A new geometrically nonlinear topology optimization formulation for controlling maximum displacement

Abstract

This article presents a novel formulation for geometric nonlinear topology optimization problems. In practical engineering, maximum deflection is frequently used to quantify the stiffness of continuum structures, yet not applied generally as the optimization constraint in geometrically nonlinear topology optimization problems. In this study, the maximum nodal displacement is formulated as a sole constraint. The p-mean aggregation function is adopted to efficiently treat a mass of local displacement constraints imposed on nodes in the user-specified region. The sensitivities of the objective and constraint functions with respect to relative densities are derived. The effect of the aggregate parameter on the final design is further investigated through numerical examples. By comparison with final designs from the traditional formulation, i.e. minimization end compliance with the volume fraction constraint, or minimization of total volume subject to multiple nodal displacement constraints, the optimized results clearly demonstrate the necessity for and efficiency of the present approach.

KEYWORDS:

• Topology optimization
• geometric nonlinearity
• SIMP method
• lightweight design
• maximum deflection

Acknowledgements

We thank Professor Krister Svanberg for providing the source code of MMA. This article was completed during the epidemic of COVID-19. The authors dedicate this article to Chinese doctors and nurses due to their great efforts against the disease.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 11902085]; National Natural Science Foundation of Beijing [grant number 2182067]; Fundamental Research Funds for the Central Universities [grant number 2018ZD09].