Abstract.
This paper analyses the convexity of the problem formulations for topological optimization of compliant mechanisms. In this context, a ground structure is assumed to consist of membranes with variable thickness or trusses with variable cross-sectional area. It is proven that the objective function of maximum mechanical or geometrical advantage may not be convex even though the constraints for the problem formulations give rise to a convex set. The constraints include volumetric constraint and a bound on input displacement. The nonconvex objective functions are shown analytically with two examples using truss elements. Also, it is illustrated numerically with an example using bilinear quadrilateral elements. It is concluded that nonconvex objective functions also attribute to difficulties in arriving at the globally optimal topology of compliant mechanisms, in addition to the number of design variables and constraints. As the problem is more complicated, the solution of the problem requires robust and reliable optimization techniques.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received January 27, 2000 Revised manuscript received August 8, 2000
Rights and permissions
About this article
Cite this article
Lau, G., Du, H. & Lim, M. Convex analysis for topology optimization of compliant mechanisms. Struct Multidisc Optim 22, 284–294 (2001). https://doi.org/10.1007/PL00013283
Issue Date:
DOI: https://doi.org/10.1007/PL00013283