A modified gradient projection method for static and dynamic topology optimization

ABSTRACT

A variable updater based on the modified gradient projection (MGP) method is proposed for topology optimization. Both static and dynamic problems are considered and formulated using the solid isotropic microstructure (or material) with penalty method. Based on Rosen's gradient projection method, the search direction is obtained by projecting the gradient vector (sensitivity) to the volume constraint plane. Fixed step length is used to guarantee a high convergence rate, and then the iterative solutions are revised to satisfy the upper and lower boundaries. A gradual projecting strategy is suggested to reduce grey elements. Static and dynamic numerical examples are tested to verify the characteristics of the MGP method. The results show that compared with the optimality criterion method and method of moving asymptotes, the convergence rate and computational efficiency of the MGP method are much higher, while the boundaries of the optimal structures are much clearer and the objective function value is smaller.

KEYWORDS:

• Topology optimization
• SIMP
• modified gradient projection
• optimality criterion
• method of moving asymptotes

Acknowledgement

The original code for MMA was kindly provided by Professor Svanberg.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 91648108, U1601202, 5167506 and 11702065], National Key Research and Development Program of China [grant number 2017YFF0105902], Guangdong Natural Science Foundation [grant numbers 2015A030312008 and 2015A030308004], Guangdong Science and Technology Plan [grant numbers 2015B010104006, 2015B010104008 and 2013B010402014] and Science and Technology Program of Guangzhou [grant number 201510010281].