Swan - Topology Optimization Laboratory

"It is not enough for code to work." ― Robert C. Martin

Swan is a Topology Optimization software developed in Matlab. Currently, it supports the resolution of 2D and 3D topology optimization problems with density or level-set as design variables. Swan aims to offer an adaptable framework that allows to implement new optimization techniques or functionalities fastly, thanks to its modular design.

_{Minimization of compliance subject to volume for a 3D cantilever beam, using Level Set methods.}

Current features

Swan currently supports the resolution of macro and micro* scale problems defined in terms of the following design variables:

• Density
• Level Set

_{*Note: 3D micro scale problems are not available yet.}

Intermediate material properties are determined by the following implemented interpolation schemes:

• SIMP
• SIMP-ALL

Swan's modular design allows to combine several functions to define different optimization problems. Each function can be used as a cost or a constraint in the optimization problem. The functions that are currently implemented are:

• Compliance
• Volume
• Perimeter
• Non-self adjoint compliance (used to minimize/maximize displacements)
• Homogenized elasticity matrix (used in micro scale problems)

In terms of optimization techniques, the following optimizers are implemented:

• Density: Projected Gradient, MMA and IPOPT.
• Level-set: SLERP, Projected SLERP and Hamilton-Jacobi

Unconstrained optimizers are combined with an Aumgmented Lagrangian to solve constrained problems.

Contact

For any inquiries, please contact us by opening an issue.

Current active developers are: Àlex Ferrer (@FerrerFerreAlex), Marc Núñez (@marcnunezc) and Oriol Trujillo (@Trujillo94)

Previous developers are acknowledged: Ferran De la Fuente, Nacho Izquierdo Pérez, Raül Rubio Serrano, Albert Torres Rubio

References

M. P. Bendsøe, Optimal shape design as a material distributionproblem, Structural optimization, vol. 1, no. 4, pp. 193–202, Dec1989. [Online]. Available: https://doi.org/10.1007/BF01650949

S. Amstutz, H. Andrä, A new algorithm for topology optimization using a level-set method, J. Comput. Phys. 216 (2) (2006) 573–588.

K. Svanberg, The method of moving asymptotes – a new method for structural optimization, International Journal for Numerical Methods in Engineering, 1987, 24, 359-373.

S. Amstutz, C. Dapogny, and A. Ferrer, A consistent relaxation of optimal design problems for coupling shape and topological derivatives, Numerische Mathematik, vol. 140, no. 1, pp. 35–94, Sep 2018. [Online]. Available: https://doi.org/10.1007/s00211-018-0964-4

G. Allaire, F. Jouve, A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method, J. Comput. Phys. 194 (1)(2004) 363–393, http://dx.doi.org/10.1016/j.jcp.2003.09.032.

A. Wächter and L. T. Biegler, On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming, Mathematical Programming 106(1), pp. 25-57, 2006