Abstract
In this paper, we introduce geometry optimization into an existing topology optimization workflow for truss structures with global stability constraints, assuming a linear buckling analysis. The design variables are the cross-sectional areas of the bars and the coordinates of the joints. This makes the optimization problem formulations highly nonlinear and yields nonconvex semidefinite programming problems, for which there are limited available numerical solvers compared with other classes of optimization problems. We present problem instances of truss geometry and topology optimization with global stability constraints solved using a standard primal-dual interior point implementation. During the solution process, both the cross-sectional areas of the bars and the coordinates of the joints are concurrently optimized. Additionally, we apply adaptive optimization techniques to allow the joints to navigate larger move limits and to improve the quality of the optimal designs.
Highlights
Truss design problems are often formulated based on the so-called ground structure approach (Dorn et al 1964), in which a set of joints are distributed in the design space and are connected by potential bars
We address truss design problems with global stability constraints using a linear buckling model that is formulated as a nonlinear semidefinite programming problem
We have introduced geometry optimization to an existing truss topology optimization with global stability constraints formulation, posed as a nonlinear semidefinite programming problem
Summary
Truss design problems are often formulated based on the so-called ground structure approach (Dorn et al 1964), in which a set of joints are distributed in the design space and are connected by potential bars. We address truss design problems with global stability constraints using a linear buckling model that is formulated as a nonlinear semidefinite programming problem Such problems have been extensively studied by Ben-Tal et al (2000), Kanno et al (2001), Levy and Su (2004), Kocvara (2002), Stingl (2006), and Evgrafov (2005) and solved, for example by Fiala et al (2013) and Kocvara and Stingl (2003), but always for cases where the nodes or joints are assumed to be fixed.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
