Ground Structure Based Discrete Topology Optimization Including Flexural Elements via MATLAB

Abstract

Ground structure-based topology optimization is a method of topology optimization that is well suited to the built engineering practice. Rather than using a continuum where optimal load path is shown as a distribution of density of material under some constraint, a ground structureapproach uses a mesh of nodes to generate a redundant set of possible linear connections under a chosen proximity limit. In this manuscript a method of ground structure based topology optimization for maximum stiffness under a prescribed volume constraint, reducing structural weight and thereforecost, is explored and expanded to include flexural elements. The intent of this addition is to more accurately model (and hence optimize) the behavior of structural elements that form the lateral system of a building to best place elements in preliminary design. The benefit of the method employedis that only one variable, member cross-sectional area, is required in the numerical optimization algorithm for both the placement and sizing of both axial and flexural members. This work considers rectangular and wide-flange sections, but can be extended to other families of structural members.The basis of this paper is the MATLAB ground structure implementation called GRAND, or GRound structure Analysis and Design. Several types of numerical examples are discussed with the objective of highlighting the methods capabilities and shortcomings. The examples addressedinclude a braced frame, moment frame, and hybrid solution.