structural designs. However, in general, the final topology consists of a large number of undesirable thin bars that may add artificial stiffness and degenerate the condition of the system of equations, sometimes even leading to an invalid structural system. Moreover, most work in this field has been restricted to linear material behavior, yet real materials generally display nonlinear behavior. To address these issues, we present an efficient filtering scheme, with reduced-order modeling, and demonstrate its application to two- and three-dimensional topology optimization of truss networks considering multiple load cases and nonlinear constitutive behavior. The proposed scheme accounts for proper load levels during the optimization process, yielding the displacement field without artificial stiffness by simply using the truss members that actually exist in the structure (spurious members are removed), and improving convergence performance. The nonlinear solution scheme is based on a Newton-Raphson approach with line search, which is essential for convergence. In addition, the use of reduced-order information significantly reduces the size of the structural and optimization problems within a few iterations, leading to drastically improved computational performance. For instance, the application of our method to a problem with approximately 1 million design variables shows that the proposed filter algorithm, while offering almost the same optimized structure, is more than 40 times faster than the standard ground structure method.

### Keywords

Ground structure method Filter Hyperelastic trusses Topology optimization Potential energy Tikhonov regularization Newton-Raphson Line search## Notes

### Acknowledgments

The authors acknowledge the financial support from the US National Science Foundation (NSF) under projects #1559594 (formerly #1335160) and #1321661, from the Brazilian agency CNPq (National Council for Research and Development), and from the Laboratory of Scientific Computing andVisualization (LCCV) at the Federal University of Alagoas (UFAL). We are also grateful for the endowment provided by the Raymond Allen Jones Chair at the Georgia Institute of Technology. The information provided in this paper is the sole opinion of the authors and does not necessarily reflect the views of the sponsoring agencies.

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